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https://ceur-ws.org/Vol-1356/ICTERI-2015-CEUR-WS-Volume.pdf
Sotiris Batsakis
Heinrich C. Mayr
Vitaliy Yakovyna
Mykola Nikitchenko
Grygoriy Zholtkevych
Vyacheslav Kharchenko
Hennadiy Kravtsov
Vitaliy Kobets
Vladimir Peschanenko
Vadim Ermolayev
Yuriy Bobalo
Aleksander Spivakovsky
(Eds.)
ICT in Education, Research
and Industrial Applications:
Integration, Harmonization
and Knowledge Transfer
Proceedings of the 11th International Conference,
ICTERI 2015
Lviv, Ukraine
May, 2015
Sotiris Batsakis
Batsakis, S., Mayr, H. C., Yakovyna, V., Nikitchenko, M., Zholtkevych, G.,
Kharchenko, V., Kravtsov, H., Kobets, V., Peschanenko, V., Ermolayev, V., Bobalo,
Yu. and Spivakovsky, A., (Eds.): ICT in Education, Research and Industrial
Applications: Integration, Harmonization and Knowledge Transfer. Proc. 11th Int.
Conf. ICTERI 2015, Lviv, Ukraine, May 14-16, 2015, CEUR-WS.org, online
This volume represents the proceedings of the 11th International Conference on
ICT in Education, Research, and Industrial Applications, held in Lviv, Ukraine, in
May 2015. It comprises 45 contributed papers that were carefully peer reviewed (3-4
reviews per paper) and selected from 119 submissions.
The volume opens with the abstracts of the keynote talks and tutorial. The rest of
the collection is organized in 2 parts. Part I contains the contributions to the main
ICTERI conference, structured in four topical sections: (1) Teaching ICT and Using
ICT in Education; (2) Model-Based Software System Development; (3) Machine
Intelligence, Knowledge Engineering and Management for ICT; and (4) ICT in Indus-
trial Applications. Part II comprises the contributions of the four workshops co-
located with ICTERI 2015, namely: the International Workshop on Information
Technologies in Economic Research (ITER 2015); the International Workshop on
Methods and Resources of Distance Learning (MRDL 2015); the International Work-
shop on Algebraic, Logical, and Algorithmic Methods of System Modeling, Specifi-
cation and Verification (SMSV 2015); and the International Workshop on Theory of
Reliability for Modern Information Technologies (TheRMIT 2015).
Copyright © 2015 for the individual papers by the papers’ authors.
Copying permitted only for private and academic purposes. This vol-
ume is published and copyrighted by its editors.
Preface
ICTERI, the International Conference on Information and Communication Technolo-
gies in Education, Research, and Industrial Applications: Integration, Harmoniza-
tion, and Knowledge Transfer, has become a considerable and stable international
ICT conference. It is a real pleasure for all ICTERI players, that in contrast to 2014,
the 11th edition could bring scholars and expert representatives physically together
again for exchanging and discussing new ideas and findings, and for networking
across all political borders. This is all the more pleasing as, despite of all current chal-
lenges, the Ukrainian ICT community proves its vigor and global integration.
We gladly present you the proceedings of ICTERI 2015, which was held in Lviv,
Ukraine, on May 14-16, 2015. The conference scope was determined by the corner-
stones of ICT Infrastructures and Techniques, Knowledge Based Systems, Academ-
ia/Industry ICT Cooperation, and ICT in education. Special emphasis was given to
real world applications of ICT solutions. Therefore, the contributions had to describe
original, not previously published work, and to demonstrate how and to what purpose
and extent the proposed solutions are applied or transferred into use.
For the main conference, 42 full papers were submitted and evaluated by at least
three peers per paper. Finally, 16 have been selected and accepted after revision in
accordance with the reviewers comments. This corresponds to an acceptance rate of
38%. The program was rounded off with the two outstanding keynote talks on Rigor-
ous Semantics and Refinement for Business Processes by Klaus-Dieter Schewe and on
Smart Learning Environments: a Shift of Paradigm by David Esteban. The tutorial on
Systematic Business Process Modeling in a Nutshell by Heinrich C. Mayr comple-
mented the program, in particular regarding the emphasis on the synergy of education
and industrial applications.
ICTERI 2015 continued the tradition of hosting co-located events, this year by of-
fering four workshops:
4th Int. Workshop on Information technologies in economic research (ITER 2015)
3rd Int. Workshop on Methods and Resources for Distance Learning (MRDL 2015)
4th Int. Workshop on Algebraic, Logical, and Algorithmic Methods of System
Modeling, Specification and Verification (SMSV 2015)
Int. Workshop on Theory of Reliability for Modern Information Technologies
(TheRMIT 2015)
In total, these workshops attracted 77 submissions, from which 29 were selected by
the particular program committees. This again led to an acceptance rate of 38%.
Clearly, the conference would not have been possible without the engaged support
of many people including the authors, members of our Program Committee, workshop
organizers and their program committees, local organizers, and, last but not least,
generous donators. We express our special thanks to all of them.
May, 2015
Sotiris Batsakis, Heinrich C. Mayr, Vitaliy Yakovyna, Mykola Nikitchenko,
Grygoriy Zholtkevych, Vyacheslav Kharchenko, Hennadiy Kravtsov, Vitaliy Kobets,
Vladimir Peschanenko, Vadim Ermolayev, Yuriy Bobalo, Aleksander Spivakovsky
Committees
General Chairs
Yuriy Bobalo, Lviv Polytechnic National University, Ukraine
Aleksander Spivakovsky, Kherson State University, Ukraine
Steering Committee
Vadim Ermolayev, Zaporizhzhya National University, Ukraine
Heinrich C. Mayr, Alpen-Adria-Universät Klagenfurt, Austria
Mykola Nikitchenko, Taras Shevchenko National University of Kyiv, Ukraine
Aleksander Spivakovsky, Kherson State University, Ukraine
Mikhail Zavileysky, DataArt, Russian Federation
Grygoriy Zholtkevych, V.N.Karazin Kharkiv National University, Ukraine
Program Chairs
Sotiris Batsakis, University of Huddersfield, UK
Heinrich C. Mayr, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria
Vitaliy Yakovyna, Lviv Polytechnic National University, Ukraine
Workshop Chairs
Mykola Nikitchenko, Taras Shevchenko National University of Kyiv, Ukraine
Grygoriy Zholtkevych, V.N.Karazin Kharkiv National University, Ukraine
Tutorial Chair
Vadim Ermolayev, Zaporizhzhya National University, Ukraine
IT Talks Chairs
Aleksander Spivakovsky, Kherson State University, Ukraine
Mikhail Zavileysky, DataArt, Russian Federation
Local Organization Chair
Dmytro Fedasyuk, Lviv Polytechnic National University, Ukraine
Publicity Chair
Nataliya Kushnir, Kherson State University, Ukraine
Web Chair
Eugene Alferov, Kherson State University, Ukraine
Program Committees
MAIN ICTERI 2015 Conference
Program Committee
Jan Aidemark, Linneaus University, Sweden
Eugene Alferov, Kherson State University, Ukraine
Costin Badica, University of Craiova, Romania
Nick Bassiliades, Aristotle University of Thessaloniki, Greece
Sotiris Batsakis, University of Huddersfield, UK
Lukas Chrpa, University of Huddersfield, UK
Michael Cochez, University of Jyväskylä, Finland
Anatoliy Doroshenko, National University of Technology "Kyiv Polytechnic Institute", Ukraine
Vadim Ermolayev, Zaporizhzhya National University, Ukraine
David Esteban, TECHFORCE, Spain
Wolfgang Faber, University of Huddersfield, UK
Anna Fensel, STI, University of Innsbruck, Austria
Vladimir Gorodetsky, St. Petersburg Institute for Informatics and Automation
of the Russian Academy of Science, Russian Federation
Brian Hainey, Glasgow Caledonian University, UK
Sungkook Han, Wonkwang University, South Korea
Ville Isomottonen, University of Jyvaskyla, Finland
Mirjana Ivanovic, University of Novi Sad, Serbia
Jason J. Jung, Yeungnam University, South Korea
Samia Kamal, Oxford Brookes University, UK
Natalya Keberle, Zaporizhzhya National University, Ukraine
Vitaliy Kobets, Kherson State University, Ukraine
Oleksandr Kolgatin, H.S. Skovoroda Kharkiv National Pedagogical University, Ukraine
Christian Kop, Alpen-Adria-Universität Klagenfurt, Austria
Hennadiy Kravtsov, Kherson State University, Ukraine
Vladislav Kruglik, Kherson State University, Ukraine
Sergey Kryukov, Southern Federal University, Russian Federation
Vladimir Kukharenko, National Technical University "Kharkiv Polytechnic Institute”, Ukraine
Nataliya Kushnir, Kherson State University, Ukraine
Vira Liubchenko, Odessa National Polytechnic University, Ukraine
Alexander Lyaletski, Taras Shevchenko National University of Kyiv, Ukraine
Dmitry Maevsky, Odessa National Polytechnic University, Ukraine
Frederic Mallet, Universite de Nice-Sophia Antipolis, France
Wolf-Ekkehard Matzke, MINRES Technologies GmbH, Germany
Heinrich Mayr, Alpen-Adria-Universität Klagenfurt, Austria
Mykola Nikitchenko, Taras Shevchenko National University of Kyiv, Ukraine
Tope Omitola, University of Southampton, UK
Olga Ormandjieva, Concordia University, Canada
Simon Parkinson, University of Huddersfield, UK
Vladimir Peschanenko, Kherson State University, Ukraine
Gary Pratt, Eastern Washington University, USA
Carlos Ruiz, playence, Spain
Abdel-Badeeh Salem, Ain Shams University, Cairo, Egypt
Wolfgang Schreiner, RISC, Johannes Kepler University Linz, Austria
Pavlo Serdyuk, Lviv Polytechnic National University, Ukraine
Vladimir A. Shekhovtsov, Alpen-Adria-Universität Klagenfurt, Austria
Mariya Shishkina, Institute of Information Technologies and Learning Tools
of the National Academy of Pedagogical Sciences of Ukraine, Ukraine
Martin Strecker, IRIT, Paul Sabatier University, Toulouse, France
Ilias Tachmazidis, University of Huddersfield, UK
Olga Tatarintseva, Satelliz, Ukraine
Vagan Terziyan, University of Jyväskylä, Finland
Ville Tirronen, University of Jyvaskyla, Finland
Nikolay Tkachuk, National Technical University "Kharkiv Polytechnic Institute”, Ukraine
Mauro Vallati, University of Huddersfield, UK
Leo Van Moergestel, Utrecht University of Applied Sciences, The Netherlands
Maxim Vinnik, Kherson State University, Ukraine
Paul Warren, Knowledge Media Institute, the Open University, UK
Vitaliy Yakovyna, Lviv Polytechnic National University, Ukraine
Yulia Nosenko (Zaporozhchenko), Institute of Information Technologies and Learning Tools
of the National Academy of Pedagogical Sciences of Ukraine, Ukraine
Iryna Zaretska, V. N. Karazin Kharkiv National University, Ukraine
Grygoriy Zholtkevych, V. N. Karazin Kharkov National University, Ukraine
Additional Reviewers
Kalliopi Kravari, Aristotle University of Thessaloniki, Greece
Rustam Gamzaev, National Technical University "Kharkiv Polytechnic Institute”, Ukraine
Eleftherios Spyromitros-Xioufis, Aristotle University of Thessaloniki, Greece
Emmanouil Rigas, Aristotle University of Thessaloniki, Greece
ITER 2015 Workshop
Workshop Chairs
Vitaliy Kobets, Kherson State University, Ukraine
Sergey Kryukov, Southern Federal University, Russian Federation
Sergey Mazol, Academy of Public Administration, Minsk, Belarus
Tatyana Payentko, National University of State Tax Service of Ukraine, Ukraine
Program Committee
Tom Coupe, Kyiv School of Economics, Ukraine
Dorota Jelonek, Częstochowa University of Technology, Poland
Ludmila Konstants, American University of Central Asia, Kyrgyz Republic
Sergey Kryukov, Southern Federal University, Russian Federation
Sergey Mazol, Academy of Public Administration, Minsk, Belarus
Marin Neykov, University of National and World Economy (UNWE), Bulgaria
Nina Solovyova, Kherson State University, Ukraine
Ekaterina Vostrikova, Astrakhan State University, Russian Federation
Alexander Weissbult, Kherson State University, Ukraine
MRDL 2015 Workshop
Workshop Chairs
Vladimir Kukharenko, National Technical University “Kharkiv Polytechnic Institute”, Ukraine
Yulia Nosenko (Zaporozhchenko), Institute of Information Technologies and Learning Tools
of the National Academy of Pedagogical Sciences of Ukraine, Ukraine
Hennadiy Kravtsov, Kherson State University, Ukraine
Program Committee
Olga Gnedkova, Kherson State University, Ukraine
Alexander Kolgatin, H.S. Skovoroda Kharkiv National Pedagogical University, Ukraine
Evgen Kozlovskiy, Kherson State University, Ukraine
Vladislav Kruglik, Kherson State University, Ukraine
Michael Sherman, Kherson State University, Ukraine
Maria Shishkina, Institute of Information Technologies and Learning Tools
of the National Academy of Pedagogical Sciences of Ukraine, Ukraine
Tatyana Zaytseva, Kherson State Maritime Academy, Ukraine
SMSV 2015 Workshop
Workshop Chairs
Wolfgang Schreiner, RISC, Johannes Kepler University Linz, Austria
Mykola Nikitchenko, Taras Shevchenko National University of Kyiv, Ukraine
Michael Lvov, Kherson State University, Ukraine
Martin Strecker, IRIT, Paul Sabatier University, France
Program Committee
Anatoliy Doroshenko, Glushkov Institute of Cybernetics of the National Academy of Sciences
of Ukraine, Ukraine
Louis Feraud, Paul Sabatier University, France
Alexander Letichevsky, Glushkov Institute of Cybernetics of the National Academy of Sciences
of Ukraine, Ukraine
Alexander Lyaletski, Taras Shevchenko National University of Kyiv, Ukraine
Frederic Mallet, University of Nice Sophia Antipolis, France
Vladimir Peschanenko, Kherson State University, Ukraine
TheRMIT 2015 Workshop
Workshop Chairs
Vyacheslav Kharchenko, National Aerospace University “KhAI”, Ukraine
Elena Zaitseva, Žilina University, Slovakia
Bogdan Volochiy, Lviv Polytechnic National University, Ukraine
Program Committee
Mario Fusani, ISTI-CNR System and Software Evaluation Center, Italy
Vladimir Sklyar, National Aerospace University "KhAI", Ukraine
Iosif Androulidakis, Ioannina University Network Operations Center, Greece
Yuriy Kondratenko, Black Sea State University named after Petro Mohyla, Ukraine
Vitaly Levashenko, Žilina University, Slovakia
Dmitriy Maevskiy, Odessa National Polytechnic University, Ukraine
Vladimir Mokhor, Pukhov Institute for Modeling in Energy Engineering, NASU, Ukraine
Oleg Odarushchenko, Research and Production Company Radiy, Ukraine
Olexandr Gordieiev, University of Banking of National Bank of Ukraine, Kyiv, Ukraine
Yurij Ponochovny, Poltava National Technical University, Ukraine
Jüri Vain, Tallinn University of Technology, Estonia
Sergiy Vilkomir, East Carolina University, USA
Vladimir Zaslavskiy, Taras Shevchenko National University of Kyiv, Ukraine
Local Organizing Committee
Orest Lavriv, Lviv Polytechnic National University, Ukraine
Lyudmyla Novgorodska, Lviv Polytechnic National University, Ukraine
Leonid Ozirkovsky, Lviv Polytechnic National University, Ukraine
Oksana Soprunyuk, Lviv Polytechnic National University, Ukraine
Sponsors
Oleksandr Spivakovsky’s Educational Foundation (OSEF,
http://spivakovsky.fund/) aims to support gifted young people,
outstanding educators, and also those who wish to start up
their own business. OSEF activity is focused on the support
and further development of educational, scientific, cultural,
social and intellectual spheres in the Kherson Region of
Ukraine.
DataArt (http://dataart.com/) develops industry-defining ap-
plications, helping clients optimize time-to-market and mini-
mize software development risks in mission-critical systems.
Domain knowledge, offshore cost advantages, and efficiency
– that's what makes DataArt a partner of choice for their glob-
al clients.
Lviv Polytechnic National University
(http://www.lp.edu.ua/en) is the largest technological universi-
ty in Lviv. Since its foundation in 1844, it was one of the most
important centres of science and technological development in
Central Europe. Presently, the university comprises
16 institutes where students from Ukraine and other countries
are enrolled in 64 bachelor, 123 master, and 99 PhD pro-
grammes.
Logicify (http://logicify.com/) is an outsourcing company
providing software development services. Compay helps cus-
tomers with issues and projects involving software. Logicify
has been working in a variety of industries and fields, includ-
ing telecom, video sharing, social media, insurance. It has
several teams with specialized skills in different technologies
that can relate to specific industries.
Organizers
Ministry of Education and Science of Ukraine
http://www.mon.gov.ua/
Lviv Polytechnic National University, Ukraine
http://www.lp.edu.ua/en
University of Huddersfield, UK
http://www.hud.ac.uk/
Alpen-Adria-Universität Klagenfurt, Austria
http://www.uni-klu.ac.at/
Kherson State University, Ukraine
http://www.kspu.edu/
Taras Shevchenko National University of Kyiv, Ukraine
http://www.univ.kiev.ua/en/
V.N. Karazin Kharkiv National University, Ukraine
http://www.univer.kharkov.ua/en
Zaporizhzhya National University, Ukraine
http://www.znu.edu.ua/en/
Institute of Information Technologies and Learning Tools
of the National Academy of Pedagogical Sciences
of Ukraine, Ukraine; http://iitlt.gov.ua/en/
DataArt Solutions Inc., Russian Federation
http://dataart.com/
Table of Contents
Invited Contributions
Rigorous Semantics and Refinement for Business Processes . . . . . . . . . . . . . 1
Klaus-Dieter Schewe
Smart Learning Environments: a Shift of Paradigm . . . . . . . . . . . . . . . . . . . . 3
David Esteban
Tutorial
Systematic Business Process Modeling in a Nutshell . . . . . . . . . . . . . . . . . . . 4
Heinrich C. Mayr
Part I: Main ICTERI Papers
Teaching ICT and Using ICT in Education
Using ICT in Training Scientific Personnel in Ukraine: Status and
Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Aleksandr Spivakovsky, Maksim Vinnik and Yulia Tarasich
On the Results of a Study of the Willingness and the Readiness to Use
Dynamic Mathematics Software by Future Math Teachers . . . . . . . . . . . . . . 21
Elena Semenikhina and Marina Drushlyak
An Analysis of Video Lecture in MOOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Jyoti Chauhan and Anita Goel
Using Fuzzy Logic in Knowledge Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Marika Aleksieieva, Aleksandr Alekseev, Kateryna Lozova and Tetiana
Nahorna
Model-Based Software System Development
Knowledge-Based Approach to Effectiveness Estimation of Post
Object-Oriented Technologies in Software Maintenance . . . . . . . . . . . . . . . . 62
Mykola Tkachuk, Kostiantyn Nagornyi and Rustam Gamzayev
Provably Correct Graph Transformations with Small-tALC . . . . . . . . . . . . . 78
Nadezhda Baklanova, Jon Hael Brenas, Rachid Echahed, Christian
Percebois, Martin Strecker and Hanh Nhi Tran
A Study of Bi-Objective Models for Decision Support in Software
Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Vira Liubchenko
Method of Evaluating the Success of Software Project Implementation
Based on Analysis of Specification Using Neuronet Information
Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Tetiana Hovorushchenko and Andriy Krasiy
Machine Intelligence, Knowledge Engineering and Management for
ICT
Calculation Method for a Computer’s Diagnostics of Cardiovascular
Diseases Based on Canonical Decompositions of Random Sequences . . . . . 108
Igor P. Atamanyuk and Yuriy P. Kondratenko
Synthesis of Time Series Forecasting Scheme Based on Forecasting
Models System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Fedir Geche, Vladyslav Kotsovsky, Anatoliy Batyuk, Sandra Geche and
Mykhaylo Vashkeba
C-Clause Calculi and Refutation Search in First-Order Classical Logic . . . 137
Alexander Lyaletski
Principles of Intellectual Control and Classification Optimization in
Conditions of Technological Processes of Beneficiation Complexes . . . . . . . 153
Andrey Kupin and Anton Senko
ICT in Industrial Applications
A Composite Indicator of K-society Measurement . . . . . . . . . . . . . . . . . . . . . 161
Kseniia Ilchenko and Ivan Pyshnograiev
Implementing Manufacturing as a Service: A Pull-Driven Agent-Based
Manufacturing Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Leo Van Moergestel, Erik Puik, Daniël Telgen and John-Jules Meyer
ICT and e-Business Development by the Ukrainian Enterprises: the
Empirical Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Nataliia Medzhybovska
Geospatial Intelligence and Data Fusion Techniques for Sustainable
Development Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Nataliia Kussul, Andrii Shelestov, Ruslan Basarab, Sergii Skakun, Olga
Kussul and Mykola Lavreniuk
Part II: ICTERI Workshop Papers
ITER Workshop Papers
Risk Assessment of Use of the Dnieper Cascade Hydropower Plants . . . . . 204
Andriy Skrypnyk and Olha Holiachuk
Behavioral Aspects of Financial Anomalies in Ukraine . . . . . . . . . . . . . . . . . 214
Tetiana Paientko
The Formation of the Deposit Portfolio in Macroeconomic Instability . . . . 225
Andriy Skrypnyk and Maryna Nehrey
Dynamic Model of Double Electronic Vickrey Auction . . . . . . . . . . . . . . . . . 236
Vitaliy Kobets, Valeria Yatsenko and Maksim Poltoratskiy
Which Data Can Be Useful to Make Decisions on Foreign Exchange
Markets? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Karine Mesropyan
Econometric Analysis of Educational Process on the Web Site . . . . . . . . . . 262
Alexander Weissblut
The Multidimensional Data Model of Integrated Accounting Needed for
Compiling Management Reports Based on Calculation EBITDA Indicator 276
Viktoria Yatsenko
Statistical Analysis of Indexes of Capitalization of the Ukrainian Firms:
an Empirical Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Anastasiia Kolesnyk and Ihor Lukianov
MRDL Workshop Papers
The Hybrid Service Model of Electronic Resources Access in the
Cloud-Based Learning Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Mariya Shyshkina
Methods and Technologies for the Quality Monitoring of Electronic
Educational Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Hennadiy Kravtsov
SMSV Workshop Papers
Realisation of ”Black Boxes” Using Machines . . . . . . . . . . . . . . . . . . . . . . . . . 326
Grygoriy Zholtkevych
An Interleaving Reduction for Reachability Checking in Symbolic Modeling 338
Alexander Letichevsky, Oleksandr Letychevskyi and Vladimir Pescha-
nenko
Abstracting an Operational Semantics to Finite Automata . . . . . . . . . . . . . 354
Nadezhda Baklanova, Wilmer Ricciotti, Jan-Georg Smaus and Martin
Strecker
The Static Analysis of Linear Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Michael Lvov and Yulia Tarasich
Defining Finitely Supported Mathematics over Sets with Atoms . . . . . . . . . 382
Andrei Alexandru and Gabriel Ciobanu
On a Strong Notion of Viability for Switched Systems . . . . . . . . . . . . . . . . . 396
Ievgen Ivanov
Natural Computing Modelling of the Polynomial Space Turing Machines . 408
Bogdan Aman and Gabriel Ciobanu
TheRMIT Workshop Papers
Discrete and Continuous Time High-Order Markov Models for Software
Reliability Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Vitaliy Yakovyna and Oksana Nytrebych
Evolution of Software Quality Models: Green and Reliability Issues . . . . . . 432
Oleksandr Gordieiev, Vyacheslav Kharchenko and Mario Fusani
Service and Business Models with Implementation Analysis of
Distributed Cloud Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
Olga Yanovskaya, Maria Anna Devetzoglou, Vyacheslav Kharchenko
and Max Yanovsky
Automated Development of Markovian Chains for Fault-Tolerant
Computer-Based Systems with Version-Structure Redundancy . . . . . . . . . . 462
Bogdan Volochiy, Oleksandr Mulyak and Vyacheslav Kharchenko
Features of Hidden Fault Detection in Pipeline Digital Components of
Safety-Related Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
Alex Drozd, Miroslav Drozd and Viktor Antonyuk
The Control Technology of Integrity and Legitimacy of LUT-Oriented
Information Object Usage by Self-Recovering Digital Watermark . . . . . . . . 486
Kostiantyn Zashcholkin and Olena Ivanova
Functional Diversity Design of Safety-Related Systems . . . . . . . . . . . . . . . . . 498
Ivan Malynyak
Computer’s Analysis Method and Reliability Assessment of
Fault-Tolerance Operation of Information Systems . . . . . . . . . . . . . . . . . . . . 507
Igor P. Atamanyuk and Yuriy P. Kondratenko
Distributed Datastores: Towards Probabilistic Approach for Estimation
of Dependability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
Kyrylo Rukkas and Galyna Zholtkevych
Direct Partial Logic Derivatives in Analysis of Boundary States of
Multi-State System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Elena Zaitseva, Vitaly Levashenko, Jozef Kostolny and Miroslav Kvas-
say
Automation of Building the Safety Models of Complex Technical
Systems for Critical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
Bohdan Volochiy, Bohdan Mandziy and Leonid Ozirkovskyy
Scenario-Based Markovian Modeling of Web-System Availability
Considering Attacks on Vulnerabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Vyacheslav Kharchenko, Yurij Ponochovny, Artem Boyarchuk and Ana-
toliy Gorbenko
1
Rigorous Semantics and Refinement for Business
Processes (Abstract)⋆
Klaus-Dieter Schewe1,2
1
Software Competence Center Hagenberg, Austria, kd.schewe@scch.at
2
Johannes-Kepler-University Linz, Austria, kd.schewe@cdcc.faw.jku.at
Keywords. Business process model, Abstract State Machine, semantics, refine-
ment, exception handling
ICTERI Key Terms. Mathematical Model, Methodology, Formal Method,
Process, Integration
For the modelling of business processes it is necessary to integrate models for con-
trol flow, messaging, event handling, interaction, data management, and excep-
tion handling. In principle, all common business process models such as BPMN
[14], YAWL [13], ARIS [11] or S-BPM [6] follow such an approach. Though it
is claimed that the models have already reached a high level of maturity, they
still lack rigorous semantics as pointed out in [1, 5, 15]. Furthermore, quite a few
aspects such as data management, interaction and exception handling have only
been dealt with superficially as pointed out in [12].
The first concern regarding rigorous semantics has been discussed in detail
by Börger in [2] for BPMN, which led to an intensive investigation of BPMN
semantics on the grounds of Abstract State Machines (ASMs, [4]), in particular
for OR-synchronisation [3]. The monograph by Kossak et al. defines a rigorous
semantics for a large subset of BPMN leaving out some ill-defined concepts [8].
The second concern can be addressed by means of horizontal refinement.
On grounds of ASMs necessary subtle distinctions and extensions to the control
flow model such as counters, priorities, freezing, etc. can be easily integrated in
a smooth way [12]. Conservative extensions covering messaging can be adopted
from S-BPM [6], while events in BPMN have been handled in [7]. For the event
model it is necessary and sufficient to specify what kind of events are to be ob-
served, which can be captured on the grounds of monitored locations in ASMs,
and which event conditions are to be integrated into the model. Extensions con-
cerning actor modelling, i.e. the specification of responsibilities for the execution
of activities (roles), as well as rules governing rights and obligations lead to the
integration of deontic constraints [10], some of which can be exploited to simplify
the control flow [9]. In this way subtle distinctions regarding decision-making re-
sponsibilities in BPM can be captured.
⋆
The research reported in this paper was supported by the Austrian
Forschungsförderungsgesellschaft (FFG) for the Bridge Early Stage project “Ad-
vanced Adaptivity and Exception Handling in Formal Business Process Models”
(adaBPM) under contract 842437.
2
In the talk a glimpse of the rigorous, ASM-based semantics for business pro-
cesses is presented. The focus is on the control flow with specific emphasis on
priority handling. This is followed by a discussion of horizontal refinement focus-
ing on the introduction of disruptive events and associated exception handling. A
simplified example capturing the effects of external change to a running process
is used for illustration.
References
1. Abramowicz, W., Filipowska, A., Kaczmarek, M., Kaczmarek, T.: Semantically
enhanced business process modelling notation. In: Hepp, M., et al. (eds.) S-BPM.
CEUR Workshop Proceedings, vol. 251. CEUR-WS.org (2007)
2. Börger, E.: Approaches to modeling business processes: a critical analysis of
BPMN, workflow patterns and YAWL. Software & Systems Modeling 11(3), 305–
318 (2012)
3. Börger, E., Sörensen, O., Thalheim, B.: On defining the behavior of OR-joins in
business process models. Journal of Universal Computer Science 15(1), 3–32 (2009)
4. Börger, E., Stärk, R.: Abstract State Machines. Springer-Verlag, Berlin Heidelberg
New York (2003)
5. Dumas, M., La Rosa, M., Mendling, J., Reijers, H.A.: Fundamentals of Business
Process Management. Springer (2013)
6. Fleischmann, A., et al.: Subject-Oriented Business Process Management. Springer-
Verlag, Berlin Heidelberg New York (2012)
7. Kossak, F., Illibauer, C., Geist, V.: Event-based gateways: Open questions and
inconsistencies. In: Mendling, J., Weidlich, M. (eds.) Business Process Model and
Notation, Lecture Notes in Business Information Processing, vol. 125, pp. 53–67.
Springer, Berlin, Heidelberg (2012)
8. Kossak, F., et al.: A Rigorous Semantics for BPMN 2.0 Process Diagrams. Springer-
Verlag (2014)
9. Natschläger, C., Kossak, F., Schewe, K.D.: BPMN to Deontic BPMN: A trusted
model transformation. Journal of Software and Systems Modelling (2015), to ap-
pear
10. Natschläger-Carpella, C.: Extending BPMN with Deontic Logic. Logos Verlag,
Berlin (2012)
11. Scheer, A.W.: ARIS - Business Process Modeling. Springer, Berlin, Heidelberg
(2000)
12. Schewe, K.D., et al.: Horizontal business process model integration. Transacions
on Large-Scale Data- and Knowledge-Centered Systems 18, 30–52 (2015)
13. ter Hofstede, A.M., et al. (eds.): Modern Business Process Automation: YAWL
and its Support Environment. Springer, Heidelberg (2010)
14. Weske, M.: Business Process Management. Concepts, Languages, Architectures.
Springer (2012)
15. Wong, P.Y., Gibbons, J.: A process semantics for BPMN. In: Liu, S., Maibaum,
T., Araki, K. (eds.) Formal Methods and Software Engineering. Lecture Notes in
Computer Science, vol. 5256, pp. 355–374. Springer, Berlin Heidelberg (2008)
3
Smart Learning Environments: a Shift of Paradigm
David Esteban1
1
TECHFORCE, Vía Augusta, 2bis planta 5ª E-08006 Barcelona, Spain
desteban@techforce.eu
Abstract. The incorporation of Information and Communication Technologies
(ICT) as a supporting mechanism in educational processes has already been
proved as an important driver in reinforcing both teaching and learning. The ex-
tensive development of Learning Management Systems (LMS), software plat-
forms aimed at supporting and articulating e-learning, education courses and
training programs, is already backed by a relevant ICT industry, with significant
market penetration. The emergence of the new concept of Smart Learning Envi-
ronments (SLEs) is shifting the main focus of LMSs on courseware towards a
more efficient and effective approach focused on teaching and learning pro-
cesses, thus in the students themselves and in the teachers as key players. The
evolving concept of SLEs encompasses blending educational technologies with
appropriate considerations and guidance developed by pedagogical and educa-
tional neuroscience domains, thus opening up room for interesting scientific and
technological challenges.
Keywords. Information and Communication Technology, Learning Manage-
ment System, Smart Learning Environment
Key Terms. InformationCommunicationTechnology, TeachingMethodology,
TeachingProcess, Environment
4
Systematic Business Process Modeling in a Nutshell
Heinrich C. Mayr1
1
Alpen-Adria-Universität Klagenfurt,
Universitätsstrasse 65-67 Klagenfurt, 9020, Austria
Heinrich.Mayr@aau.at
Abstract. In-depth business process management is crucial for any institution
and enterprise in a competitive world. Although this insight is by no means
new, the daily practice draws another picture: Certainly, many enterprises have
defined their overall strategy including IT issues at least roughly, and, based
here on, have documented their business processes somehow. Rarely however,
do they manage their business processes comprehensively in the sense of cover-
ing analysis, design, measurement, continuous optimization, and IT support.
The key prerequisite for allowing such comprehensive handling of business
processes is to describe these processes transparently and completely, using a
modeling language that is appropriate for the particular context including all
stakeholders concerned.
The aims of this tutorial, therefore, are threefold: (1) the participants will learn
about the fundamentals of business processes and their contexts; (2) the key
features of popular business process modeling languages like Adonis and
BPMN; and (3) guidelines for selecting an appropriate modeling approach in-
cluding the customization to the given environment.
Intended audience: Practitioners and researchers who are interested in a sys-
tematic approach to business process management, and have basic knowledge
in modeling and information systems engineering.
Keywords. Business process fundamental, business process context, business
process modeling language, selection of the modeling approach, customization
Key Terms. Process, ProcessPattern, Technology, Methodology, Model
5
Using ICT in Training Scientific Personnel in Ukraine:
Status and Perspectives
Aleksandr Spivakovsky, Maksim Vinnik and Yulia Tarasich
Kherson State University, 27, 40 rokiv Zhovtnya St., 73000 Kherson, Ukraine
{Spivakovsky, Vinnik, YuTarasich}@kspu.edu
Abstract. Today an enormous amount of problems in building a system of
efficient education and science is on the discussion agenda in Ukraine. A
decrease in the number of scientists in the country has been observed in the last
15 years. At the same time, the amount of postgraduate students and people
aiming at obtaining their doctorate is increasing. Notably, similar indicators are
also observed in the majority of post-soviet countries. One complicating factor
is that the system of scientific personnel training in Ukraine is very restrictive
and closed. The proportion of research results published using a free access
scheme to the overall bulk of publications is still very small, in particular if
compared to the level of ICT development. Therefore, a major part of the
publications still remains inaccessible from the outside. In this study we
investigate the openness and accessibility of the preparation of the academic
staff in Ukraine. As a result we come up with a proposal of requirements to the
ICT infrastructure in this area.
Keywords: Information and communication technology, Education and
learning process, ICT infrastructure, Open Science.
Key Terms: ICT Infrastructure, Research.
''If it's not on the Web, it doesn't exist at all''
Sarah Stevens-Rayburn & Ellen N. Bouton, 1997
1 Introduction
The main catalyst for socio-economic development of a state potential is the ability to
create, collect, and effectively manage knowledge that is comes out from the best
scholarly research practices. The countries which have made it to their development
strategy and implemented the effective interaction with the business enjoy TOP
ratings in the World rankings. In the age of information technologies, it takes one not
years, but rather days to bear the bell of scientific research and excel the competitors.
The companies which are the first in the market are more likely to benefit from a
positive effect caused by the introduction of new knowledge. Globalization is
adjusting the cooperation between science and industry. More and more funds are
invested in scientific research and development to capture the leadership in the
market. A modern country's development is stimulated by the transition from a
resource-based economy to hi-tech. There is an opportunity to create “intellectual
6
dollars” without any resource, but people. The results of intellectual work become a
hard currency. For example, Japan, though it had no natural resources, managed to
become the leader in world's economy. The monetary value of the biggest hi-tech (IT)
companies is at a scale of the budgets of some developed countries (Apple – $ 711
billion, Microsoft – $ 349 billion, Google – $ 365 billion).
The Open Science (OS) movement gains popularity in the world of clerisy, aiming
to make research results and source data accessible to public at all levels. However,
there is a conflict between the desire of scientists to have access to shared resources
and make profit by using these resources [1]. In recent years, many governments try
to impose the policy of openness regarding scientific knowledge, especially, if it is
funded with public money. One way is the enforcement of providing open access to
the results of all research projects performed at public expense. An indicative example
is the US, which grant annually about $ 60 billion for research. In 2008, the US
Congress imposed the obligation to grant free access in a year after the first
publication to all the research papers based on the studies conducted by the National
Institute for Health (which receives circa the half of the total public funding for
science). Similar measures are now considered by many other countries.
Today, a lot of research in Ukraine is devoted to the problems of higher education
and, in particular, the use of ICT for training students, creating information and
communication environments in the universities, etc. However, in the scholarly
literature insufficient attention is paid to the development of information and
communication models of interaction with ІCT in academic staff training. Moreover,
today we are talking about the need for openness and accessibility of scientific
activity, whereas a substantial part of the scholarly output never reaches its reader
within and even more outside the professional academic community. This problem is
particularly acute in the post-soviet countries. Regionalism of entire areas in science,
convention, low connection with contemporary scientific trends, low level of foreign
language knowledge by scientists, lack of self-developing scientific community, low
competition with other countries, lack of motivation, poor funding, brain drain, and a
number of other factors result in the continuing archaism of scientific brainpower
training in Ukraine.
Scientometrics is rapidly developing nowadays. Using information technology
allows creating new services for the development of scientific and research activity.
Many global companies invest billions of dollars in services to support research
activity, thereby creating a serious market not for the research results but for the
research process support. Herewith the trend shifts toward commercial projects. The
examples of such companies are Apple, Microsoft, Google, Elsevier, Thomson
Reuters, not to mention many others. The most outstanding services with rapidly
growing impact are Google Scholar, Scopus, Orcid, Academia.edu, Research Gate,
Mendeley, arXiv.org, cs2n, Epernicus, Myexperiment, Network.nature, Science-
community. These services contribute to satisfying the needs of the scientific
community. In fact, these positively influence scientific and technical progress and
create a new paradigm of scientific research. A big number of the recently created
scientometric services allow assessing the relevance of the research results by a
scientist, the number of his publications, citations, storage, etc. Having these
measurements at hand opens up new opportunities and prospects. Our time is
characterized by the high rates of the accumulation of new knowledge, in particular in
7
the form of research results. Provided that the integration of research activities is
currently (and naturally) low, a huge amount of scientific and research information
falls out of search visibility and accessibility. Information technology is the only way
to arrange and create effective search tools for acquiring the necessary knowledge.
The objective of our research is to investigate the transparency of specialized
scientific bodies and offer the vision of their supporting ICT infrastructure.
Accordingly, the rest of the paper is structured as follows.
Present article includes such sections, as description of the methodological and
experimental parts (2-4), discussion of basic components of DC’s ICT infrastructure
and main ways and methods of their realization (5).
2 Related Work
David [2] mentions that the goal of Open Science is to do scientific research in a way
that facts and their distribution is made available at all the levels of the concerned
public. The same article states that the movement arose in the XVII century. Due to
the fact that the public demand for access to scientific knowledge has become so large
that there was a need for a group of scientists to share their resources with each other,
so that they could conduct research collectively [2].
The term E-Science (or eScience) was proposed by John Taylor, the Director-
General of the United Kingdom Office of Science and Technology in 1999 and was
used to describe a large funding initiative, starting from November 2000. E-Science
has been interpreted more broadly since as "the application of computer technology to
the implementation of modern scientific research, including training, experimentation,
accumulation, dissemination of results and long-term storage and access to all
materials obtained through the scientific process. These may include modeling and
analysis of facts, electronic/digitized laboratory notebooks, raw materials and built-in
data sets, handwritten production and design options, preprints and print and/or
electronic publications"[3].
Koichiro Matsuura, the President of UNESCO, wrote in his preface to [4]:
“Societies that are based on the knowledge will need to share them to keep their
human nature”.
In 2014, the IEEE eScience community proposed a condensed definition [5]:
“eScience encourages innovation in collaborative, computationally or facts intensive
research in all the disciplines throughout the research life cycle”.
Michael Nielsen, a physicist and propagandist of Open Science, colorfully
describes in [6] the way the new instruments need to look like to facilitate the
dissemination of the culture of cooperation and openness among scientists. One of
such tools exists now. This is arXiv – a site that allows physicists to publish preprints
of their works before the official publication of the article. This promotes to get in
faster feedback and to disseminate the new discoveries. Nielsen also acts for
publishing not only conclusions, but all the original data – this is the thing physicists
have been dreaming of for a long time. Journals could help them do that if they
wanted to [6].
8
The peer review system for scientific papers on one hand offers an opportunity to
obtain a (preliminary) critical assessment of a manuscript, but on the other hand it
slows down the publication of research results. In this system, a review process is
rarely accomplished in less than a month. The reviewers often request authors to
revise some parts of the material or conduct additional studies. As a result, the time
before the publication stretches for about six months or more. However, Michael
Eisen, the co-founder of the Public Library of Science (PLoS), mentioned that
according to his experience the "most serious incompletes are detected only after the
article is published." The same applies to other scientific works, including
dissertations for a degree [7]. The cases are known in history when after many years
after the defense a person was divested a degree and even was fired after the
examination of his work regarding qualitative or even plagiarism.
Tugo Pagano and Maria Alessandra Rossi suggest [8] that politics aimed at
overcoming the disadvantages of excessive privatization of knowledge can play an
important role in stimulating the economy. Efforts should be focused to maintain and
enhance the role of open science. The institutions of open science have allowed the
flourishing of industrial development from the beginning, and should have a much
more important role in the architecture of the future post-crisis global economy. This
can be achieved through the institute of World Research Organization (WRO) which
can master some of the benefits of open science to overcome the well-known free
rider problem associated with contributions to the last.
In 2004, the research group Laboratorio de Internet from Spain, which studies
educational and scientific activities on the Internet, started the Webometrics
(www.webometrics.info) project with the aim to rate University web sites. The
subject of their analysis is the university domain. Webometrics researchers emphasize
that the presence of a university website allows to simplify the publication of
scientific works by faculty and research staff, compared to the publication in print,
and also provides the information the fields of their professional activities. Online
publications are much cheaper than paper publications and have broader potential
audience. Publishing online facilitates to broadening the access to academic resources
for scientific, commercial, political, and cultural organizations both from within a
country and abroad. The rating scale is based on the four criteria that take into
account the entire Web data within the university domain: Visibility, Presence,
Openness, and Excellence. Each criterion has a weight corresponding to its
importance [9].
The report by UNESCO on information technology in education [4] shows that in
Ukraine there is a “rapid advancement of ICT into the sphere of education, which
needs continuous improvement in the efficiency of use of the new ICT in the
educational process, timely updates of educational content, and an increase in the
quality of ICT training”. However, there are some problems which are primarily
associated with the low psychological, methodological, and pedagogical readiness of
teachers to the rapid changes in information technology.
The issue of the openness of an education system and science often comes up in
relation to international research funding instruments, such as Tempus, Erasmus, and
others, and related projects. Every year, they attract the attention of many Ukrainian
and foreign universities, research organizations and structures.
9
In 2006-2008 our Kherson State University (KSU) participated in the following
European projects: Tempus TACIS CP No 20069-1998 “Information Infrastructure of
Higher Education Institutions”; Tempus TACIS МР JEP 23010-2002 “UnіT-Net:
Information Technologies in the University Management Network”; US Department
of State Freedom Grant S-ECAAS-03-GR-214(DD) “Nothern New York and
Southern Ukraine: New Partnership of University for Business and Economics
Development”, which resulted in the development and implementation of scientific
and management processes of analytical information systems and services. More
detailed information can be found in the articles by G. Gardner [10], V. Ermolayev
[11], A. Spivakovsky [12].
The results on the interrelation of ICT and educational process and the influence of
ICT on professional and information competencies of the future university graduates
have been presented in our previous publications [13, 14]. The authors have also
conducted the investigation of the technical component of the feedback services
implementation in KSU [15] and their impact on the preparedness of the students to
use ICT for educational and non-educational purposes, and forming the ICT
infrastructure in a higher educational institution [16, 17].
3 Experimental Settings
Today, Ukraine possesses a historically established system of scientific training. The
foundations of this system were laid in the Soviet Union. This system is very similar
to the system of post-soviet countries.
According to the State Statistics Service, 2011 [18], Ukraine had 14 895 “doctors
of science” and 84 979 “candidates of science” (the analog of a PhD) covering arts,
legal studies, and sciences. Among them 4 417 doctors and 16 176 candidates of
science work in sciences. In addition, as reported by the ”Voice of Ukraine”
newspaper, the National Academy of Sciences of Ukraine employs today 2 564
doctors and 7 956 candidates of science [18].
In the last 19 years the number of researchers in Ukraine, decreased by more than
100 thousand people, while the number of graduate students increased by almost 2
times (Fig. 1 shows an example). The trend similar to the decrease in the research
staff members can be observed in the numbers of domestic research and development
organizations (Fig. 2 shows an example).
10
Fig. 1. The dynamics in the numbers of research staff, PhD students, and university graduates
in Ukraine (1995-2013).
In Ukraine there are 988 Dissertation Committees (DC) [19]. DC are the expert
councils in different scientific domains which form the National organizational
infrastructure, accepting candidate and doctoral dissertations for examination, doing
the expertise, hosting the defenses of dissertations, and further awarding advanced
academic degrees. The aim of this infrastructure is to foster the development of the
innovative elite of Ukraine which is considered as a driving force for scientific and
technological progress.
Fig. 2. The dynamics in the numbers of Ukrainian organizations performing research and
development (1995-2013).
Given the importance of the DC infrastructure, the foci of this study are to:
Assess the openness and accessibility of the preparation of academic staff in
Ukraine within the system using the DC.
Specify the requirements for the construction of the ICT infrastructure in this area
We will analyze the performance of DC based on the following principles:
1. The availability of information;
2. Openness;
11
3. Weight;
4. Scientific;
5. Social significance.
The research into the current state of the system of interaction with ICT of the DC,
the Higher Attestation Commission of Ukraine, and graduate students is impossible
without the analysis, comparison and synthesis, abstract approach to the definition of
the basic patterns of the use of information technologies, and logical approach to the
description of possible implementations of innovative teaching methods. Hence, the
study of this issue requires the use a carefully designed combination of exploratory,
empirical, and statistical methods. Therefore, several methods are used:
Exploratory – the analysis, synthesis, comparison, generalization and
systematization of relevant information acquired from psychological and
educational literature legal documents, standards and information resources. These
sources are consulted and further generalized to define the essence of the
information competency of university students and assess the theoretical and
methodological bases of information competency formation. Pedagogical modeling
is employed to build the model of informatics competency.
Empirical – questionnaires, surveys, testing, and self-esteem; pedagogical
experiments are used to test the hypotheses of the study
Statistical – the methods of mathematical statistics are employed to determine the
reliability of the results on the basis of quantitative and qualitative analysis of the
empirical data
The analysis of the public (available on the Internet) information on the availability
of data on DC, and collecting the opinions of graduate students using a questionnaire
on the use of information technology in their dissertation projects are the main
research methods.
Considering that the DCs function as university bodies, such sites as Top 100
universities in the World, Top 10 European universities, Top 50 universities in
Russia, Top 25 universities in Poland, Top 10 universities in the USA, Top 15
universities in UK, Top 20 universities in Asia [20], Specialized DC of Ukraine were
the object of information analysis. Overall, 300 university sites were analyzed in the
reported research.
The study of the current status the use of ICT to support the activities of DC the
following assessment aspects:
1. The availability of a web site for a DC and its analysis;
2. The degree of openness of the information provided for a DC: information about
the members, dissertation abstracts, theses, etc;
3. Information security;
4. The existence of DC pages in social networks;
5. The availability of a feedback service.
Let us consider in more detail each of the assessment aspects.
1. While exploring the web sites of universities regarding the availability of
information about the activities of the respective DC, we have selected to use the
following four criteria:
12
A university web site provides the information on the DC and a link to its own
website
A DC does not have a separate web site, but it has a page on the university web site
A University website provides a brief information about the DC
There is no information about the DC neither on the university website nor in
social networks
2. The openness to the information about a DC for public:
Any Internet user can see the information
A user can view the data only after registration on the web site
Only the staff and students of the university can see the information
3. Feedback facilities:
Providing a contact phone number;
Providing a contact e-mail address(es);
Providing the list of contact persons;
Providing the Skype ID for contacts;
Providing the schedule of DC works.
4. The availability of information (pages) in social networks:
Due to a substantial impact of social networks on the communication among
people today, it has been decided to account for the relevant indicators in our study
an analysis of the availability of information about DC: the availability of accounts
or groups in social networks such as Vkontakte, Facebook, Google+, Twitter
To analyze the availability of video records of defense meetings the analysis of the
YouTube content relevant to a DC has been also undertaken
5. The technical characteristics of DC web sites used in our study are detailed in
Table 1.
Table 1. Technical criteria for the analysis and evaluation of DC websites.
Criterion Description
Number of The number of DC-relevant pages on a web site is the indicator
Web Pages influencing the ranking of the site in search results.
Frequency of The frequency of updating information about the activities of a DC is
Updates analyzed using the scale: weekly, monthly or annually
Authentication The main elements and authentication mechanism are analyzed under this
System aspect.
Usability The assessment of ease of use and operation of the system is done under
this aspect, namely how well, clearly and correctly the interface is
implemented and web site is structured. It is also assessed if a user can
quickly find the information he or she needs. We conducted a brief
analysis of layout. We also checked the availability dynamic elements
and search functionality.
13
Platform The web sites were categorized as implemented using CMS and hand-
coded.
SEO Under this aspect the ranking of a web site by search engines for specific
user requests was analyzed.
Validity Under this aspect we looked at the number of errors found by the web site
validator (http://validator.w3.org/).
Multimedia A study on the website of the libraries of audio and video recordings
content protections scientific papers, photographs, etc.
The questionnaire which has been used to survey the use of ICT by graduate
students in their preparation to defense consisted of 3 components:
Quantitative indicators of the use of ICT by graduate students in the process of
working with their DC.
The availability of training courses for the use of ICT in the preparation to defense
The readiness of the subjects to authorize the open storage of their research results
(articles, theses, dissertations) and review materials such as audio, video, etc.
4 Experimental Results
The result of the analysis of the websites of the universities of Ukraine regarding the
information on DC, personal web pages and sites of DC members is pictured in Fig.
3. Only 9% of the reviewed DC have their own web sites. 84% of DC related
information can be found on University web sites, taking into account that full
information concerning the DC activities has been found only for 47% of the
reviewed DC. 7% of the reviewed DC have no presence on the Internet. These results
pinpoint the major problems in the transformation of the contemporary Ukrainian
scientific community into the Open Science community.
Fig. 3. The availability of DC related information on the web sites.
Only 4 DC web sites exploit a user authentication functionality distinguishing user
roles. So, it can be stated that only 1% of the reviewed DC have created some ICT
based prototypes for the interaction between the applicants and the Ministry of
Education.
About 30% of the reviewed DC update the information on their web sites every
week, whereas 51% of the information on these sites is updated several times per year
14
(Fig. 4 shows an example). Consequently, the question arises on the reliability and
relevance of this information.
Fig.4. Frequency of updates.
As per the information on the reviewed web sites, the DC have no means to track
scientometric indicators of the members of the DC, the candidates for a degree, and
persons that had defended their theses in a particular DC, not to mention the presence
of analysts defended dissertations and access to them, which makes the qualitative
assessment of their activities impossible. 32 websites have usability problems in terms
of the ease of use of their interfaces and poorly implemented site (keyword-based)
search functionality. The latter is implemented on only 27 of the reviewed resources.
Only 17 of the examined web sites provide the information on or references to
resources like a “library”.
Regarding the minimally present contact information of a DC (a phone number,
address, contact person name, document templates), it is provided only on 4 of the
reviewed web sites. Moreover, the contact phone number is mentioned only on 2 of
them. Thus, in order to find the information a DC of relevance to a PhD project, one
should get their list and addresses in the Ministry of Education and Science of
Ukraine (where one also needs to go) and search for a relevant DC at the specified
address. This is only the first problem in the application process. The required
documents have also to be submitted to a DC by coming in person, since there is not a
single web site that allows you to exchange the information and documents with a DC
in the process of registration, filing and review of the thesis and so on.
The results of the review of the availability of information about Ukrainian DC in
social networks are shown in Fig. 5.
As can be seen in Fig. 5, 14 DC have a personal group or page in Vkontakte, 11 –
in Facebook, 7 – in Twitter and 4 – in Google+. It is also important that YouTube is
used, though to a small degree. So, a certain degree of openness of our science may be
noted, in particular the openness of the preparation of the scientific staff.
The analysis of quantitative indicators of the use of ICT by graduate students for
working with a DC is shown in Table 2.
15
Fig. 5. The use of social networks in the work of DC.
The study reveals that only 2-3% of the respondents know what is a scientific
database (SDB) or a citation index, 7% use these systems from time to time to find the
necessary information, and only 4% have their own profiles in such scientometric
systems and databases like Scopus, Google Scholar, Mendeley, RSCI or others. It is
important that the majority of the respondents are not interested in creating their own
profiles in such scientometric systems. The main reason for that is the lack of
recognition of their utility. Moreover, some of the profiles were created directly by
the organizations where scientists work, or automatically by the systems that store
their scientific articles. Thus the majority of respondents did not know whether they
have a profile in any of the systems, whether these exist or not.
80% of respondents do not think much about how their scientific publications are
stored –in a paper or electronic form, and they believe that it is not of great
importance. Thus, the majority of publications are going out of press in a paper form
and are not further digitized – so remain unavailable to the scientific world.
Table 2. Quantitative indicators of the use of ICT by graduate students for working with a DC.
Do not Use Rarely Use Always use
Use of the Working with DC website 80% 15% 5%
Internet to Search of information about 93% 5% 2%
search for the members of DC in SDB
information Own profiles in SDB 95% 4% 1%
about DC Work with electronic 40% 50% 10%
repositories (theses and
abstracts)
Use of email 30% 40% 30%
Use of Skype 84% 10% 6%
93% of respondents answered negatively about attending any course (or lectures)
to get prepared for the use of ICT in their dissertation project (SDB, repositories,
etc.).
Analyzing the readiness to the open storage of research results (articles, theses,
dissertations) and materials of dissertation defense such as audio or video, we
observes the following:
16
1. The majority of the respondents (80%) support the publication of electronic copies
of their scientific papers on the Internet, but at the same time consider it
unnecessary and inconvenient. Further, all the respondents point out that the
Ministry of Education and Science of Ukraine (MESU) has the publication
requirements (regarding the number of papers and form of publication, paper or
electronic) to qualify for a degree which do not motivate providing open access.
MESU requires that a qualified candidate has 5 publications at the MESU
approved venues, one of which can only be published in an electronic edition and
another one in an international or indexed international SDB. Thus, none of the
applicants target to publish the electronic copies of their papers on the Internet. In
some cases, this problem is solved by posting electronic copies on a digest web site
or putting these into an electronic repository of a scientific institution of the
applicant. Otherwise the articles remain inaccessible to the outside world.
2. The Problem with open access to the protected dissertations and abstracts is
identical to the previous. In addition, the human factor needs to be taken in
consideration. Providing free access to abstracts or theses means making these
open for further examination after publication, hence the increase of the author’s
responsibility for its contents and quality. Therefore, open storage of scientific
work of this type stimulates quality improvement. We see it in the results of the
evaluation of the respondents ' answers to this question. Notably, 80% of the
respondents agree that the understanding that their work could be read by any other
scientist clearly affects the quality of publications.
As an example, let us compare the quantities of the full versions of theses and
abstracts stored in the repositories in Ukraine to numbers in the repositories in
Germany, Great Britain, and Spain (top 30 repositories of each country rated by
Webometrics, http://www.webometrics.info, were examined) – see Table 3. Ukraine
has 38 repositories in total while having more than 400 universities.
Table 3. Numbers of dissertations and abstracts in open access repositories.
UKRAINE GERMANY UK SPAIN
Dissertation 1858 71656 16724 3586
Abstract 3532 22882 23617 18582
Only 15% of the respondents agree that online video protection is useful, 30% – to
deposit their audio and video files providing open access, while the remaining 45%
believe that audio and video recording is unnecessary or even harmful as it bothers
and disturbs focusing on the defense talk. To the question “if they would like and are
ready to use specialized systems to work with a DC and MESU” 90% of the
respondents gave a positive answer. The most significant motive to this answer is
potential reduction of time and financial expenses for data processing (sending and
receiving documents, access to the proper information and so on).
17
5 Our Vision of an ICT Infrastructure for a DC
As experimentally proven above, the effective implementation of the elements of OS
must assume the existence of an appropriate ICT infrastructure as a scientific and
educational system as a whole and its component parts (schools, universities, DC, and
others) in particular.
The main elements of the ICT infrastructure of OS are researchers (academic
staff), data and processes.
Speaking of ICT infrastructure DC we can determine its components as follows:
Researcher – the applicants, the members of a DC, the employees of MESU, and
other users of the system have access to relevant information and participate in
information processing, communication, and computing processes
Data – information about the work of DC, their employees, applicants, archives of
theses, scientific publications, etc. as a tool to open exchange, recombination, and
reuse are the important components of the infrastructure;
Process – the procedures, services, tools, and methodologies that are used to
collect, perform the transformation, analysis, visualization and storage of data,
build models and simulations. The management of these processes is done both on
the side of users (researchers) and of the specialized services and systems.
Fig.7. User roles and their main features.
As pictured in Fig. 7, all the user roles have both generic and specific abilities in
using the system. All roles can retrieve publicly available information while working
with documentation is allowed only to certain roles.
The workflow of the system is presented in Fig. 8 and proposes almost complete
automation of all communication processes. It should be noted that the
implementation of a similar service involves not only the functionality described
above, but also the implementation of some add-ons and extra features. One of the
additional features of interest is related to solving the problem of retrieving the
information about the available DC discussed above. The task of collecting correct
and complete scientometric data regarding the DC members, candidates, and
18
graduates is of particular importance and interest. It is difficult to compile by hand a
report for an individual DC based on the scientometric information even if all the
mentioned actors have their profiles, say at Google Scholar. The task of reporting
about all relevant DC, or the graduates interested in applying to a relevant DC, is even
more complicated.
Fig. 8. Algorithm of DC system work.
We currently possess a number of modules relevant for the solution of this
problem. For example, the problem outlined above may be solved using our
publication.kspu.edu service. The main task of this service is automating the
collection and processing of information on scientometric indicators of scientist
retrieved from his or her Scopus and Google Scholar profiles and building
consolidated ratings for departments, institutes, and universities.
The service provides the possibility to generate the required scientometric
indicators and ratings on the DC web site, hence offering an additional degree of
openness of their activities. In addition, we assume that this form of presenting
information contributes to establishing vigorous competition in the research staff
training market, and therefore has an impact on the quality indicators.
19
An electronic repository of a DC is also a mandatory component of the system
which store all theses and abstracts in electronic form and, if possible, in the public
domain.
The competition on the market puts in front the requirement of using social
networks in the activities of a DC. The results of the study presented in Section 4
provide clear evidence about their rare use. We believe that the inclusion of the use of
social networks in the workflow will provide a valuable addition to the information
and communication services of the architected infrastructure.
6 Concluding Remarks and Future Work
Building a system of efficient education and science in Ukraine today is complicated
by many serious problems. In the last 15 years we observed a decrease in the number
of scientists in the country. At the same time, the numbers of postgraduates and
doctorates are increasing.
A system of training of scientific personnel in Ukraine is among the most
restrictive and closed ones in the world. A similar trend is observed in the majority of
post-soviet countries. The proportion of scientific research results published under a
open access is still very small compared to the level of ICT development. The main
part of research results still remains inaccessible for an external users.
The use of ICT in training scientific personnel and representing the results of their
research appears to be extremely weak. The preparation, protection and storage of
information is done without using ICT, therefore it requires significant time and
resource.
To partly overcome some of the problems, we propose a concept of the ICT
infrastructure for the interaction of researchers, a DC, and the Ministry of Education
and Science of Ukraine. The main elements of this infrastructure are the following:
the web sites and services for supporting the applicants to a DC; the services and
systems of interaction between a DC and the Ministry of Education and Science of
Ukraine; electronic data storages for publications, theses, and abstracts; decreasing of
time spent on a research process without harming its quality; additional expertise;
transparency and credibility of research; building qualitatively new communications
between scientists; ability to obtain research information swiftly and in required forms
(especially government); fighting corruption (decreasing human factor in DC
activities).
An important and influential part of establishing an effective process for training
scientists is training researchers to use this process and respective tools based on ICT.
Training scientists to use ICT in their research activities creates additional
opportunities for scientific and technical progress. This training can be conducted in
magistrates, postgraduate and doctorate curricula. In this research we presented the
project that is now being realized using the DC in Kherson State University as a case
study. The next phase of our research is the investigation of the efficiency of using the
described model and its influence on qualitative characteristics of science.
20
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21
On the Results of a Study of the Willingness and the
Readiness to Use Dynamic Mathematics Software by
Future Math Teachers
Olena Semenikhina1, Marina Drushlyak1
1
Sumy Makarenko State Pedagogical University, Romenska St. 87, Sumy, Ukraine
e.semenikhina@fizmatsspu.sumy.ua, marydru@mail.ru
Abstract. The article presents the results of pedagogical research on the will-
ingness and the psychological readiness to use dynamic mathematics software
by future math teachers. We used nonparametric method for dependent samples
– the McNemar’s test. The hypothesis, that the study of Special course on the
use of dynamic mathematics software for future teachers has a positive impact
on the willingness and the psychological readiness to use such software in their
own professional activities, is confirmed at the significance level of 0.05.
Additionally, the results of the experiment on the willingness and the readiness
to support the teaching of some subjects (algebra, planimetry, solid geometry
and analysis) with dynamic mathematics software and the willingness and the
readiness to use some dynamic mathematics software (Gran (Gran1, Gran2d,
Gran3Н), GeoGebra, abri, MatСKit, DG, GS) by Ukrainian math teachers is
given.
Keywords. The study of mathematics, computer applications in the study of
mathematics, special course, dynamic mathematics software, the McNemar’s
test.
Key Terms. InformationCommunicationTechnology, TeachingProcess,
TeachingMethodology.
1 Introduction
Ukrainian education has always tried to involve leading technologies and tools that
have spread in the world and improve the level of education of ordinary Ukrainians.
That is why since the end of the last century information technology has started to be
actively implemented in the learning process (also in mathematics). Specialized
software appeared and the main purpose of them was computational and visual
support of solving of math problems. Later the software, that allows to model
processes and to observe the changes in constructions, appeared. But the use of such
22
software was limited in schools because of a number of reasons, among which the
insufficient technical equipment of schools, the lack of targeted preparation of
teachers to use specialized software, the lack of software with a clear (Ukrainian,
Russian) interface, a small number of teacher’s guides, etc.
Now there is a great amount of software which can be used in teaching
mathematics. We previously conducted an analisis of the current tendencies of math-
ematics software use in education in [1]. But the workload of school teachers does not
let them to monitor the appearance of such software, to learn the tools and to use them
at their lessons. The main part of Ukrainian math teachers are 40 and more years old.
This means that they were not acquainted with mathematics software during their
preparation, and they used information technologies on the level of Internet users and
Word, Excel, owerPoint. They do not use software consciously, because they believe
that chalk-and-Board style is better at studing mathematics.
These and other reasons have led us not only to enter the Special course of the study
of mathematics software in the curricula of preparation of modern teachers, but to
study the impact of this course on the willingness and the readiness to use mathemat-
ics software in the professional activity of math teachers.
2 Research of the Willingness and the Psychological Readiness of
Future Math Teachers to Use Dynamic Mathematics Software
During 2010-2014, we have investigated the problem of the willingness and the
psychological readiness to use mathematics software by future math teachers [2].
We allocate dynamic mathematics software (DMS), that can model and modify
mathematical objects interactively. We consider Gran, DG (Ukraine), GeoGebra
(GG, Austria), MathKit, Live Mathematics (LM) (Russia), Cabri (France), The
geometer's Sketchpad (GS, USA), etc. We allocate these software for the following
reasons: 1) software Gran and DG are recommended by the Ministry of Education
and Science of Ukraine; 2) software MathKit and Live Mathematics are actively used
by Russian teachers, as evidenced by a great number of methodological works of
math teachers; 3) software Cabri, The geometer's Sketchpad and GeoGebra are the
most popular in the world, as evidenced by the numerous translations of monographs
and multi-lingual interfaces of these software.The work with them intuitive and
identical – basic objects are built, then they can be dynamically changed and user can
observe certain quality properties and quantitative characteristics. The study of
features of these software and recommendations for their use are generalized by us in
[3-10].
The base of the reaserch was Sumy Makarenko State Pedagogical University.
Preparation of math teachers is in accordance with the curricula. The introduction of
these software was during the study of methodology of mathematics and during the
study of a special course "Computer Applications in the Study of Mathematics" (fur-
ther Special course). The program of the Special course was described in [11-13] and
was improved during the years 2008-2014. The experience of the involvement of
23
dynamic mathematics software in support of teaching mathematics in the school was
during teaching practice (see Table 1).
Table 1. The extract from the curriculum of the speciality “Mathematics*”
Course Feachers Note
Semester 6;7;8
Methodology The course contains the module “Computer
of Credits 2,5;2;2 support for learning mathematics” – 7-th
mathematics semester, 12 hours.
Class hours 46;46;44
At the beginning of the third quarter, within 2
Semester 8
Teaching months, on the basis of city schools
practice It is supposed to teach 10 math lessons at 5-9
Credits 6
classes
Semester 8 It is supposed to study different dynamic math-
Special
Credits 3,5 ematics software during solving algebra, geome-
course
Class hours 50 try, analysis problems
At the beginning of the teaching practice students learn how to solve mathematical
problem with the use of dynamic mathematics software (DMS) at the lessons of Spe-
cial courses. During the teaching practice they have the opportunity to see (or not to
see) and analyze lessons of those teachers who use DMS in their own professional
activity.
We believe that during this period the basis for the motivation of the learning and
further use of DMS in professional activities is formed. Therefore, the Special course,
which is studied immediately after the teaching practice, becomes the factor of impact
on the student, which gives the opportunity to talk about the willingness and the read-
iness to use DMS in the future professional activity.
Because these personal characteristics can be formed within the teaching of the
Special course, it was natural to involve such statistical methods, that give the oppor-
tunity to talk about the dynamics of change based on data about the initial and final
state of the object. So we fixed the internal state of the willingness and the psycholog-
ical readiness of the student to use DMS with the help of questionnaires at the begin-
ning and at the end of the study of the Special course (see Table 2).
Table 2. The questionnaire
№ Questionnaire Answers
1. Do You need to use DMS at the lessons of algebra (planimetry, Yes
solid geometry, mathematical analysis)? Why? Yes, not at all
No
24
№ Questionnaire Answers
2. Do You want to use DMS at the lessons of:
a) algebra; Yes/No
b) planimetry; Yes/No
c) solid geometry; Yes/No
g) mathematical analysis? Yes/No
Why?
3. Do You feel readiness to use DMS at the lessons of:
a) algebra; Yes/No
b) planimetry; Yes/No
c) solid geometry; Yes/No
g) mathematical analysis? Yes/No
Why?
4. Specify a priority of DMS that You like. Gran
DG
GG
Specify a priority of DMS, which is better to use at math lessons MathKit
on Your opinion. GS
Cabri
It was applied the McNemar’s test [14], because the scale of results in questions 1-
3 has two items ("Yes" or "No"). This method is nonparametric and used to compare
distributions of objects in two sets according to some property on the scale with two
categories (e.g., "like - dislike ", "ready - not ready," "willing - unwilling" and others).
For a McNemar’s test the following conditions are required: 1) random sample; 2)
dependent sample; 3) pairs (хі, yi) are mutually independent (the members of the
sample have no effect on each other); 4) the scale has only two categories.
The research was conducted from 2010 to 2014. Each year we have accumulated the
results of the sample with volume 37, 35, 38, 37, 31, respectively. The total number of
respondents amounted to 178 people. We selected results from them at random.
2.1 The Use of Dynamic Mathematics Software in the Study of Mathematics
in Secondary Schools
The beginning of our research was associated with the study of the status of the use of
DMS in the study of mathematics in secondary schools. Through conversations with
teachers, graduates, teachers-methodists of our region it was found that the “poor” use
of DMS in the learning process is not only due to the limited number of computers in
schools, but due to lack of the willingness of teachers to involve such software to the
solution of mathematical problems. Although they did not deny the feasibility of this
approach, but noted, among other things, about the inability to use DMS (68%), the
need for additional time to study them (87%), the small number of methodological
literature on the use of DMS (90%) and the lack of collections of tasks, which can be
solved by using DMS (36%).
25
2.2 The research of the Willingness of Future Math Teachers to Use Dynamic
Mathematics Software in Their Professional Activities
Searching for ways to solve the problem, we have suggested that a focused study of
the Special course will have a positive impact on the willingness of future math
teachers to use DMS in their profession.
The test of the assumption was carried out according the McNemar’s test on taken
results in the amount of 30 pieces from 178 at random.
Hypothesis 0: the Special course does not impact on the willingness of students to
use DMS in the future math teacher’s profession. Hypothesis а: the Special course
has a positive impact on the willingness of future math teachers to use DMS.
We had two series of observations: Х={x1, x2, …, xN} and Y={y1, y2, …, yN}, where
(хі, yi) are the results of measuring of the willingness to use DMS in the future
professional activity of the same object (the willingness of the student before and after
the Special course). In our notation, xі or yі takes the value 0 if the object of study
does not wish to use DMS at any of the classes (algebra, planimetry, analysis, solid
geometry) and 1 otherwise. The results of the dual survey recorded in the Table 3.
Table 3. The survey on the willingness to use DMS
The second surve
The first surve yi=0 yi=1
xi=0 а=6 b=10 a+b=16
xi=1 c=2 d=12 c+d=14
a+c=8 b+d=22 N=30
In the conditions of the experiment parameter а determined the number of students
who both times said “No”; the parameter b was the number of students who the first
time said "No" and the second time said "Yes"; the parameter c was the number of
students who the first time said "Yes" and the second time said "No"; the parameter d
was the number of students who both times said "Yes".
To apply the McNemar’s test we will find Тexper= min(b,c), if n = b + c < 21. For
our data Тexper= 2, since n = 10 + 2 = 12 ᦪ 20. Statistics of the criterion for
significance level α = 0,05 is р = 0,019. According to the rule of decision [14] we
have 0,019 < 0.025. We have to reject hypothesis Н0 and accept the alternative one,
and since b ᦫ c, then we consider that the impact of the study of the Special course on
the willingness to use DMS is not only statistically correct, but also positive.
2.3 The research of the Readiness of Future Math Teachers to Use Dynamic
Mathematics Software in Their Professional Activities
In parallel with the research of the willingness to use DMS we explore the personal
readiness of future math teachers to use DMS in their professional activities (question
3 of the questionnaire).
26
The hypothesis H0: the Special course does not impact on the psychological readi-
ness of students to use DMS in their professional activities.
Then the hypothesis а: the Special course impacts on the psychological readiness
of future math teachers to use DMS.
The test of the assumption was carried out according the McNemar’s test on taken
results in 40 pieces from 178 questionnaires at random (see Table 4).
Table 4. The survey of psychological readiness to use DMS
The second surve
The first surve yi=0 yi=1
xi=0 а=7 b=16 a+b=23
xi=1 c=6 d=11 c+d=17
a+c=13 b+d=27 N=40
Since n = b + c = 22 ᦫ 20, the statistics of criterion is calculated according the
formula Тexper= (b – c)^2 / (b + c) = 4,54. The assumption of the fairness of the null
hypothesis is approximated like the χ2 distribution with one degree of freedom (υ=1).
For significance level α=0,05 the critical value of the test is Тcritic=3,84. The obtained
value of Тexper=4,54 ᦫ Тcritic=3,84, therefore, the hypothesis 0 is rejected and the
alternative hypothesis, indicating that the impact of the Special course on the readi-
ness to use DMS in future professional activity is significant and cannot be explained
by random variation, is accepted.
2.4 The research of the Willingness of Future Math Teachers to Use Different
Dynamic Mathematics Software in Their Professional Activities in Teaching of
Some Subjects
Because the questionnaire was on the research of the willingness to use DMS at
the lessons of algebra, planimetry, solid geometry and analysis, and on the research of
the use of different DMS (Gran (Gran1, Gran2Н, Gran3Н), GeoGebra, abri,
MathKit, DG, GS), we were able to fix and process results about the willingness to
use DMS in teaching of some subjects – algebra, planimetry, solid geometry, analysis
(see Table 5) and about the willingness to use different DMS – Gran, DG, GeoGebra,
MathKit, GS, abri (see Table 6).
For each position of the table 5 we have the rejection of the null hypothesis H0 and
the acceptance of alternative hypothesis, i.e., at the significance level α=0,05 we can
say about the positive impact of the studing of the Special course on the willingness
of future math teachers to use DMS at the lessons of algebra, planimetry, analysis and
solid geometry.
27
Table 5. The survey of the willingness to use DMS in teaching of different subjects
Indices of the McNemar’s test
Quantitative indices
Question. Do You wish to use (α=0,05)
DMS at the lessons of: b+с Тек Р Н
a b c d N Но
а
algebra 6 11 2 11 30 13 2 0,011 0 1
planimetry 2 15 5 8 30 20 5 0,021 0 1
analysis 5 12 3 10 30 15 3 0,018 0 1
solid geometry 6 14 4 6 30 18 4 0,015 0 1
Table 6. The survey of the willingness to use some DMS
Indices of the McNemar’s test
Question. Do You Quantitative indices
(α=0,05)
wish to use:
a b c d N b+с Тек Р Но На
Gran 8 11 2 9 30 13 2 0,011 0 1
DG 5 12 3 10 30 15 3 0,018 0 1
GG 2 12 2 14 30 14 2 0,006 0 1
MathKit 6 14 4 6 30 18 4 0,015 0 1
GS 12 10 6 2 30 16 6 0,227 1 0
Cabri 20 6 3 1 30 9 3 0,254 1 0
For indeces of the table 6 we have the acceptance of hypothesis H0 for the last
two rows. This means that at the significance level 0.05, future math teachers wish to
use software Gran, DG, GG, MathKit, but we have no reason to say about the will-
ingness to use GS and Cabri. We can explain this because of "poor" interface of GS
and the absence of Ukrainian (or Russian) interface of Cabri.
Visualization of the obtained results during the experiment years is given in
Fig. 1-2.
28
Fig. 1. The percent of people willing to use DMS at different math lessons
Fig. 2. Increase in the number of people willing to use DMS (%)
Also we give some information about the "attractiveness" of software according to
the survey of future and working math teachers, which was conducted at scientific-
methodical seminars (on the basis of physics and mathematics faculty) (see Table 7,
Fig. 3-10).
29
Table 7. The attractiveness of software (%)
Gran DG GG
Year T S T S T S
2010 0,93 0,59 0,74 0,68 0,28 0,68
2011 0,75 0,71 0,51 0,80 0,32 0,91
2012 0,86 0,71 0,83 0,66 0,45 0,79
2013 0,68 0,43 0,54 0,54 0,68 0,78
2014 0,40 0,32 0,13 0,48 0,66 0,97
MathKit GS Cabri
Year T S T S T S
2010 0,11 0,32 0,00 0,24 0,00 0,00
2011 0,11 0,57 0,02 0,43 0,00 0,00
2012 0,17 0,66 0,08 0,32 0,00 0,11
2013 0,19 0,86 0,03 0,35 0,05 0,08
2014 0,13 0,94 0,00 0,19 0,07 0,13
Fig. 3. The attractiveness of DMS for teachers
30
Fig. 4. The attractiveness of DMS for students
Fig. 5. The attractiveness of GRAN Fig. 6. The attractiveness of DG
Fig.7. The attractiveness of GG Fig.8. The attractiveness of GS
31
Fig. 9. The attractiveness of MathKit Fig. 10. The attractiveness of Cabri
2.5 The research of the Readiness of Future Math Teachers to Use Different
Dynamic Mathematics Software in Their Professional Activities in Teaching of
Some Subjects
Because the questionnaire was on the research of the psychological readiness to use
DMS at the lessons of algebra, planimetry, solid geometry and analysis, as well as the
readiness to use different DMS (Gran (Gran1, Gran2Н, Gran3Н), GeoGebra, abri,
MathKit, DG, GS), then we could fix the results of the readiness to use DMS in teach-
ing of different subjects (algebra, planimetry, solid geometry, analysis) (see Table 8).
Table 8. The survey of the readiness to use DMS in teaching of different subjects
Indices of the McNemar’s
Do You feel the readiness to use Quantitative indices
test (α=0,05)
DMS at the lessons of:
a b c d N n=в+с T_2 Н0 На
algebra 6 17 7 10 40 24 4,17 0 1
planimetry 2 21 9 8 40 30 4,80 0 1
analysis 5 18 7 10 40 25 4,84 0 1
solid geometry 4 17 15 4 40 32 0,13 1 0
For all items, except the last, we have the rejection of the null hypothesis H0 and
the acceptance of the alternative hypothesis, i.e., at the significance level α=0,05, we
can say about the positive impact of studing of the Special course on the
psychological readiness of future math teachers to use DMS at the lessons of algebra,
planimetry, analysis. However, experimental results do not give grounds to say about
the positive impact on the readiness to use DMS at the lessons of solid geometry.
Increase in the number of students who feel the readiness to use DMS at the math
lessons is presented in Fig. 11.
32
Fig. 11. Increase in the number of people psychologically ready to use DMS
3 Conclusion
Thus, this research allows to state the following.
1. Future math teachers understand the need to use DMS and welcome the studing
of the Special course, since the research of the willingness and the readiness to use
DMS demonstrates a positive dynamics. The assumption about the positive impact of
the studing of the Special course on the psychological state of students is confirmed at
the significance level of 0.05 according to the McNemar’s test. In other words, after
the studying of the Special course "Computer Applications in Teaching Mathematics"
the number of students, who have the willingness and feel the readiness to use DMS
in future professional activity, increases.
2. Most students focused on using DMS at the lessons of algebra, planimetry and
analysis. We explain this because of not only a sufficient number of DMS and good
tools in such software, but enough number of teacher’s guide for their application and
free access to DMS with Ukrainian or Russian interface.
The percentage of students, who are willing to use DMS at the lessons of solid ge-
ometry, is too small. We explain this not only because of small number of software
and “poor” tools in such software, but of lack of Russian or Ukrainian interface in
them. Also there is the lack of methodical material of solving solid geometry
problems with the use of specialized software.
3. Teachers, who work at the school, have the willingness and the inner readiness to
use DMS, but face with the limited access to computer classes. The involvement of
DMS, as they say, is possible only during extracurricular activities.
4. GRAN and GeoGebra are the most popular in Ukraine. In recent years there has
been a decline in the use of the first and great attachment to the second. We explain
that because of free access and frequent updating of GeoGebra, the steady growth of
33
its tools (in particular, the version GeoGebra 5.0 with 3d-tools was tested in 2013,
and is distributed now).
5. Russian software athKit finds his supporters (the latest version is license, but
the early versions can be found in Internet). It is attractive because of ”rich” tools and
automated control, which is not provided in other DMS.
6. Students and teachers prefer Gran and DG. We explain that because of the free
distribution, the Ukrainian interface, a sufficient number of researches in periodicals,
the recommendations of the Ministry of Education and Science of Ukraine (also at the
lessons of computer science).
Note that students prefer GS, MathKit and abri more then teachers. We explain
that becourse of the lack of Ukrainian interface, the license and the unwillingness of
teachers to work with unfamiliar DMS.
7. According to the research we note the increasing demand for GeoGebra (it was
pointed out by the future and working math teachers). We believe that it is necessary
to pay attention just at it, because GG is continuously updated, freely distributed, has
interface on 30 languages, that confirms its popularity.
8. Future research should be conducted towards the creation of methodical support
of school math courses based on GG. During the preparation of future math teachers
we need to focus not only on traditional for the Ukrainian school software Gran, DG,
but also on the other DMS, which are widely distributed in Internet and used by
teachers.
References
1. Semenikhina, E., Drushlyak, M.: The Necessity to Reform the Mathtmatics
Education in the Ukraine. Journal of Research in Innovative Teaching. 8, 51--62
(2015)
2. Semenikhina, O., Shishenko, I.: Consequences of the Spread of IT and the Shift in
Emphasis of Teaching Mathematics in Higher School. Vyscha Osvita Ukrainy. 4,
71--79 (2013)
3. Semenikhina, O., Drushlyak, M.: Use of Computer Toos of IGE CABRY 3D at a
Solving of Stereometry Problems. Informatika ta informatsiyni tehnologiyi v
navchalnih zakladah. 4, 36--41 (2014)
4. Semenikhina, O., Drushlyak, M.: Computer Tools of Dynamic Mathematics Soft-
ware and Methodical Problems of Their Use. Information Technologies and
Learning Tools. 42 (4), 109--117,
http://journal.iitta.gov.ua/index.php/itlt/article/view/1055#.VCqAD0Hj5nE.
(2014)
5. Semenikhina, O., Drushlyak, M.: On Checking Tools in the IGE MathKit.
Naukoviy visnik Melitopilskogo derzhavnogo pedagogichnogo universitetu.
Seriya: Pedagogika. 13 (2), 189--195 (2014)
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6. Semenikhina, O., Drushlyak, M.: Geometric Transformations of the Plane
and Computer Tools for Their Implementation. Komp’yuter v shkoli i sim’yi.
7(119), 25--29 (2014)
7. Semenikhina, E., Drushlyak, M.: Computer Mathematical Tools: Practical Experi-
ence of Learning to Use Them. European Journal of Contemporary Education. 9
(3), 175--183 (2014)
8. Drushlyak, M.: Computer Tools “Trace” and “Locus” in Dynamic Mathematics
Software. European Journal of Contemporary Education. 10 (4), 204--214 (2014)
9. Semenikhina, E., Drushlyak, M.: Creation of Own Computer Tools in the
Dynamic Mathematics Environment. Informatika ta informatsiyni tehnologiyi v
navchalnih zakladah. 5(53), 60--69 (2014)
10. Semenikhina, E., Drushlyak, M.: GeoGebra 5.0 Tools and Their Use in Solving
Solid Geometry Problems. Information Technologies and Learning Tools. 44(6),
124--133,
http://journal.iitta.gov.ua/index.php/itlt/article/view/1138/866#.VKKRJc-eABM
(2014)
11. Semenikhina, E.: The Course for the Study of Dynamic Mathematics Software as
a Necessary Component of Training of Modern Math Teacher. In: Modern Trends
in Physics and Mathematics Education: School – University. Revised Extended
Papers of International scientific-practical conference, pp. 75--78, Solikamsk State
Pedagogical Institute (2014)
12. Semenikhina, E.: On the Nessesity to Introduce Special Courses on Computer
Mathematics. Vestnik TulGU. Seriya. Sovremennyie obrazovatelnyie tehnologii v
prepodavanii estestvenno-nauchnih distsiplin, 12, 102--107 (2013)
13. Semenikhina, O., Drushlyak, M.: The Study of Specialized Mathematics Software
in the Context of the Development of the System of Math Teachers Preparation.
In: Proceedings of IX International Conference ITEA-2014, pp. 61--66, Interna-
tional Research and Training Center for Information Technologies and Systems,
Kyiv (2014)
14. Grabar, M., Krasnyanskaya, K.: The Application of Mathematical Statistics in
Educational Research. Nonparametric Methods. Pedagogika, Moscow (1977)
35
An Analysis of Video Lecture in MOOC
Jyoti Chauhan1, and Anita Goel2
1
Department of Computer Science ,University of Delhi, Delhi, India
jyotich2009@gmail.com
2
Department of Computer Science, Dyal Singh College, University of Delhi, Lodhi road, New
Delhi, India
goel.anita@gmail.com
Abstract. Video is a content delivery form used for delivering lecture content
in Massive Open Online Course (MOOC). While institutions plan to launch
MOOC on their own platform or adapt an existing one, there is a need to
specify the features required for video lecture in MOOC. In this paper, we
present a checklist of features for video lecture incorporated in MOOC from the
learner‟s perspective. The use case based approach has been followed for
identifying the features of video lecture in MOOC. The checklist helps during
requirement specification of video in MOOC as the provider select the desired
features from the checklist.
Keywords. Video Lecture, Video Analysis, MOOC, Online Education, Feature
Checklist
KeyTerms. ICT Component, Characteristic, Academia, Environment,
Management
1 Introduction
Online learning uses technology and electronic media for delivering and receiving
courses. It is considered as most promising development in education that provides
education with technology. With technology globalization, the concept and
methodology of learning, and teaching has undergone a change. The technology usage
in education provides global learning environment that allows accessing the course
material anytime, anywhere, connect other students, and get access to the content
without considering any geographical boundary. The significant changes in technology
usage in online education has seen emergence of MOOC in 2008. It is a popular way to
offer online courses globally by the universities and education providers.
MOOC uses web-based tools and environments to deliver education [1]. It
provides online courses aimed at unlimited participation and open access via the web
[2]. It is being used across the globe for offering online courses. Some of the popular
MOOC providers are - Coursera1, edX2 and Udacity3 in United States, FutureLearn4 in
1
https://www.coursera.org
2 https://www.edx.org/
3 www.udacity.com
4 www.futurelearn.com
36
United Kingdom, iversity5 in Germany, FUN6 in France and MiríadaX7 in Spain [3].
The course lectures in MOOC are delivered in different formats, like, text books,
lecture slides, academic papers, tutorial notes, video lectures, blog posts, article links,
quizzes and assignments.
In MOOC, video is a primary delivery mechanism to publish the recorded lecture
content. It consists of audio (voice of instructor), visual (video of lecture) and text
(caption/transcript/subtitles) in one package. The study of edX [4, 5] analyzed that
students spend most of their time on video lectures. With the increasing popularity of
the video lecture, MOOC providers are continuously improving video lecture content
delivery as well as its production.
A video lecture in MOOC is a combination of several elements like, lecture by the
teacher, quiz, and lecture slides. For viewing the video lecture, MOOC provides an
interface to the student. The video interface has several controls, using which the
student can perform settings for the view of the video lecture. The content in video
lecture is delivered in different types and formats. The accessing of the content is
possible with video lecture options.
For offering MOOC, interested institutions have an option to go for self-hosted
platforms or use proprietary platform. When using self-hosted platform, the providers
have a choice to 1) develop their own MOOC platform, or 2) use open source platform.
Generally, the open source platform is a preferred choice, which may require
modification and customization as per the user needs. When developing a new MOOC
platform, there is a need to specify the features that has to be provided to the video
lectures presented here. Although video lecture are being delivered by MOOC
providers, there is no mention of its feature specifications.
In this paper, we focus on creation of the requirement checklist for the video in
MOOC. It helps during the development, in selecting and specifying the requirements
for video lecture to be included in MOOC.
Here, we present the feature requirement of video lecture that facilitates selecting
requirements for functionalities of video in MOOC. The functionality of MOOC video
is classified in two components, namely, 1) Video Interface, and 2) Video Lecture
Content. It aids the MOOC platform developer during requirement specification phase.
The features required for MOOC video can be selected from checklist.
For formulating the feature checklist of video lecture in MOOC, a study of MOOC
platforms was conducted. We chose popular MOOC providers that provide different
functionalities for delivered video lecture. We studied Coursera, edX, and Udacity.
“Coursera is by far the largest MOOC provider” [6] reported by Class Central. The
most popular MOOC providers as reports by [7] [8] [9] are Coursera, edX, and
Udacity. Since these are using different platforms, covers diversity in terms of
functionalities provided and mechanism used to deliver video content, our analysis can
be applied to any video lecture in a MOOC.
The video feature requirement presented has been used to a few open source
platforms to identify the functionality provided by them. The checklist of feature has
been applied for the functionality visible to student.
In this paper, Section 2 is a survey of related work. Section 3 provides an overview
of the video lectures in MOOC. Section 4 explains the methodology used for our study.
Section 5 discusses the controls of video interface. Section 6 explains the video lecture
5 https://iversity.org/
6 https://www.france-universite-numerique-mooc.fr/
7 https://www.miriadax.net/
37
content. Section 7 describes the analysis of video lecture feature in detail. Section 8
illustrates some examples on which our analyzed features have been applied. Section 9
lists the benefits. Section 10 enumerates the limitation. Section 11 states the
conclusion.
2 Related Work
For video in MOOC, much work has been done related to understanding student
behavior. In [4] [10] [11] [12] [13], student behavior is studied in quantitative way.
The analysis using edX [4] and Coursera course [10] focus on student engagement
using action time of students. Student engagement studies using different methods, for
example, using clickstream metrics [11], navigation study [12] and use of framework
[13]. The qualitative findings of clickstream are combined with cognitive science [11]
and student’s goals [10]. These studies have not focused on video lecture particularly.
Some authors [14] [15] [16] focuses on different aspects of videos, like, the video
interface, its features and properties. Guo et al. [14] studies the student behavioral on
edX platform using different properties of videos like, length, speaking rate, video
type, and production type. Guidelines for the video lecture are presented by
Chorianopoulos et al. [15] with the focus on video style, editing, sharing, controlling
and analytics. In [16] Kim et al. define design implication guidelines for video
interfaces based on the student engagement, like, providing shorter videos and
navigation links.
Ortega et al. [17] perform a study based on different ECO MOOC platforms
OpenMOOC, Open EdX, iMOOC etc. and external MOOC platforms - Coursera,
Udacity, MiriadaX, OpenCourseWare-MIT, Futurelearn, and iversity. Their focus is to
study “accessibility” of MOOC platform including the video lecture. The
recommendations are about subtitles (vocal or non-vocal sounds), secondary screen
integration, downloadable text, possibility of text reader processing, interface
navigation by keyboard. However, this study is based on the published literature only
and does not cover the different aspects of video lecture.
3 Video Lectures in MOOC
Video lectures are the pre-recorded learning material that acts as a medium of
communication between the student and lecture. In MOOC, the video lectures are
primarily used to deliver lecture content. MOOC video lectures are considered as
central to the student learning experience [14]. The courses are structured as list of
video lectures consisting of activities and contents, like, walkthroughs, assessment
problems, quizzes etc. Students need to watch the video lectures of the courses for
learning. Video provides self-regulated and independent learning. It has transformed
the traditional classrooms by replacing “one-size-fits-all” approach with self-paced
learning, and from curriculum/teacher centric to student centric learning.
Video in MOOC provides an interface to the students for managing the delivered
lecture. The interface provides different kinds of controls to the students. These
controls help to, navigate and view the content by play, pause, stop, increase/decrease
speed, volume and toggling to full screen mode etc. It also allows the student to
38
download the video in different formats and view it offline. The video lectures may
also be made available to students who are not enrolled in the course, via YouTube8
and other video sharing websites.
The video lecture content is the lecture delivered by the teacher which may contain
caption and in-video activity like, quiz. The lecture material provided with a video
lecture may be presentation slides, transcript of video, related document etc. The
lecture material is provided in different formats. According to Clark and Mayer [18],
the transcript helps in understanding the complex domain-specific video lecture
content. Sometimes the text content of video is presented in different languages.
Different MOOC providers use different types of video presentation styles, lecture
material, video interfaces and activities for the video lecture.
4 Methodology
MOOC providers use diverse mechanisms to deliver their video lecture. Videos are
different in terms of the available features, delivered content and formats and interface
used to display the lecture video. The features not only vary with the provider but even
with change in MOOC with the same provider. We gathered the information about
video by viewing the video lectures by different MOOC providers.
For our study, we selected three most popular MOOC providers - Coursera, edX
and Udacity. For our sample data set, we identified courses provided by various
universities in different areas, for diversity. The courses provided by universities, like,
Stanford, Duke and Harvard; in subjects like, medical chemistry, biology and
computer science, were selected. We watched more than two thousand videos across
the three different providers and manually analyzed them. Our sample set includes
videos of short and long duration, interactive and non-interactive with different
presentation styles. Table 1 shows MOOC providers, courses offered, university
offering the course and number of videos viewed, from the selected sample.
Our experience and observation while watching the video lecture act as the baseline
for the extraction of features and their segregation into different categories.
The long duration videos are time consuming to watch. So it is required to skip
some portions of video but not to miss any important feature. For this reason, the frame
of the video must be seen at any instant of time to check the relevance of that frame.
This kind of provision is provided by the feature named as Poster Frame. But it is not
provided by all platforms. As a result, the video need to be watched either by simply
play or by fast forwarding the video using speed +. During playing a video lecture in
edX, it showed an error once. Since edX provides help support we reported the
problem and got it resolved. The reason behind this kind of problem is, at times the
video player is not supported by the all browser. Therefore, we may need to change the
player which is possible using change player feature as provided by Coursera. The
language barrier is also a problem noticed in a few courses. According to nationality of
different instructors, accent and vocalization of the lecture instruction varies. So the
availability of caption on the video interface panel is very helpful for better
understanding of the content. Also, the caption provides multilingual support.
8 www.youtube.com
39
Table 1. Video selection for our study.
MOOC Video
Course University
Providers Watched
Compilers Stanford University 96
Machine Learning Stanford University 113
Coursera Introduction to Mathematical Thinking Stanford University 76
Child Nutrition and Cooking 2.0 Stanford University 46
Medical Neuroscience Duke University 199
Cryptography I Stanford University 66
Introduction to Computer science Harvard University 200
United States Health Policy Harvard University 119
edX Data Analysis For Genomics Harvard University 141
The Chemistry of Life KyotoUx 120
Biomedical Imaging Udx 51
Artificial Intelligence In Robotics Georgia Tech 208
Exploratory Data Analysis Facebook 180
Udacity
Intro to Computer Science Univ. of Virginia 312
Mobile Web Development Google 176
The availability of downloading feature which is provided for offline learning support
makes it possible to watch the lecture without dependency on the network connection.
Accessibility of different quality of the video lecture and High Definition (HD)
support allowed us to watch the video on larger screen with better quality. After
watching the video, attempting the quiz and assignment of the course, the student may
require to track the progress, like, how many quizzes are there in a lecture, how many
them have not been visited yet. But for doing so, the student needs to go back to the
lecture and check each lecture separately. The options available are also not easily
navigable. Currently the progress bar feature is not being provided even by several
popular providers like, Coursera. One of the new features noticed in this analysis
process is embedded quiz. It allows attempting the quiz while watching the video
lecture and interacts with the video interface. It helps to check grasping of the learner
from the watched video lecture. This experience helped to identify and categorize the
features that were analyzed during the video watching sessions.
We analyzed video lecture by the sample data set from perspective of student. It
helps to categorize the video lecture into different component and to segregate the
features provided by them.
5 Video Interface
MOOC provides video interface to the student for viewing the lecture videos. The
interface has several controls that allow students to make settings for the display of the
video lecture. We categorize the controls on the video interface into four categories –
(1) Display time, (2) View setting, (3) Advance setting, and (4) Help support.
40
1) Display time shows the current time during video watching and total duration
of the video.
2) View setting is related to playing the video, like, play/pause, change volume or
speed of video. By default, the video is displayed in normal mode which can
be toggle to full screen mode. View settings allow the student to control the
setting for play ( ), pause ( ), speed (+/-), volume (+/-), full screen mode
( ), navigate to previous/next videos ( , ) etc. It also allows setting for
rewind and replay ( ) video.
3) Advance setting include are additional controls provided on the video
interface. It allows the student to switch to HD mode to watch video lecture
with better quality. The poster frames of the video on time bar seen at any time
without playing it are part of advance setting. The settings also provide
multiple video player facility which allows changing the player. The video text
is provided in different languages that can be chosen from the caption option.
The format of the caption can also be changed like, font and background color,
opacity of window. The controls for advance setting may or may not be
provided in all video interfaces.
4) Help Support allows reporting of problem faced during the watching of video
lecture. Discussion forums are provided for problem reporting. Help for
shortcut keys allow interface navigation using the keyboard.
Fig. 1. Video interface controls for video lecture in Udacity.
Different MOOC providers provide different kinds of controls on their video
interface. Display setting and view settings are among the common controls provided
on video interface. Fig. 1 shows different controls available in the video interface of a
video lecture in Udacity - progress bar, caption text, play/pause, volume slider, current
time/total time of video, full screen mode, add to watch later, watch on YouTube,
caption on/off and language selection, and setting for selecting speed, video quality,
and subtitle options.
41
6 Video Lecture Content
The video lecture content is the lecture delivered by the teacher which may contain
caption and in-video activity like, quiz. The support material provided with a video
lecture may be presentation slides, transcript of video, related document etc. The
support material of the lecture is provided in different formats. The transcript helps in
understanding as it provides text of the instruction given by video lecture instructor.
Sometimes the text content of video is presented in different languages. Different
MOOC providers use different types of video presentation styles, support material,
video interfaces and activities for the video lecture.
The lecture content of the video has some activities embedded in it for better
explanation and interaction with the students. The video lectures also have
accompanying material that helps in better understanding of the lecture. We categorize
the content of video lecture into two parts- 1) Lecture Material and 2) Embedded Quiz.
1) Lecture Material- The video lecture content is provided in the form of slides,
video of the lecture, transcript of the video etc. The content is available in
different formats, for example, mp3/mp4, ppt and pdf. The lecture material can
be downloaded to support offline learning which may also be available in
different qualities.
2) Embedded Quiz is the in-video activity that is incorporated to make video
lecture session more interactive. Students can attempt the quiz while watching
the video lecture. The quiz has several options and parameters, like, question
type that may be Multiple Choice Question (MCQ), true-false or descriptive.
Different types of video lecture content are delivered by the MOOC providers
which have diverse features and controls.
7 Video Lecture Feature Checklist
The features provided by each MOOC platform vary. Therefore to understand the
features of the video lecture in MOOC, the analysis has been performed on video
lecture of three popular MOOC providers - Coursera, edX and Udacity. In our study
the main focus is to identify the features of the video lecture in MOOC. The video
lecture in MOOC consists of two components - Video interface and Video Lecture
Content. We arrive at the detailed feature checklist by identifying the features provided
by each component of video lecture. We analyzed the features for video lecture
components including their presentation style.
Video Interface provides controls to the student for viewing the video lecture in
MOOC. The features provided by video interface are mainly controls that provide
control of the interface to a student. A video lecture also provided different types of
content to their student. Video lecture content provided several options for accessing
the lecture material. The categorization of video interface and video lecture content
helps to segregate the provided controls, features and presentation style, from student’s
perspective.
42
For arriving at the feature checklist, the features provided by the component and
control identified in previous sections are applied on the chosen MOOC providers of
our study. From our analysis we find some of the features are provided by each of the
MOOC providers, like, current/total time, play/pause, and video mp4 format support. It
suggest that these are the basic features need to be made available for student. The
inclusion of some feature provides better functioning but does not affect the basic
functioning of the video lecture. For example, availability of HD support, multiple
languages for caption, availability of different quality video named as optional or
advance features etc. These are named as optional or advanced features.
The different levels of availability of feature or control from student’s perspective,
are classified into three catagories-
Basic – are the most important features that are available in all platforms. It is
denoted by weight „3‟.
Optional – are the features that are not necessary but may be helpful. The
feature supported by any of the two platforms is an optional feature. It is
denoted by weight „2‟.
Advanced – are the features that are required for specific purpose. Feature
available only by single platform is an advanced feature. It is denoted by
weight „1‟.
On the basis of availibility of a feature, weights are assighned to each identified
feature. The weighted feature checklist of features helps to select the features and
options that need to be made available to a student in video lecture of MOOC. Table 2
lists the weighted feature checklist of video lecture in MOOC. Each feature is
presented in different way by the MOOC providers.
The Video Interface and its options are provided in diverse styles. It is displayed
either as a separate pop-up window or incorporated in the lecture page. Each provider
use different presentation style for viewing controls, like, video speed is displayed in
terms of range of pixels from .50x to 2.0x. Navigation of the video lecture is control
using previous/next control, selecting from the video lecture list or from the progress
bar that displays the video lectures. An advance setting control, to change format of the
caption allow changing font (family, color, size), background (color, opacity), window
(color, opacity), character (edge, style) and text opacity. Help support controls are
provided as help, discussion forum, mail etc.
Video lecture Content is presented in different presentation styles. The activities are
displayed in the progress bar. For example, color variation is used to differentiate, in-
video activity inclusion, visited, playing video etc. Embedded quiz in the video are
incorporated at different places either in between or at the end of video. Quiz further
has various parameters that need to be considered. The quizzes differ in types, options
available, question types etc. For example, quiz may be graded or non-graded; different
controls in quiz; type of questions in quiz - MCQ, descriptive and true/false; correct
answer response for the attempted question, and many more. The presentation style of
the video interface and video lecture content are summarized in Table 3.
43
Table 2. The weighted feature checklist of video lecture of some MOOC providers.
Coursera
Feature Control
Udacity
Weight
edX
Display Cuirrent Time 3
Time Total time 3
Play/Pause 3
Volume Slider 3
View Full screem mode 3
Setting Modify Speed 3
Caption On/Off 3
Video Navigation 3
Interface HD support X 2
Poster Frame X X 1
Advance Change video player X X 1
Setting
Caption multilingual support X 2
Change Caption format X X 1
Report problem 3
Help
Support Go to Discussion Forum 3
Keyboard Shortcut Help X X 1
Download Transcript Srt 3
Pdf X X 1
Text X 2
Lecture Slides Ppt X X 1
Material pdf X 2
Video (mp3/mp4) 3
Video quality X 2
Progress bar X X 1
Video Availability X 1
Lecture Grading 2
Content Control Submit 2
Skip X 1
Continue 2
Embedded
Quiz Re-watch Instr. X 1
Type MCQ X 1
Descriptive X 1
Display Response 2
Allowed attempts >1 X 1
Show Quiz presence X 1
44
Table 3. Presentation style of video lecture of some MOOC providers.
Feature Option Coursera edX Udacity
Speed .75x-2.0x .50x-2.0x .25x-2.0x
View
Navigation Prev./Next List Prev./Next,
Setting
Prog. Bar
Player Option Flash,
Html5
Advance Caption Lang. 9 1 More than 60
Video
Setting (#)
Interface
Caption Format Font, Window,
Background
Report problem Help Discussion Discussion
Help Forum Forum
Support Discussion Video Lecture Lecture page
Link on Interface Page
Lecture Progress Progress Bar
Material
Display Cor./Incor No
Video Response
Lecture Correct Answer Attempt> In Transcript
Content max
Quiz Attempt 3 1
Allowed
Show Quiz Color No
presence
Location Anywhere At end
8 Case Study
The features of the MOOC video has been applied to three open source MOOC
platforms. Sakai9, Open edX10, CourseBuilder11 are MOOC platforms of Sakai
foundation, edX and Google respectively, whose video interface have been chosen for
our study. Study is focused on the two components of video lecture named, Video
Interface and Video Lecture Content, and features provided to a MOOC student.
Sakai is an educational software platform developed for higher education by
University of Michigan. Since its release in 2005, being used by more than 350 world’s
great colleges and universities organizations of diverse profiles list; over 4 million
students worldwide [19]. It uses video lecture mechanism to offer lecture content.
Open edX is an open source release of edX platform in 2013. It is founded by
Harvard university and Massachusetts Institute of Technology (MIT) [20]. Universities
and educational providers are using it freely to offer their own MOOCs. Many
9 https://sakaiproject.org
10 http://code.edx.org/
11 https://code.google.com/p/course-builder/
45
websites and MOOCs are launched on Open edX, listed at [21]. For our study we
analyzed the Stanford OpenEdX [22] which is running on Open edX platform.
CourseBuilder is a software used to offer online courses. It provides an opportunity
to universities and educational to offer their own MOOCs. It runs on google
infrastructure[23] and is used world wide for offering MOOCs. We studied University
of Auckland, New Zealand [24] that is running on CourseBuilder platform. Evaluation
has been performed by student and guest account on their demo site.
Table 4. The feature checklist of video lecture for open source MOOC platforms.
Univ. of Auckland
Stanford OpenEdX
CourseBuilder
Feature
Control
Level
Sakai
Cuirrent Time
Total time X
Play/Pause
Volume Slider
Basic Full screem mode
Modify Speed X X
Caption On/Off X
Video Navigation X X
Interface Report problem
Go to Discussion Forum
HD support X X
Advance
Caption multilingual support X X
Poster Frame X X
Change video player X X X
Optional
Change Caption format X
Keyboard Shortcut Help X X X
Download Transcript Srt X X
Basic
Video mp3/mp4
Progress bar X X X
Download Transcript Text X
Advance Slides Pdf X
Video Quality X X X
Video Download Transcript pdf X X
Lecture Slides ppt X
Content Progress bar X X X
Embedded L Grading
Optional Quiz 2 Controls X
Display reponse
L Allowed attempts >1 X
1 Show Quiz presence X
46
Table 5. The presentation style of Video lecture in some open source MOOC platforms.
Univ. of
Stanford
Feature Control Sakai Auckland
OpenEdX
CourseBuilder
View Speed .50x-2.0x
Setting Navigation Prev./Next Using List
Player option
Advance
Video Caption Lang. (#) 1 1
Setting
Interface Caption Format
Report problem Mail Problem Mailing list
Help
Support Discussion Link Discussio Lecture
Mailing list
on n Forum page
Lecture Progress
Display Response Cort./Incor
Correct Answer Instant/End
Video
Attempts
Lecture 1
Quiz Allowed
Content
Show Quiz
No
presence
Location Anywhere
Our weighted feature checklist is applied to video lecture components for different
levels features provided by some open source MOOC platforms. In our case study, we
applied our analysis for Video Interface and Video Lecture Content, and their
presentation style on three MOOC platforms.
Table 4 and 5 displays a comparative feature checklist for each video lecture
component and their presentation styles.
Some of the key findings are discussed here. Display time, one of the very common
options is not provided by Sakai. Caption is also not present in Sakai. Stanford
OpenEdx and University of Auckland CourseBuilder provide advance settings to better
control of the video lecture interface while Sakai do not provide this facility. All
platforms allow help support control for reporting the problem but in different ways.
Downloading of the downloadable transcript is available only in Stanford OpenEdX
but limited to text format; While University of Auckland CourseBuilder allows only
viewing the transcript. Different quality of the video and progress bar is not supported
by any provider studied. CourseBuilder is the only one providing embedded quiz.
Table 6 shows University of Auckland CourseBuilder provide most of the features
for MOOC videos to their students for video interface as well as content. Also, the
presentation style used for video lecture content that is very limited for platforms other
than the University of Auckland CourseBuilder. Table 6 and Table 7 list the percentage
of features supported and their level respectively, by the open source platforms
mentioned in our study..
Fig. 2 displays coverage of Video Interface and Video Lecture Content components
of video lecture in MOOC in our case study. Some of the key findings are as follows:
The maximum controls are provided by CourseBuilder.
All view setting options are available in Open edX.
Advance settings are not present in Sakai.
47
Each MOOC provider uses a similar number of controls for help support.
Embedded quiz are only present in CourseBuilder video lecture.
Fig. 3 shows the provided features by some the providers in different levels. Some
of the key observations about these are:
The maximum basic features are provided by Stanford OpenEdX.
Stanford OpenEdX is the only one that provided advance features or video
interface.
Optional features for video interface are not available in Sakai.
The basic and advance features of video lecture content are equally supported
by all the platforms, in our case study.
The number of optional features available in University of Auckland
CourseBuilder is double, in comparison to the other providers in our study.
Table 6. Percentage of features supported by some open source MOOC platforms.
Stanford Univ. of Auckland
Component Controls Sakai
OpenEdX CourseBuilder
Display Time 50% 100% 100%
View Setting 50% 100% 66%
Video Interface
Advanced Setting 0% 40% 20%
Help Support 66% 66% 66%
Video Lecture Lecture 38% 25% 37%
Content Embedded Quiz 0% 0% 50%
Table 7. Percentage of feature level by some open source MOOC platforms.
Stanford Univ. of Auckland
Component Level of Feature Sakai
OpenEdX CourseBuilder
Basic 60% 100% 80%
Video Interface Advance 0% 50% 0%
Optional 0% 25% 25%
Basic 50% 50% 50%
Video Lecture
Content Advance 33% 33% 33%
Optional 12% 12% 24%
48
Fig. 2. Graph showing percentage features used by some open source MOOC platforms.
Fig. 3. Graph showing percentage of feature level used by some open source MOOC platforms.
9 Benefits
The features we presented provide aid for including videos in MOOC. For deriving our
list, most popular MOOC platforms has been studied. Our list of features benefits the
developers of MOOC for incorporating lecture video in their platform. We see that
neither of the platforms provides all the features of video to their students.
Mostly, ad-hoc approach is used for providing video lecture to their students. Either
the existing open source platforms are used which have their own mechanism for video
lecture that needs to be extended sometimes or developing a new platform that needs
identification of features that need to incorporated in video lecture. In both the cases,
there is high probability of generating basic requirements of features. Developer of
MOOC may not be able to elicit the options for video lecture.
49
The feature checklist presented here can be used by MOOC developers. It lists the
features available in MOOC videos that need to be available for the student. During the
feature elicitation, the developer can use the checklist to choose the desired options,
with less effort. It facilitates the developer to include more options for videos. The
video lecture mechanism developed using our checklist provides more interactivity to
the interface and make it student oriented.
10 Limitations
For our analysis, we studied the most popular MOOC platforms. There may be some
options that are provided by other MOOC providers that have not been studied.
However the new options can be easily included in the checklist. Also the derived
analysis is for video in MOOC. It is insufficient for standalone video interface creation.
It may require some for options and features for standalone video interfaces, which are
out of scope of this paper.
11 Conclusion
In this paper, we present a weighted checklist of features for the videos in MOOC. The
checklist covers the features including different presentation styles of components of
video lecture that are video interface and video lecture content. The requirement
checklist is useful during incorporating videos features in MOOC. It eases the task of
requirement specification for video software in MOOC by selecting and choosing the
desired requirements of features from the checklist. The checklist presented here is
extensible in nature and can be updated easily to add any new feature and option.
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51
Using Fuzzy Logic in Knowledge Tests
Aleksandr Alekseev 1, *, Marika Aleksieieva 2, Kateryna Lozova 1, Tetiana Nahorna 1
1 Sumy State University, Faculty of Technical Systems and Energy Efficient Technologies,
Sumy, Ukraine
2
Harvard University, Graduate School of Arts and Sciences,
Cambridge, Massachusetts, USA
alekseev_an@ukr.net, maleksieieva@fas.harvard.edu,
katarina_lozovaya@ex.ua, nagorna-t@mail.ru
Abstract. An article describes the specialties of nonlinear scale formation of
coincidence of standard answer with student’s answer, basing on application of
fuzzy logic during the test control of knowledge. It is given the detailed exposi-
tion of the mathematical apparatus that is used for substantiation the decision-
making on the formation of the coincidence scale of answers. The author notes
that using of the coincidence scale of answers gives the student an opportunity
to express doubt and specify any degree of true answer ranging from “False” to
“True”. In this case test results are measured in the opposite terms from clear to
fuzzy logic when the final mark is determined by the match of the answers. For
example, if reference answer is equal to student’s one it means that he/she
knows the materials, and vice versa if the reference answer does not match, stu-
dent does not know the topic. There are some types of the test tasks in the test-
ing with using the coincidence scale of answers. The article describes the pecu-
liarities off the parameter assignment of strictness the fuzzy-logic system. The
results of experimental verification of the proposed innovations’ effectiveness
are given. These results allow stating the improvement of the measurement ca-
pabilities off the test with using the coincidence scale of answers basing on ap-
plication of fuzzy logical calculations.
Keywords: Pedagogical measures, Knowledge test control, Measuring scale,
Fuzzy logic, Strictness parameter, Test questions.
Key Terms: ICT Tool, Quality Assurance Process, Teaching Methodology,
Teaching Process, Technology
1 Introduction
Fast and accurate evaluation of knowledge formation remains is a relevant task for
long-existing forms of learning. Moreover, it has become an increasingly important
for the recently emerged distance learning or blended learning (partial implementation
* Professor of Department of Manufacturing Engineering, Machines and Tools, Doctor of
Pedagogy., Associate Professor
52
of distance learning technologies into classes that are conducted traditionally). The
most important characteristics of the different forms of learning remains objective
monitoring of students' academic achievements and construction of effective teaching
methods based on it.
Further development of the theory and practice of the test control gives significant
prospects for achievement of such goals. Using the information and telecommunica-
tion technologies, the test control successfully completes and improves existing tradi-
tional forms and methods of knowledge control. Computerized testing carries out a
number of pedagogical functions assigned to knowledge test control, and becomes an
effective means of summarizing the results of learning at all stages of education, from
an entrance test to a comprehensive final exam.
2 Preconditions for using the fuzzy logic in the scaling of
students' answers
Educational measurement technologies are developing in the close cooperation with
the achievements of pedagogy, psychology, sociology and other empirical sciences,
which are characterized by using the quantitative and quality indicators, differ by
levels of manifestation of properties that are not measured directly. Due to this, there
is no exception in the development of scaling tools applied to interpret the student’s
responses in higher education institutions with a computerized test control of
knowledge.
The problem connected to the need in making available for the respondents in-
volved in the questionnaire, or student who participates in the test control of
knowledge, scale transfer of their judgments about the object of evaluation in the
quantitative description of the level of assessed property has been known for a long
time. Currently, there are several solutions proposed by different authors.
One of the first solutions was proposed by L. Thurstone [9]. The procedure of con-
structing the L. Thurstone scale is to provide an opinion about the level of assessed
property in the frame of a set of evenly distributed judgments. Text description of
each judgment is assigned a value of the level bar graph properties which corresponds
to an interval scale. The scale constructed in such way is an interval one and its usage
gives the possibility to apply a sufficiently wide range of statistical methods of pro-
cessing the measurements results. However, a large amount of preparatory work relat-
ed to the construction of the interval scale, relative equality of intervals, limit the
possibilities of its application for the evaluation of students' knowledge.
The scale, developed by R. Likert [5], suggests the existence of the alternative
judgments that reflect extreme levels of the assessed properties. These judgments can
be formulated as "strongly agree" through "uncertainty" to "strongly disagree" for the
test control. In addition, R. Likert scale bar graph set intermediate values associated
with the specific levels of the assessed properties. In the text description no more than
three of these intermediate values are commonly used, for example, "Somewhat
agree", "neither yes nor no," "Somewhat agree".
53
The R. Likert scale is an ordinal scale, and despite the fact that, usually, its con-
struction does not require the time-consuming preliminary work in the practice of
educational measurement finds limited application. This is due to the fact that within
the ordinal scales we can only arrange objects in ascending or descending order esti-
mates of measurable properties at the lowest possible statistical treatment of the re-
sults of evaluations. Besides, the accuracy of pedagogical measurements with the use
of scales that were developed due to approaches of R. Likert including numerical
grading based scales limited by number of intermediate values, the number of which
usually does not exceed 10-15.
Despite significant progress, reached for the last years in the different field of
knowledge in the developing sphere, systematization and the field of analysis the
results of practical application the methods of scaling the properties of qualitative and
quantitative indicators, we have to realize that new approaches have limited applica-
tion for the interpretation the student’s responses on the knowledge test control.
To improve the accuracy of the pedagogical measurement, including the empow-
erment of statistical processing of the measurement results, it is necessary, in our
view, to use such benefits in scaling the student responses using the ratio scale (name,
by the definition of S.S. Stevens [8]). The mathematical apparatus of fuzzy logic will
help to do things mentioned above.
3 Basic Provisions
During a traditionally organized examination the roles of a teacher and a student are
allocated in accordance with the objectives of the oral control, when the teacher asks
questions in order to identify student’s generated knowledge. The student compre-
hends the questions and gives the answers, based on his/her idea of correctness of an
answer. Then the teacher makes a judgment based on the results of such statements
about the success of student’s answers to particular questions, also evaluates the
knowledge of all studied materials considering the total number of answers. Herewith,
evaluating student’s knowledge the teacher generally takes into consideration not only
the formal correctness of the answers, but also how they were given, and whether the
student was sure about the answers vs. showed a sign of insecurity, which may indi-
cate instable knowledge. At the same time the student may use interpersonal contacts
and consciously or unconsciously formulate the answer in such a way that it would let
the teacher trace the causes of the seemingly unsuccessful answer. The doubt ex-
pressed in the answer provides an experienced teacher with another information chan-
nel that allows proper evaluating of the actual level of student’s knowledge.
During classically organized test control, unlike oral examination, alienation of
teacher’s individuality occurs. Due to this fact, it is impossible to apply diagnostic
capabilities of the teacher during the control process in order to identify the actual
knowledge of the students.
Test control usually requires performing a task by selecting one of the possible an-
swers or giving an unequivocal answer formulated from a limited set of words, letters,
numbers, or graphics. In any case, the student should use his/her own experience and
54
make such an answer, which would contain the conclusion of true judgment in terms
of strict logic. However, it is not possible to express doubt or indicate how the answer
may differ from the correct one.
Checking results of the written test control the teacher has only a report of a stu-
dent containing no data about possible difficulties in formulating the response. There-
fore, the final evaluation cannot indicate whether the student was sure in the answer,
or just speculated it relying only on luck. Computerized test control is more formal
and matches the reference answers with the student’s ones.
Concerning that, the developed test control simulation model [1] proposes to per-
form computerized control of knowledge by using of an expert system (Fig. 1) based
on fuzzy logic [4]. Application of this system gives to a student the opportunity to
operate not only the classical values of logical variables like “false” and “true”, but
also to use their intermediate values fading from one extreme value (“false”) to an
opposite one (“true”).
Fig. 1. Fuzzy logic expert system
The expert system uses piecewise continuous membership functions in order to define
how evaluation of student’s knowledge and his/her expressed statement relate to
fuzzy logic subsets. These functions have transitional areas presented as segments a-b
and b-c, connecting zero and one (maximum) levels of reliability (Fig. 2).
55
Fig. 2. Membership functions for subsets of student’s statements (a) and evaluation of academ-
ic achievements (b)
A membership function for each term of the base term set of a logical variable “Level
of matching answers” ((x)) is shown in Fig. 2,a. According to the mentioned above
chart, all possible values of the function (x) are characterized as low, moderate or
high level of matching answers depending on how the student’s answer is close to the
reference one. At the same time, mismatch of the answers can be caused not only by
the incomplete knowledge, but also by insufficient confidence in knowledge, exces-
sive emotions, or any other reasons preventing the student from making an unequivo-
cal judgment about trueness of his/her conclusions.
Similar situation is with a membership function of a logical variable “Evaluation of
student’s knowledge” ((y)), where the terms of a base term set are characterized by
three gradations –“poor”, “average” and “full” (Fig. 2,b) – depending on how the
evaluation of the answer is close to one of evaluation scale criteria.
The presence of unrelated fuzzy logic sets allows to make such relevant fuzzy
statements as “if ... then...”. For example, clear logic accepts only two extreme state-
ments: “if student’s answer does not match the reference answer, then student’s
knowledge is unsatisfactory” and “if student’s answer matches the reference answer,
then the student has necessary knowledge”. Fuzzy logic accepts both these extreme
values, as well as any other intermediate statement linking the certain degree of an-
swer accuracy and the corresponding answer evaluation.
The matching of subset items of the postulating and stating parts of a statement
may apply a control function that is based on either “correlation –product encoding”
method or “correlation – min encoding” method [4]. Currently there are no evidences
confirming the preference of using one of these methods in computerized control of
knowledge. However, “correlation – product encoding” method is used in the simula-
tion model due to a number of reasons.
Sum combination method is used for getting a generalized logical statement.
Herewith, superposition of membership functions of fuzzy sets is defined as
Θsum Z =Θi Z ∀Z, iϵ[1,3] (1)
56
Transformation of a fuzzy set into a single decision taken on the basis of fuzzy logic
statements requires using the gravity center of the fuzzy set membership function –
centroid defuzzification method.
4 Strictness Parameter
The application of fuzzy logic relieves the student from necessity to speculate if
he/she is not sure in the answer. Clearly indicating the degree of trueness in the an-
swer, the student thereby provides the data giving possibility of mathematically dif-
ferentiation of his/her academic achievements with high accuracy, and to perform
unambiguous evaluation.
Mathematical application of fuzzy logic to the test control can also enter a “strict-
ness” parameter. At the oral examination the teacher can somehow “forgive” a con-
troversial answer deviating from his/her idea of trueness. But a stricter teacher will
punish this controversial answer by a worse grade. Similarly to a traditional examina-
tions conducted by teachers with different ideas of perfect knowledge of materials, the
tests based on fuzzy logic may also be evaluated in different ways.
Fig. 3 shows an example of control which lets the student to give answers in rela-
tively simple way in terms of fuzzy logic, if it is added to the test software interface.
Indicating the degree of student’s answer deviation from the reference one requires
moving a slider to any position between the leftmost (“False”) and the rightmost
(“True), and clicking “OK”. The slider location is determined and converted into
relative coordinates, which are used for further calculations in a fuzzy logic expert
system.
Fig. 3. Control of a fuzzy logic system
Rating answers and number of points accrued will depend on how the student indicat-
ed the degree of his/her answer matching the reference one. The number of points
accrued depends also on the “strictness” parameter, which is indicated by sections in
transition areas of membership functions –student’s answer matches / does not match
the reference answer, and the student learned / did not learn the controlled material.
Despite the fact that the coordinating of these segments have quantitative indication,
the level of strictness to student’s knowledge is measured qualitatively, in such terms
as “strict” (S), “stricter” (SS), “less strict” (LS), and “not strict” (NS), filling these
concepts with quantitative measurement each time. Thus, if there is a necessity to
compare the results of control, then introduction of the “strictness” parameter requires
specified adopted coordinate values for transition sections.
Fig. 4 shows the charts illustrating changes in application rate of control for enter-
ing answers when implementing different “strictness” strategies of the fuzzy logic
57
expert system. In the diagrams was considered such data – we applied the information
about the students who used the element of fuzzy-logic system in the computerized
tests.
Student’s answers do not match the reference ones
Student’s answers match the reference ones
NS LS SS S NS LS SS S NS LS SS S
| Strong | Average | Weak |
– bottom line – confidence interval
Fig. 4. Application rate of the control
The chart in Fig. 4 shows that in case of specified extreme level “Strict” the vast ma-
jority of students (over 98%), regardless of degree the preparedness (relatively strong,
average and weak students) and degree of their answers matching with the reference
ones, rarely use the opportunity to make a statement in terms of fuzzy logic. Absence
of effective incentives upon the almost confident answer, and extremely punishable
little doubt lead to the fact that students prefer to answer in terms of “False”-“True”."
Thus, the fuzzy logic expert system capacities are practically not used. Therefore, it is
not recommended to use a “strict” test system for practical purposes.
Other manifestations of “strictness” are popular enough to use fuzzy logic. It
should be noted that the level “Not strict” is often demanded by weak students, as in
case of student’s answers matching the reference answers (30,5%±3,4%), and to even
greater extent in case of answer mismatch (62,5%±4,1%). Therefore, this approach is
not recommended to be a priority in order to ensure that all students are in equal con-
ditions and none of them has any preference.
Table 1 shows the coordinates of the membership functions corresponding to the
level of “Stricter”. According to the chart in Fig. 4, it is often demanded and can be
recommended as the core level in the absence of any other preferences. This recom-
mendation can be confirmed by positive experience of use as the sole strictness pa-
rameter in the fuzzy logic system of test software SSUquestionnaire [7].
58
Table 1. Coordinates of membership function transition lines
Discussing the data shown in Fig. 4, it is necessary to underline that they do not di-
rectly recommend any of strictness degrees in the test system. So there may be differ-
ent approaches to setting the “strictness” parameter. However, it is necessary to men-
tion that regardless of the adopted approaches to setting the expert system strictness
level, it must be set up prior to the test control. Any changes in the conditions of con-
trol through adjusting the strictness parameter for specific students, groups of students
or disciplines are unacceptable. Like the oral examination, on the one hand there is
contradiction between the desire to set up individual approach to each student and
evaluate his/her achievements with the strictness degree that would enhance learning,
vs. on the other hand, the requirement of compliance with the general approach to all
students. Therefore, differentiating the “strictness” parameter in a fuzzy- logic test
system can be justified for some special cases, but the general approach requires this
parameter to be standardized, and academic achievement of any student should be
equally evaluated, regardless of any subjective or objective circumstances.
5 Types of Tests
Despite the considerable variety of standardized test questions ([3], etc.), fuzzy logic
expert system accepts only two types of tests.
The first type of tests covers the tasks containing the questions that can be an-
swered using the full range of logical variables from “False” to “True”. These are the
questions that require to confirm or deny any statement, such as “Fish live in a water”,
“2 +2 = 4” or “The sun shines at night”, “2 +2 = 5”, etc.
When performing the test of the first type a student can move the control slider of a
fuzzy logic expert system (Fig. 3) to any of the positions, which , in his/her opinion,
corresponds to the degree of answer trueness. If one of the extreme positions is select-
ed and student’s answer matches the reference answer, the highest possible score will
be awarded. If the selected extreme position of the slider does not match the reference
answer, there will be 0 points. Intermediate position of the slider will allow giving
intermediate (between zero and a maximum) number of points.
Another type of tasks includes the questions that can be answered within a half of
the range of logical variables from “Not true” (“Not false”) to “Truth”. These tasks
include questions along with two or more options of possible answers. At least one of
them is correct and at least one is wrong. For example, if the task has a question “2 +2
=?” along with three answer options “3”, “4” and “5”, and it is offered to determine
59
which one is correct, then examinee cannot select the wrong answer “3” or “5” stating
that it is false.
When performing such task, the control slider of the fuzzy logic expert system can
be moved within a range from the middle position “Not true” (or “False”) to the
rightmost position “True”. In this case, the maximum possible score will be given if
student’s answer matches the reference one and the rightmost slider position is select-
ed. In all other cases, the amount of points accrued will be determined by how stu-
dent’s answer matches the reference one (depending on the slider position).
Table 2 shows different scoring options for the two considered types of tests (max-
imum score for correctly completed task is 100 points).
Table 2. Points accrued for a completed task depending on student’s answer matching the
reference answer
Type of task Student’s answer matches the reference one
Type 1 False ¼ 1/2 ¾ True
Type 2 ½ 5/8 3/4 7/8 1
Not strict
Not strict
Not strict
Not strict
Not strict
Strict
Strict
Strict
Strict
Strict
Strictness pa-
rameter value
Answer eval-
0 0 1 30 3 70 6 90 100 100
uated, points
6 Measurement Capabilities
For the evaluation of the impact of a fuzzy logic expert system on the measurement
capabilities of test knowledge control was made an experimental research.
The experiment engaged 228 students divided between the experimental and con-
trol groups. The groups were formed on the basis of current students’ progress. Mann-
Whitney [6] checks showed that the groups are homogeneous.
The students in the experimental group were given a fully functional test program
SSUquestionnaire, also they had an opportunity to give fuzzy logical answers. Strict-
ness parameter of the fuzzy logic expert system was set up as “Stricter” and did not
change throughout the experiment.
The test program used in the control group differed from the fully functional one,
since its fuzzy logic module was disabled. The students could not move the control
slider of the fuzzy logic expert system to any intermediate position; they had been
forewarned as well.
Test results of the experimental and control groups were processed mathematically.
They helped to estimate the strength of links between successful execution of individ-
ual test items and the final estimates the students received for all of the test questions.
Pearson correlation coefficient [2] was calculated for the test results of each group
independently. It was believed that the closer the absolute value of Pearson correla-
60
tion coefficient is to one, the tighter are links and measurement capabilities of the
relevant test.
Comparison of the received data showed that the experimental group revealed
closer linear dependence between the results of individual tasks and the general test
results than the control group. Pearson correlation coefficient in the experimental
group increased from 0,52 to 0,65 compared to the control group, that indicates better
measurement properties of the test.
7 Conclusion
Elimination the identity of the person from the process of control enables using the
diagnostic capabilities of the examiner during the test. This disadvantage of test con-
trol can be mitigated by use of an expert system developed on the basis of mathemati-
cal fuzzy logic.
The advantage of the fuzzy logic expert system hides in the fact that its introduc-
tion into a test program provides students with the opportunity not only to give the
answers based on strict logic, but also to indicate any degree of answer trueness rang-
ing from “False” to “True”. A student does not have to give a definite answer, even if
he/she is required to go beyond the scope of their own knowledge. He/she can express
doubt indicating how an idea of the true answer matches or does not match the refer-
ence answer. In this case, the test results are not measured in terms of clear logic (if
the reference answer matches student’s answer, then the student knows the material,
and vice versa), but in terms of fuzzy logic, when the final evaluation is determined
by how these answers match.
The proposed justification of the decisions made by the examiner on the basis of
the fuzzy logic expert system mitigates disadvantages of computerized testing as a
tool for educational measurements, but does not eliminate these disadvantages entire-
ly. Further efforts in the improving the theory and methods of test control, including
methods directed on the fundraising the computer equipment for modeling diagnostic
functions of the teacher in the control process will enhance the reliability of results of
the evaluation of student’s knowledge.
References
1. Alexeyev, A. N., Alexeyeva, G. V.: A simulation model of the test control of knowledge
and skills. Computer-oriented educational system, Kyiv, NPU. M. Dragomanov, No 7
(14), 65 - 71. (in Ukrainian) (2009)
2. Glass, G. V., Stanley, J.C.: Statistical methods in education and psychology – Englewood
Cliffs, N.J., Prentice-Hall (1970)
3. IMS Global Learning Consortium. Accessible at http://www.imsglobal.org/question
4. Korneev V.V., Gareev A.F., Vasyutin S.V., Reich V.V.: Databases. Intelligent Processing
of Information. – Moscow: Knowledge (in Russian) (2000)
5. Likert R., Roslow S., Murphy G. A.: Simple and Reliable Method of Scoring the Thur-
stone Attitude Scales. Journal of Social Psychology, 1934. Vol. 5, 228 – 238 (1934)
61
6. Mann, H. B., Whitney, D. R.: On a test of whether one of two random variables is stochas-
tically larger than the other. Annals of Mathematical Statistics, 18, 50–60 (1947)
7. New Opportunities of Knowledge Testing using software SSUquestionnaire Version 4.10
Accessible at: http://test.sumdu.edu.ua (in Russian)
8. Stevens S. S.: Experimental Psychology. Moscow: Foreign Literature, Vol. 1 (in Russian)
(1960)
9. Thurstone L. L.: The Measurement of Social Attitudes. Journal of Abnormal and Social
Psychology, Vol. 26, 249 – 269 (1931)
62
Knowledge-Based Approach to Effectiveness
Estimation of Post Object-Oriented Technologies in
Software Maintenance
Mykola Tkachuk1, Konstiantyn Nagornyi1, Rustam Gamzayev1
1
National Technical University “Kharkiv Polytechnic Institute”,
Frunze str., 21, 61002 Kharkiv, Ukraine
{tka@kpi.kharkov.ua , k.nagornyi@gmail.com , rustam.gamzayev@gmail.com}
Abstract. A comprehensive approach to effectiveness’s estimation of post
object-oriented technologies (POOT) is proposed, which is based on structuring
and analyzing of domain-specific knowledge about such interconnected and
complex data resources within a software maintenance process as: 1) structural
complexity of legacy software systems; 2) dynamic behavior of user’s
requirements; 3) architecture-centered implementation issues by usage of
different POOT. The final estimation values of POOT’s effectiveness are
defined using fuzzy logic method, which was tested successfully at the
maintenance case-study of real-life software application.
Keywords: post object-oriented technology, effectiveness, crosscutting
functionality, knowledge-based approach, fuzzy logic.
Key terms: Software Engineering Process, Knowledge Representation,
Decision Support, Model, Metric
1 Introduction: Problem, Actuality and Research Objectives
The most part of modern software systems are developed and maintained using
object-oriented programming (OOP) [1]. Well-known and important problem to
support such applications are often modifications on many their subsystems and
development of new components to implement additional business logic due to new
user requirements. In order to emphasize this issue we propose to use in this paper the
notion “legacy software system” (LSS), similarly to the terms in software
reengineering domain (see, e.g. in [2]). Permanent changes in LSS lead to design
instability which causes a so-called crosscutting concern problem [3,4]. The OOP
actually does not solve this issue, and usage of OOP-tools increases the complexity of
an output source code.
63
During ten last years some post object-oriented technologies (POOT) were
elaborated and became intensive development, especially the most known POOT are:
aspect-oriented software design (AOSD) [5], feature-oriented software design
(FOSD) [6] and context-oriented software development (COSD) [7]. All these POOTs
utilize the basic principals of OOP, but in the same time they have additional features,
which allow solving the crosscutting problem electively. From the other hand the
usage of any POOT for LSS maintenance and reengineering is related to additional
time and other efforts in software development. That is why many researchers
emphasize the actual need to elaborate appropriate approaches to complex estimation
of POOT’s effectiveness usage in real-life software projects. It is additionally to
mention that within the context of this paper we are talking about the POOTs which
are focused on programming techniques exactly, but not about such software
management trends as Extreme Programming (XP), Rapid Application Development
(RAD), Scrum and some others [8], which also can be characterized as “post object-
oriented” approaches.
Taking into account the issues mentioned above, the main objective of the
research presented in this paper is to propose the intelligent complex approach to
effectiveness’s estimation of using POOTs in software maintenance. The rest of this
paper is organized in the following way: Section 2 analyses some critical issues in
OOP and reflects the phenomena of crosscutting functionality in software
maintenance. In Section 3 the existing POOT are analyzed and the results of their
comparing are shown with respect to software maintenance problems. In Section 4 we
present the knowledge-based approach for effectiveness’s estimation of POOT, which
is based on structuring and analyzing of domain-specific knowledge about
interconnected and complex data resources within a software maintenance
framework. Section 5 presents first implementation issues and the results of test-case
for the proposed approach. In Section 6 the paper concludes with a short summary
and with an outlook on the next steps to be done in the proposed R&D approach.
2 Some Critical Issues in Object-Oriented Programming and
Crosscutting Functionality Phenomenon in Software Maintenance
To meet new requirements existing LSS have to be refined with new classes, which
must implement their new functionality. Standard OOP toolkit “proposes” to support
additional associations between already existent and new program objects, to modify
inheritance tree for classes, to implement new or additional design patterns, e.g. the
Gang-of-Four (GoF) patterns [9]. Because of permanent modifications on source code
and doing software system re-design, developers face with “bottlenecks” of OOP:
increase coupling among classes [10]; increase of depth of inheritance tree (DIT) for
class hierarchies [11]; modification of design pattern instances [12,13]; emerging lack
of modularity in functionality realization [14].
A number of studies investigate problems of OOP mentioned above, and theirs
negative influence on LSS maintenance. High dynamic of requirement changes and
these critical issues of OOP induce and propagate an additional development problem:
this is a crosscutting concern’s phenomena. Crosscutting concern (hereby referred as
64
“crosscutting functionality” - CF) is a concern emerges on user requirements level
and often crosscuts on design level, this is a part of a business logic, which can not be
localized in the separate module on source code view but stays separate on
requirement view [15]. In literature exists a lot of researches related to CF’s
properties, multiple patterns of CF and it’s interaction with the source code of non-
crosscutting functionality, and it’s further propagation in system’s source code (see
e.g. in [13 - 16]). There are some widespread examples of software system features
which could be consider as CF: exception management, logging, transaction
management, data validation [17]. Nevertheless our own experience in software
development and LSS maintenance exposes that almost any system feature, emerged
by requirements, on source code perspective could be transformed into CF.
CF has two main properties [18]: scattering and tangling. CF’s source code scatters
among classes (components) of non-crosscutting functions, this happens because of
mismatch on end user requirement’s level of abstraction, and final realization of this
requirement as a feature on the source code level. CF’s source code tangles (mixes
up) with source code of the other functionality, no matter crosscutting or non-
crosscutting. Moreover CF could be divided into several types [19]: homogeneous
and heterogeneous. Homogeneous CF represents the same piece of source code which
crosscuts multiple locations in multiple OOP-classes of a software system.
Heterogeneous CF represents each time unique piece of source code which crosscuts
multiple locations in multiple OOP-classes of a software system (see Fig.1).
public class Line { public class
private Point p1, p2; CreditCardProcWithLogging{
Point getP1(){ return Logger _logger;
p1; } public void debit(CreditCard
Point getP2() { return card, Money amount)throws
p2; } InvalidCardException,
void setP1(Point p1){ NotEnoughAmountException,
this.p1 = p1; CardExpiredException {
Display.update(this);}} _logger.log("Starting
public class Oval { debiting"
void setPosition(Point + "Card: " + card
p2){ + " Amount: " + amount);
this.p2 = p2; // Debiting
Display.update(this); _logger.log("Debiting
} finished"
} + "Card: " + card); }
// Homogeneous CF // Heterogeneous CF
Fig. 1. Crosscutting functionality types
As a result, a presence of the CF in software system increases a complexity of the
maintenance process [20]:
• CF complicates traceability of various software design artifacts, e.g
requirements traceability [21];
• CF decreases understandability of a source code and functionality it realizes;
• source code of LSS becomes redundant;
65
• Almost impossible to reuse CF solutions, because of lack of modularity.
A conceptual approach, which allows to deal with CF, is a separation of concerns
(SoC) [22]. It envisages a decomposition and further non-invasive composition of CF
source code with the rest code of LSS. Decomposition mechanism allows to split
source code into fragments and to organize them into easy-to-handle CF-modules.
Composition mechanism supports reassembling of isolated code fragments in easy
and useful way. Usage of SoC principles makes possible to decrease coupling in LSS,
to decrease code redundancy, to reuse isolated CF-modules, to configure system by
add/remove functionality if needed.
Finally, the existing POOTs provide SoC principles and offer a lot of toolkits to
manage CF-problem in an effective way.
3 Post Object-Oriented Technologies: Main Features and Results
of Comparative Analysis
As already mentioned above (see in Section 1) nowadays there are 3 main well-
defined approaches in POOT-domain, namely: aspect-oriented software development
(AOSD) [5], feature-oriented software development (FOSD) [6] and context-oriented
software development technology (COSD) [7]. In order to reflect their essential
features with respect to the problem of CF it is useful to represent an interaction
between basic components of OOA and POOT [20].
AOSD was proposed in Research Center Xerox/PARC and it is now implemented
in many programming languages such as Java / AspectJ, C ++, .NET, Python,
JavaScript and some others [4]. AOSD allows to concentrate CF in separate modules
called aspects, which should be localized in source code infected with CF using such
means as points of intersection (point-cut) and injection (injection). Schematically
this interaction is shown in Fig. 2, (a), where the white vertical rectangles C1, C2, C3
represent OOP-classes and gray horizontal rectangles A1, A2, A3 represent the
aspects.
Fig. 2. AOSD: (а) – the conceptual scheme; (б) – the implementation facets
(compare with [19])
66
More detailed the structure of aspect is shown in Fig. 2, (b). Any aspect consists of
interconnected point-cut, of a notification (advice), and of an introduction (inner
declaration). The task of point-cut is to define a connection point between aspects and
basic methods in OOA-classes, in other words, point-cut determines those lines of
code in the OOA-methods, were notification code has be introduced. A notification is
a peace of code in OOA-language (e.g. in Java), which implements an appropriate CF,
therefore notifications can be of three types: before – such a notification is perform
before to call a OOA-method; after - a notification is made after this call; and around
- a notification is executed instead to call a OOA-method. Also AOSD allows the
introduction in OOA-classes new fields and methods that can be defined in aspects.
In the same way the FOSD and COSD schematically can be represented and
analyzed carefully (see in [20] for more details). The results of this comparative
analysis are presented in the Table 1.
Table 1. Results of comparative analysis for different POOT
POOT features / Estimation marks Type of POOT
AOSD FOSD COSD
Modeling CF features at a higher level of abstraction + + +
Implementation of homogeneous CF + +/– +/–
Implementation of heterogeneous CF +/– + +
Provide CF layers separately from a OOA-class + + +
Context-dependent activation/deactivation of layers – – +
Possibility to use several approaches simultaneously + /– + /– –
Availability of CASE-tools to support this POOT + + + /–
Even a cursory analysis of this comparison shows that for a decision on the
appropriateness and effectiveness of using an appropriate POOT to solve CF-problem
in given LSS, it is necessary to take into account a number of other additional factors,
which will be considered in the proposed approach.
4 Knowledge-Based Framework for Effectiveness’s Estimation of
Post Object-Oriented Technologies
Taking into account the results of performed analysis (see Section 2), and basing on
some modern trends in the domain of POOT-development (see Section 3), we propose
to elaborate a knowledge-based framework for comprehensive estimation of POOT-
effectiveness to use them in software maintenance. Thus we proceed from one of
possible definition of the term “knowledge” within the knowledge management
domain [23], namely: a knowledge is a collection of structured information objects
and relationships combined with appropriate semantic rules for their processing in
order to get new proven facts about a given problem domain.
Then our next task is to define and to structure all information sources, and to
elaborate appropriate algorithms and tools to process them with respect to the final
67
goal: how to estimate usage effectiveness of different POOTs in software
maintenance.
4.1 Multi-dimensional model for POOT effectiveness’s estimation
To implement the proposed knowledge-based approach the multi-dimensional
modeling space is proposed in [20], and its graphical interpretation is shown in Fig. 3.
According to this model the integrated effectiveness level is depend on two main
interplaying factors, namely: 1) what type of LSS has to be modified with usage of an
appropriate POOT; 2) what kind of POOT is used to eliminate the CF in this LSS. In
order to answer these questions the following list of prioritized tasks can be
composed:
Fig. 3. 3-D modeling space for POOT’s effectiveness estimation
(i) to define a type of given LSS with respect to its structure complexity and to
behavior of requirements, which this LSS in maintenance process is facing
with;
(ii) to calculate an average effort values for different POOT, if this one is used
to eliminate CF in an appropriate LSS;
(iii) to elaborate the metrics for CF assessment before and after LSS
modification using a given POOT;
(iv) to propose an approach to final effectiveness estimation of POOT’s usage
taking into account the results provided by activities (i) – (iii).
Below these tasks are solved sequentially, using knowledge-based and expert-
centered methods and tools.
4.2 Definition of legacy software system types
To solve task (i) from the their list given in Section 4.1 the approach to analyzing and
assessments of LSS’s type proposed in [24] can be used, which is based on the
following terms and definitions.
68
Def#1. System Type (ST) is an integrated characteristic of any LSS given as a tuple:
ST =< Structural Complexity , Requiremen tRank > (1)
The first parameter estimates a complexity level of a given LSS, and the second
one represents status of its requirements: their static features and dynamic behavior.
To calculate structural complexity (SC) the following collection of metrics was
choused: Cyclomatic Complexity (V), Weighted Method Complexity (WMC), Lack of
Cohesion Methods (LCOM), Coupling Between Objects (CBO), Response For Class
(RFC), Instability (I), Abstractness (A), Distance from main sequence (D). The final
value of SC can be calculated using formula (2), where the appropriate weighted
coefficients for each metric were calculated in [24] with help of Analytic Hierarchy
Process method [25].
SC = K V avgV + K WMC avgWMC + K LCOM avgLCOM + K CBO avgCBO + (2)
+ K RFC avgRFC + K I avgI + K A avgA + K D avgD
To evaluate the final value of SC of given LSS in terms of an appropriate linguistic
variable (LV):“Low”, “Medium”, “High”, the following scale was elaborated [24]:
2 * SC Min + SC Max
SC Min ≤ Low <
3
2 * SC Min + SC Max SC Min + 2 * SC Max
≤ Medium ≤ (3)
3 3
SC Min + 2 * SC Max
< High ≤ SC Max
3
To define the second parameter given in formula (1), two relevant features of any
requirement were considered [24], namely: a grade of it’s Priority and a level of it’s
Complexity.
Def#2. Requirements Rank is a qualitative characteristic of LSS defined as a tuple:
Requiremen tRank =< Priority, Complexty > (4)
In [24] is mentioned that in modern requirement management systems (RMS) like
IBM Rational Requisite Pro, CalibreRM and some others, the Priority and Complexity
of requirements are usually characterized by experts in informal way, e.g. using such
terms as: “Low”, “Medium”, “High”. The real example of such interface in RMS is
presented in Fig. 4, with requirement’s attributes “Priority” and “Complexity” (or
“Difficulty” in terms of RMS-technology).
Taking into account the definition for linguistic variable (LV) given in [26], the
appropriate term-sets for LVs Priority and Complexity respectively were defined in
[24] as follows:
69
Fig. 4. The list of requirements completed in RMS Rational Requisite Pro
X : Priority ; T(Priority) = {" neutral" ," actual" ," immidiate" } (5)
X : Complexity ; T (Complexity ) = {" low" , " medium " , " high " } (6)
Basing on definitions (1) – (6), the mapping procedure between 2 attribute spaces was
elaborated in [24]. These attribute spaces are defined with apprpopriate LVs, namely:
the space “Requirements Rank” with axes “Priority” and “ Complexity”; the space
“System Type” with axes “Requirements Rank” and “Structural Complexity”. This
mapping procedure in details is presented in [24], and the final result of this approach
is shown on Fig. 5. It illustrates the main advantages of the proposed approach,
namely: 1) we are able to estimate current state of system requirements w.r.t. their
static and dynamic features; 2) basing on this estimation, we can define an appropriate
type of investigated software system (e.g., some LSS in maintenance process), taking
into account it’s structural complexity and dynamic requirements behavior as well.
Fig. 5. (a) – the initial allocation of system’s requirements in the space “Requirement Rank”;
(b) – the mapped system’s position in the space “System Type”
70
4.3 An architecture-centered method for POOT effort calculation
In order to solve task (ii) from their list given in Section 4.1 it is proposed to analyze
basic architectural frames, which can be constructed for different POOT with usage of
their OOP-specification. In [20] the following definition is proposed for this purpose.
Def#3. Enhanced architectural primitive (EAP) is a minimal-superfluous
component-based scheme, which is needed to implement an interaction between basic
OOP-elements (class, field, method) and specific functional POOT-elements.
Obviously, to perform the comparative analysis of different EAP in the correct
way, they preliminary have to be represented in some uniform notation. As a such
notation the architecture description language (ADL) should be used, because: 1) this
notation is not depend on any specific programming tools; 2) in this way static and
dynamic features of AP both can be described and analyzed.
The most important modeling abstracts of ADL (see e.g. in [27]) are components,
ports and connectors, and there are such additional ADL - features as role and
interaction. They have the following definitions within the context of this paper.
Def#4. Component is a complex of functional items, which implements a certain
part of a business logic in LSS, and which is supposed to have special interfaces
(ports) for communication with other entities in an operating environment.
Def#5. Port is an interface to provide an interaction between several components.
Def#6. Connector is a special architectural item to join ports of different
components.
Def#7. Role is a special feature of a given connector to identify its communicating
ports.
Def#8. Interaction is a special feature of given connector defined using its roles.
More detailed the notion port can be characterized in the following way: 1) there is
so-called single port - this is an interface of any component to communicate with
some another one via exactly one connector; 2) furthermore there is a case-port -
this is an interface of any component to communicate with another components via
more then one connectors (e.g., using an appropriate Boolean variable as a flag to
switch communication, etc.). Similarly, the notion connector can be classified as
follows: 1) a binary connector – this is a connector with 2 fixed roles only; 2) a
multiply connector – this is a connector, which has exactly 1 input role and more then
1 output roles; 3) a case connector – this kind of connectors can have a lot of input
and output role as well.
Using the definitions Def#3 – Def#8 the appropriate EAP for all mentioned above
POOT were elaborated [20]. As one example the EAP for AOP is shown on Fig. 6,
which reflects how the specific AOP-features such as advice and inner declaration
(they are shown as rectangular icons in grey color) are interacting with basic OOP –
elements, namely: class, field and method (they are represented as crosswise icons in
white color).
71
Fig. 6. ADL-specification for the aspect-oriented EAP
To calculate the complexity coefficients (CC) of the elaborated EAP the following
formulas are proposed in [20], namely:
Component = 0.6*# POOT + 0.4*# OOP , (7)
where a Component is the CC of an appropriate EAP, # OOP is a number of
architectural OOP – components, and # POOT is a number of POOT – components
included in this EAP. These values are multiplied with the weight coefficients: 0,6
and 0,4 respectively, and these coefficients can be defined using some expert methods
(see in [20] for more details);
(7)
Connector= 0.2*# BinaryConnector + 0.3*# MultyConnector + 0.5*# CaseConnector ,
where a Connector is the CC of connectors included in an appropriate EAP, which
is calculated using the number of binary connectors: # BinaryConnector , the number of
multi-connectors # MultyConne ctor and the number of case-connectors:
# CaseConnector , with respect to the appropriate weight coefficients 0.2, 0.3 and
0.5, which also are defined by some experts [20];
Port = 0.8*# SinglePort + 0.7*# CasePort , (8)
where Port is the CC of ports included in an appropriate EAP, which takes into
account the number of single ports: # SinglePort , and the number of case ports:
# CasePort with appropriate weigh coefficients.
72
Using formulas (7) – (9) the summarized value Complexity of an appropriate
EAP, measured in so-called architectural units (a.u.) [20] can be calculated as follows:
Complexity = Component + Connector + Port (9)
The final values of CC for all POOT were calculated using formula (10), and they
are represented in Table 2 (see in [20] for more details).
Table 2. The values of architectural complexity for the different POOT
POOT type CC for CC for CC for ports Summarized
components connectors (a.u.) values of CC
(a.u.) (a.u.) (a.u.)
AOSD 4,8 1 4,3 10,1
FOSD 3,6 1 3,9 8,5
COSD 2,8 0,7 4,1 7,6
Basing on the estimation values aggregated in Table 2 it is possible to make
conclusions about average implementation efforts by usage of appropriate POOT to
solve CF-problems in legacy software systems within their maintenance.
4.4 Quantitative metrics for crosscutting in legacy software
There are different ways to characterize a nature of the CF and it’s impact to software
source code. A number of studies are dedicated to a classification, qualitative and
quantitative description of CF problem [3,14-16]. The aim of our research is to assess
an impact, which CF makes to a structure of OOP-based software system during it’s
evolution in maintenance; therefore we are focusing on quantitative facet of
crosscutting nature. To reach this goal it is proposed to perform next three steps.
Step 1: Localize source code belonged to a particular CF in a given LSS. Although
exists several source code analysis tools for CF localization, e.g., tool CIDE [28], this
problem remains really complicated for autoimmunization and demands an expert in
code structure and business-logic of an appropriate LSS.
Step 2: Calculate a specific crosscutting weight ratio of a particular CF in the
system indicated as CFratio [20]. This coefficient shows a ratio between OOP-classes,
“damaged” by a particular CF and all OOP-classes in the system, or it’s projection,
e.g. business logic realization without subordinate classes of a framework. This
coefficient possible to represent as
Ccf (10)
CFratio = ,
Ccf + C
where Ccf – number of classes in LSS, “damaged” with CF, C – number of classes
free of CF. Obviously, that CFratio ∈ [0;1] , and if CFratio = 0, it means a particular
73
functionality is not crosscutting; and if CFratio = 1, it means all classes are “damaged”
with a particular CF.
Step 3: Calculate a residual crosscutting ratio indicated as RCRratio. This metric,
based on DOS (Degree of Scattering) value, proposed in [14], namely “…DOS is
normalized to be between 0 (completely localized) and 1 (completely delocalized,
uniformly distributed)”. Nevertheless this metric does not allow to asses “damage”
degree, done by a particular CF, therefore we propose to refine DOS-metric in
following way
RCRratio = DOS ⋅ CFratio , (11)
where DOS – Degree of Scattering; CFratio – specific crosscutting weight ratio of
a particular CF. Similarly to CFratio , RCRratio ∈ [0;1] , if RCRratio = 0, it means that CF
is localized in a separate module and it is no more crosscutting; if RCRratio = 1, it
means that CF effects a whole system and is uniformly distributed.
Thus the proposed quantitative metrics (11) – (12) give to an expert a possibility to
assess a distribution nature of a CF, and to estimate a “CF-damage” for a given LSS.
4.5 Fuzzy logic approach to complex effectiveness estimation of POOT
Based on assessment of POOT average implementation efforts (see Chapter 4.3), and
assessment for residual crosscutting ratio (see Chapter 4.4) it is possible to estimate
an integrated effectiveness of POOT usage. Although because of different scale and
units of measurement for proposed assessments, it is hard to evaluate them within a
single analytical method. Therefore, for further evaluations it is proposed to use one
of algorithms of the fuzzy logic [26], namely the Mamdani’s algorithm, which
consists of 6 steps. According to this algorithm to estimate effectiveness of POOT
usage it is necessary to compose fuzzy production rules (FPR). In this paper a verbal
description for these rules is omitted, instead of this the widespread symbolic
identifiers for short description of FPR are listed in Table 3.
Table 3. A symbolic representation form for the description for FPR
Symbolic form Description
Z Zero
PS Positive Small
PM Positive Middle
PB Positive Big
PH Positive Huge
The whole system of elaborated FPR consists of 20 definitions (see in [29] for
more details), and the fragment of this FPR-system is listed below:
1. RULE_1: If “ β1 is PS” and “ β2 is Z”, then “ β3 is Z”;
74
2. RULE_2: If “ β1 is PM” and “ β2 is Z”, then “ β3 is Z”;
3. …
4. RULE_9: If “ β1 is PS” and “ β2 is PM”, then “ β3 is PM”;
5. …
Corresponding to the Mamdani’s algorithm, the next step is a fuzzifying of
variables in FPR, therefore average implementation efforts, residual crosscutting
ratio, and effectiveness of POOT usage have to be represented as LV. The output LV
EPOOT is the effectiveness of POOT-usage, the LV EPOOT is bounded on universe X ,
and it belongs to the interval [0;1]. The term set for this LV looks like:
EPOOT ∈ {non − effective, low − effective, mid − effective, effective, very − effective} ,
and it could be represented in short form as EPOOT ∈ {Z , PS , PM , PB, PH } . The
corresponding identifier for EPOOT is β3 (see FPR above), and it is shown in Fig. 7.
Fig. 7. The graphic form for LV “Effectiveness” EPOOT
The input LV CPOOT represents average implementation efforts, CPOOT is bounded
on universe X and belongs to an interval [(EAP)min; (EAP)max], where EAPmin,
EAPmax are minimum and maximum values of architectural complexity (measured in
a.u.) for appropriate LSS type respectively. The term set for the CPOOT linguistic
variable (LV) looks like: CPOOT ∈ {low, middle, high, huge} and could be represented
in short form CPOOT ∈ {PS , PM , PB, PH } . The corresponding identifier for CPOOT is
β1 (see FPR above). The graphical interpretation for this LV is similar to the graphic,
depicted on Fig. 7.
The input LV PPOOT is a residual crosscutting ratio (see formula (12)). The LV
PPOOT is bounded on universe X and belongs to interval [0;1]. The term set for this
variable looks like: PPOOT ∈ {useless, low, middle, high, huge} , and it could be
represented in short form as PPOOT ∈ {Z , PS , PM , PB, PH } . The corresponding
identifier for PPOOT is β2 (see FPR-system above). The visual interpretation is similar
to the graphic depicted in Fig. 7.
75
5 The Test-Case and Result Discussion for the Proposed Approach
To illustrate the proposed approach the real LSS for personal data management was
analyzed [29]. It consists of 15 java-classes, and it contains a homogenous realization
of “logging” crosscutting functionality. Accordingly to the LSS – type definition
method (see Section 4.2) this application belongs to the III-rd system type with rank:
{“Low structural complexity”; “High requirement rank”}. The source code of this
LSS was sequentially modified using 3 POOT: AOSD, FOSD, and COSD
respectively. The final results of POOT effectiveness estimation are shown in Table 4.
The first column lists all LSS – modifications to be compared: an initial OOP -
version, which has to be re-structured wit respect to CF-problem, and its 3
modifications done with usage of different POOT. In the second column the
summarized efforts needed for these modifications with respect to architectural-
centered complexity are calculated (see Section 4.3). The data given in the third
column of Table 4 show the level residual crosscutting ratio which is presented (for
initial OOP-version) or which is remained after its redesigning with the appropriate
POOT. The forth column indicates the final effectiveness’s estimation values for all
LSS-versions.
Table 4. Effectiveness of usage of POOT in a target system
(P)OOT Architectural Residual crosscutting Effectiveness
complexity (a.u.) ratio (%) level
(%)
OOP 122.51 69.52 6,7
AOSD 79.43 0,15 73,3
FOSD 116.16 29.06 34,4
COSD 115.88 8.78 32,8
The results achieved show, that OOP actually is not enough effective to solve
crosscutting problem (done with 6.7% only). The most preferable approach to
eliminate this issue in the given type of LSS (as mentioned above, this is the III-rd
system type according to LSS-classification proposed in Section 4.2), is an AOSD
which provides effectiveness level over than 70%.
It is also to mention, although an effectiveness level of COSD and FOSD is lower
than AOSD, over 30% for homogenous CF, it is still much better result than OOP.
Taking into account a qualitative advantage of these two another technologies,
namely: a possibility to implement a heterogeneous CF also (see Table 1), it can be
reasonable to use one of them for LSS-maintenance to deal with such kind of CF in
much effective way than AOSD.
6 Conclusions and Future Work
In this paper we have presented the intelligent approach to effectiveness’s estimation
of modern post object-oriented technologies (POOT) in software development, which
76
aims to utilize domain-specific knowledge for this purpose. This knowledge base
includes such important and interconnected data resources as: 1) structural complexity
of legacy software; 2) dynamic behavior of user’s requirements; 3) architectural-
centered implementation efforts of different POOT. To process these data the
quantitative metrics and expert-oriented estimation algorithms were elaborated. The
final complex estimation values of POOT’s effectiveness assessment are defined
using fuzzy logic method, which was successfully tested on some real-life legacy
software applications.
In future we are going to extend a collection of metrics for POOT-features
assessment, and to apply some alternative (to fuzzy logic method) approaches to final
decision making. Besides that it is supposed to develop an appropriate software
CASE-tool for expert’s data handling in the proposed knowledge-based estimation
framework.
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von-Guericke University Magdeburg (2007)
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78
Provably correct graph transformations
with small-tALC ⋆
Nadezhda Baklanova2 , Jon Haël Brenas1 , Rachid Echahed1 ,
Christian Percebois2 , Martin Strecker2 , Hanh Nhi Tran2
1
CNRS and Université de Grenoble
2
Université de Toulouse / IRIT
Abstract. We present a prototype for executing and verifying graph
transformations. The transformations are written in a simple imperative
programming language, and pre- and post-conditions as well as loop in-
variants are specified in the Description Logic ALC (whence the name
of the tool). The programming language has a precisely defined oper-
ational semantics and a sound Hoare-style calculus. The tool consists
of the following sub-components: a compiler to Java for executing the
transformations; a verification condition generator; and a tableau prover
for an extension of ALC capable of deciding the generated verification
conditions. A description of these components and their interaction is
the main purpose of this paper.
Keywords: Graph Transformations, Programming Language Seman-
tics, Tableau Calculus, Description Logic
Key Terms: ModelBasedSoftwareDevelopmentMethodology, Formal-
Method, MathematicalModel, VerificationProcess
1 Introduction
Provably correct transformations of graph structures become increasingly impor-
tant, for example for pointer manipulating programs, model driven engineering
(such as EMF [1]) or the Semantic Web (with representation formats such as
RDF [2]).
Contributions: This paper presents a new language, called small-tALC, and ac-
companying programming environment for executing graph transformations and
reasoning about them. Let us characterize in a few words what our work is about
and what it is not about:
– The primary aim of our development is to be able to reason about graph
transformations in a pre- / post-condition style: can we ensure that any
graph satisfying the pre-condition is transformed into a graph satisfying
the post-condition? Essential ingredients of such a setup are a language for
describing the transformations, and an assertional formalism for specifying
the pre- and post-conditions.
⋆
Part of this research has been supported by the Climt project (ANR-11-BS02-016).
79
– The transformation language is an imperative programming language with
special operations for manipulating graphs. This language is endowed with
traditional control flow constructs (selection and loops) and elementary state-
ments for adding and deleting arcs of a graph. There is a select statement
that can be understood as a generalized, non-deterministic assignment oper-
ation and whose purpose is to perform matchings of rules in a target graph.
After a high-level overview of small-tALC (Section 2), we will give a more
detailed account of the program logic (in Section 3.1) and transformation
language (in Section 3.2). Our transformation language is by no means a
full-fledged programming language: for example, arithmetic operations are
excluded.
– The transformation language is not graphical, but textual. We do not ques-
tion the utility and appeal of a graphical notation, but this issue is orthogonal
to our concerns. We can imagine to couple small-tALC with existing graphical
editors, such as Henshin [3], in the sense of translating a graphical descrip-
tion of a rule to our textual format. The usefulness of the inverse direction is
less evident, because the textual format is more expressive (offering, among
others, nested loops and branching statements).
– The transformation language is executable, by a translation to Java (see
Section 4): a code generator translates small-tALC to Java code, which can
then transform graphs specified in an appropriate format.
Altogether, we are thus primarily interested in proofs of correctness of graph
transformations, for which two major approaches have emerged:
1. Model checking of graph transformations: given an initial graph and a set of
transformation rules, check whether the graph can eventually evolve into a
graph having certain properties, or whether specific properties can be ascer-
tained to be always satisfied. This kind of reasoning is possible in principle
(the initial graph can be specified by a pre-condition, invariants can be spec-
ified as loop conditions, eventuality properties as post-conditions), but our
approach is clearly not geared towards this activity.
2. Full correctness proofs: given an arbitrary graph satisfying the pre-condition,
verify that it evolves into a graph satisfying the post-condition. This is the
kind of verification we are aiming at.
Full correctness proofs are hard, and undecidability of the generated proof
obligations is a major concern for rich logics [4]. We propose to use a rela-
tively simple logic, ALC, belonging to the family of Description Logics (DLs).
We summarize the logic in Section 3.1, and the fine-tuned interplay of the logic
and the transformation language (among others: branching and loop conditions
are formulas of this logic) brings it about that the proof obligations extracted
from programs are decidable, as argued in Section 5. We are currently working
on extending this approach to more expressive description logics, with the pur-
pose of being able to tackle realistic problems in the areas of UML-style model
transformations and RDF graph database transformations.
80
The work described here has reached the state of a sound prototype. In the
corresponding sections, we will make precise which parts of the development are
completed to which degree, and indicate which missing parts still have to be
filled in. The small-tALC environment is available from the following web page,
where it will be regularly updated: http://www.irit.fr/~Martin.Strecker/
CLIMT/Software/smalltalc.html.
Related work: Hoare-like logics have already been used to reason on graph trans-
formations (see, e.g. [5]) but, as far as we are aware, no tool has been imple-
mented. small-tALC, which is also based on a Hoare-like calculus, allows one
to decide the verification problem, of programs operating on graphs, when the
properties are expressed in the ALC logic. Some implementations of verification
environments for pointer manipulating programs exist [6], however they often
impose severe restrictions on the kind of graphs that can be manipulated, such
as having a clearly identified spanning tree.
Other tools dedicated to reasoning on graph transformations have been pro-
posed. For example, the GROOVE [7] system implements model-checking tech-
niques using LTL or CTL formulas and thus departs from small-tALC techniques.
The computation of weakest preconditions from a graph rewriting system
is described by Habel, Pennemann and Rensink [8,9]. This work is concerned
with extraction of weakest preconditions, but no proof system for the formulas
is given. Pennemann [10] then describes a method of translating the extracted
formulas to a resolution theorem prover. Radke [11] uses a more expressive logic:
MSO. The spirit of the work described in this paper is similar, but we explicitly
restrict the expressiveness of the logical framework to obtain decidable proof
problems.
In a similar vein, Asztalos et al. [12] describe the verification of graph trans-
formations based on category-theoretic notions and by translation to a logic for
which no complete calculus is provided.
Raven3 is a tool suite designed to handle and manipulate graph automata.
In some sense Raven tends to generalize model-checking techniques from word
to graph processing. Therefore techniques behind Raven tool are not directly
comparable to small-tALC.
Alloy [13] is a popular framework for specifying and exploring relational
structures, and it has been used to analyze graph transformations [14] written
in the AGG transformation engine. Alloy interfaces with model checkers and can
display counter models in case a transformation does not satisfy its specification.
For verification, Alloy uses bounded model checking: errors for graphs of a certain
size are systematically detected, but has the disadvantage that graphs beyond
that size are not covered. As opposed to this, the proof method presented here
is exhaustive, being based on a complete, decidable calculus.
3
http://www.ti.inf.uni-due.de/research/tools/raven
81
2 System Description
2.1 User’s View
To explore the perspective of a user of small-tALC, we will walk through pro-
cessing a simple program, but before, let us take a look at the kind of graphs
we will be transforming, such as the example graph in Figure 1a (displayed with
RDF-Gravity4 ). We will be processing graphs in RDF [2] format. These graphs
consist of nodes and typed edges. The graphs are simple: there cannot be multi-
ple edges of the same type between two nodes, but several edges, each of different
type. In the example, there is only one type of relation (also called role): r. Here,
instance node a0 is linked with nodes a1, a2 and a3; similarly b0 with b1 and
b2. Nodes can be typed. In our example, we have two types (also called concepts)
A and B. Nodes ai are of type A, and nodes bj of type B. It is a matter of display
to represent concepts as (meta-)nodes in Figure 1a, and also the (meta-)relation
type as arc linking a node to its type, but these meta-entities are subject to a
different treatment than object nodes and relations.
a b
r r
c_1: -B A c_2: B
(b) Counter model after
(a) Input graph failed proof
Fig. 1: Graph structures
Let us now turn to transformation programs, as the one depicted in Figure 2.
A program is composed of one or several parameterized rules; and a parameter-
less main rule whose purpose is to specify the input- and output graph to be
transformed and to identify the root nodes of the input graph. Rules can be as-
similated to non-recursive procedures or macros. Procedural abstraction is so far
not fully developed in our framework, so the analysis presented in the following
concentrates on rule bodies.
The rule ex_rule has a precondition (pre) saying that node a is only con-
nected (via arcs of type r) to nodes of type A, and that b is only connected to
4
http://semweb.salzburgresearch.at/apps/rdf-gravity/
82
concepts A, B; roles r; rule main () {
vars a, b;
rule ex_rule (a, b) { ingraph "input_graph.rdf";
vars c; outgraph "output_graph.rdf";
pre: (a : ([!] r A)) && (b : ([!] r B)); a := node("a0");
select c with (b r c); b := node("b0");
add (a r c); ex_rule(a, b);
post: (a : ([?] r B)); }
}
Fig. 2: An example program
nodes of type B. The program now does the following: among the nodes that b
is connected to, we non-deterministically pick a node c and introduce an arc r
between a and c. For example, the program might introduce an arc between a0
and b1 in the graph of Figure 1a (or between a0 and b2). We can now assert
that after running this program, the node that variable a points to is connected
via r to at least one element of type B, as expressed in the postcondition.
Suppose the example program is in file example.trans. Running the verifier
as follows confirms that the program is correct, i.e. that any graph satisfying
the precondition is transformed into a graph satisfying the postcondition.
> graphprover example
starting proof ...formula valid
Let us modify the post-condition, claiming that a is exclusively connected to
elements of type B: post: (a : ([!] r B));
When running the verifier again, we see that the property is incorrect, and
that a counter-model has been created (see Figure 1b, here displayed with
Graphviz5 ). This counter-model describes the state at the beginning of the pro-
gram, namely a graph with four nodes, where c1 is of type A and not of type
B, and c2 of type B. Clearly, when connecting a with c2 , the post-condition is
violated.
We correct the post-condition, saying that a is only connected to elements
of type A or B: post: (a : ([!] r (A [||] B))); Running the verifier again
convinces us that this property is satisfied.
How does the verifier validate or invalidate a program? The approach is clas-
sic: from the annotated program, we extract a proof obligation by computing
weakest pre-conditions (see Section 3.2). This is an ALC formula that is sent
to a tableau decision procedure (described in Section 5.2). A failed proof at-
tempt produces a saturated tableau from which a counter-model can always be
extracted.
83
Operational Program Decision
semantics logic procedure
Code Extraction (Scala/Java)
Program Eclipse
prover environment
(verified) (unverified)
Fig. 3: Schema of formal development
2.2 Developer’s View
Major parts of small-tALC have a strong formal basis and are being developed in
a proof assistant. We use Isabelle [15], but the formalization is easily adaptable
to related proof assistants. Essential ingredients (see Figure 3) are the formal-
ization of the program logic, the semantics of the programming language and
a decision procedure of the extension of ALC we use (the latter has currently
not been completely verified yet). This formalization (written in Isabelle’s own
functional and proof language) is automatically extracted to a general-purpose
programming language, which is Scala in our case. We therefore obtain a highly
reliable program prover, which is coupled with interface functionality (such as
parsers and viewers) provided by Eclipse / Xtext to obtain the verifier described
in Section 2.1. The transformation engine, described more in detail in Section 4,
is so far unverified, but at least the Java code generator (Section 4) could be
formally verified with by now standard compiler verification techniques.
3 Foundations
3.1 Logic
Our logic is a three-tier framework, the first level being Description Logic (DL)
concepts, the second level facts, the third level formulas (Boolean combinations of
facts and a simple form of quantification). Formulas occur not only in assertions
(such as pre- and postconditions), but also in statements (Boolean conditions
and select statement).
Concepts: In this paper, we concentrate on the description logic ALC [16]. For a
being atomic concept names and r role (or relation) names, the abstract syntax
of concepts C can be defined by the grammar:
5
http://www.graphviz.org/
84
C ::= ⊥ (empty concept) |a (atomic concept)
| ¬C (complement)
| C ⊓ C (intersection) | C ⊔ C (union)
| ([?] r C) (some) | ([!] r C) (all)
| Cτ (explicit substitution)
The semantics of DLs is given by Kripke structures or, differently speaking,
by typed graphs. Under this interpretation, concepts represent sets of individuals.
The constructors ¬, ⊓, ⊔ (in Ascii notation: !,[&&],[||]) then have the obvious
meaning. ([?] r C) is the set of individuals x such that there is at least one r-
typed edge (x r y) between x and y, where y belongs to C. Dually, ([!] r C) is
the set of individuals x all of whose r-edges go to individuals of type C.
The last constructor, explicit substitution [17], is a particularity of our frame-
work, required for a gradual elimination of substitutions, as further described in
Section 5.5. We have three kinds of substitutions τ :
– Replacement of a variable by another variable, of the form [x := y],
– Adding a node v to / removing a node from an atomic concept a, of the form
[a := a + {v}] respectively [a := a − {v}],
– Adding an edge (v1 , v2 ) to / removing an edge from a role r, of the form
[r := r + {(v1 , v2 )}] respectively [r := r − {(v1 , v2 )}].
Facts: Facts make assertions about an instance being an element of a concept,
and about being in a relation. The grammar of facts is defined as follows:
f act ::= i : C (instance of concept)
| iri (instance of role)
| i (¬r) i (instance of role complement)
| i ≡ i (equality of instances)
| i 6≡ i (inequality of instances)
Please note that since concepts are closed by complement, facts are closed by
negation (the negation of a fact is again representable as a fact), and this is the
main motivation for introducing the constructors “instance of role complement”
and “inequality of instances”.
Formulas: A formula is a Boolean combination of facts. We also allow quantifi-
cation over individuals i (but not over relations or concepts), and, again, have
a constructor for explicit substitution. We overload the notation ⊥ for empty
concepts and the Falsum.
f orm ::= ⊥ | f act | ¬f orm
| f orm ∧ f orm | f orm ∨ f orm
| ∀i.f orm | ∃i.f orm
| f orm τ
In Figure 2, we use the Ascii notation !, &&, || for negation, conjunction
and disjunction. The extension of interpretations from facts to formulas is stan-
dard. As usual, a formula that is true under all interpretations is called valid.
When calculating weakest preconditions (in Section 5.1), we obtain formulas
which essentially contain no existential quantifiers; we keep them as constructor
85
because they can occur as intermediate result of computations. We say that a
formula is essentially universally quantified if ∀ only occurs below an even and ∃
only below an odd number of negations. For example, ¬(∃x. x : C ∧ ¬(∀y. y : D))
is essentially universally quantified.
3.2 Programming Language
The programming language is an imperative language manipulating relational
structures. Its distinctive features are conditions (in conditional statements and
loops) that are restricted formulas of the logic ALC, in the sense of Section 3.1.
It has a non-deterministic assignment statement select ... with allowing to
select an element satisfying a fact. Traditional types (numbers, arrays, inductive
types) and accompanying operations are not provided; the language is thus only
targeted at transformations of graphs.
Statements of our language are defined by the following grammar:
stmt ::= Skip (empty statement)
| select i with f orm (assignment)
| delete(i : C) (delete element from concept)
| add(i : C) (add element to concept)
| delete(i r i) (delete edge from relation)
| add(i r i) (insert edge in relation)
| stmt ; stmt (sequence)
| if f orm then stmt else stmt
| while f orm do stmt
Please note that the keywords add and delete are overloaded for nodes and
for edges. There is no direct support for creating or deleting nodes in a graph,
only for “moving” them between concepts. We intend to simulate node creation
and deletion by providing a predefined concept heap such that add(n: heap)
corresponds to creating node n and delete(n: heap) to deallocating node n.
Details still have to be worked out.
The semantics is a big-step semantics with rules of the form (st, σ) ⇒ σ ′
expressing that executing statement st in state σ produces a new state σ ′ .
The rules of the semantics are given in the Figure 4. Beware that we overload
logical symbols such as ∃, ∧ and ¬ for use in the meta-syntax and as constructors
of f orm.
We do not enter into the details (also see the Isabelle formalization). Intu-
itively, the states σ manipulated by the operational semantics are the same as the
interpretations of formulas, and they describe the current structure of a graph:
which nodes are contained in each concept; which pair of nodes are contained in
a role; and which variables are bound to which nodes. We write σ(b) to evaluate
the condition b (a formula) in state σ.
Most of the rules are standard, apart from the fact that we do not use expres-
sions, but formulas as conditions. The auxiliary function delete_edge modifies
the state σ by removing an r-edge between the elements represented by v1 and
v2 , and similarly for generate_edge. There are analogous functions for adding /
deleting in concepts.
86
(c1 , σ) ⇒ σ ′′ (c2 , σ ′′ ) ⇒ σ ′
(Skip) (Seq)
(Skip, σ) ⇒ σ (c1 ;c2 , σ) ⇒ σ ′
σ ′ = delete_edge v1 r v2 σ σ ′ = generate_edge v1 r v2 σ
(EDel) (EGen)
(delete(v1 r v2 ), σ) ⇒ σ ′ (add(v1 r v2 ), σ) ⇒ σ ′
∃vi.(σ ′ = σ [v:=vi] ∧ σ ′ (b))
(SelAssT)
(select v with b, σ) ⇒ σ ′
σ(b) (c1 , σ) ⇒ σ ′ ¬σ(b) (c2 , σ) ⇒ σ ′
(IfT) (IfF)
(if b then c1 else c2 , σ) ⇒ σ ′ (if b then c1 else c2 , σ) ⇒ σ ′
σ(b) (c, σ) ⇒ σ ′′ (while b do c, σ ′′ ) ⇒ σ ′ ¬σ(b)
(WT) (WF)
(while b do c, σ) ⇒ σ ′ (while b do c, σ) ⇒ σ
Fig. 4: Big-step semantics rules
The statement select v with F (v) selects an element vi that satisfies formula
F , and assigns it to v. For example, select a with a : A ∧ (a r b) selects an
element a which is and instance of concept A and being r-related with a given
element b.
select is a generalization of a traditional assignment statement. There may
be several instances that satisfy F , and the expressiveness of the logic might
not suffice to distinguish them. In this case, any such element is selected, non-
deterministically. Let us spell out the precondition of (SelAssT): Here, σ [v:=vi] is
an interpretation update for individuals, modifying σ for variable v and assigning
it a value vi in the semantic domain. We check whether the formula b would be
satisfied under this choice, and if it is the case, keep this assignment. In case
no satisfying instance exists, the semantics blocks, i.e. the given state does not
have a successor state, which can be considered as an error situation.
4 Executing Graph Transformations
Generating Java Code: For processing small-tALC programs such as the one in
Figure 2 and generating Java code, we use the Eclipse environment and, in partic-
ular, the Xtext6 facilities for parsing, syntax highlighting and context-dependent
help. The program prover is currently not fully integrated in this framework, so
6
http://www.eclipse.org/Xtext/
87
that the interaction with the prover is performed via shell commands as described
in Section 2.1.
In order to generate Java code for small-tALC programs, we parse the pro-
gram and then traverse the syntax tree with Xtext/Xtend, issuing calls to ap-
propriate Java functions that manipulate a graph (which is initially the input
graph provided in the program’s main rule). Here is a glimpse at the Xtend code
snippet that translates statements, in particular the add statement for roles:
def statement(Stmt s){
switch s{
Add_stmt: add(s.lvar,s.role,s.rvar)
...
}
}
def add(String lvar,String role,String rvar)’’’
«graph».insertEdge(«lvar»,«role»,«rvar»);’’’
Thus, a small-tALC program fragment add(a r b); is translated to a Java
call g.insertEdge(a, r, b);, where the graph g is the current graph.
Transforming Graphs: Once a Java program has been generated for a given
small-tALC program, it can be compiled and linked with a library that provides
graph manipulating functions such as the above-mentioned insertEdge. When
executing this program, it remains to read an input file containing a graph
description, to perform the transformation and to output the new graph. We
represent graphs in the RDF [2] format. Parsing and printing of RDF files is
based on the Apache Jena framework7 .
5 Reasoning about Graph Transformations
5.1 Weakest Preconditions
For proving program correctness, we use a standard approach in program ver-
ification. For proving that a program prog establishes the postcondition Q if
started in a state satisfying the precondition P , we calculate the weakest pre-
condition of prog with respect to Q and then show that P implies this weakest
precondition.
The details are inspired by the description in [18]: we compute weakest pre-
conditions wp (propagating post-conditions over statements and taking loop in-
variants for granted) and verification conditions vc that aim at verifying loop
invariants. Both take a statement and a DL formula as argument and produce a
DL formula. For this purpose, while loops have to be annotated with loop invari-
ants, and the while constructor becomes: while {f orm} f orm do stmt. Here,
the first formula (in braces) is the invariant, the second formula the termination
condition. The two functions are defined by primitive recursion over statements,
see Figure 5 for the definition of wp (and the Isabelle sources for vc).
7
http://jena.apache.org/
88
wp(Skip, Q) = Q
wp(delete(v : C), Q) = Q[C := C − {v}]
wp(add(v : C), Q) = Q[C := C + {v}]
wp(delete(v1 r v2 ), Q) = Q[r := r − (v1 , v2 )]
wp(add(v1 r v2 ), Q) = Q[r := r + (v1 , v2 )]
wp(select v with b, Q) = ∀v.(b −→ Q)
wp(c1 ; c2 , Q) = wp(c1 , wp(c2 , Q))
wp(if b then c1 else c2 , Q) = ite(b, wp(c1 , Q), wp(c2 , Q))
wp(while{iv} b do c, Q) = iv
Fig. 5: Weakest preconditions and verification conditions
Without going further into program semantics issues, let us only state the fol-
lowing soundness result that relates the operational semantics and the functions
wp and vc:
Theorem 1 (Soundness). If vc(c, Q) is valid and (c, σ) ⇒ σ ′ , then σ(wp(c, Q))
implies σ ′ (Q).
What is more relevant for our purposes is the structure of the formulas gen-
erated by wp and vc, because it has an impact on the decision procedure for the
DL fragment under consideration here. Besides the notion of “essentially univer-
sally quantified” introduced in Section 3.1, we need the notion of quantifier-free
formula: A formula not containing a quantifier. In extension, we say that a state-
ment is quantifier-free if all of its formulas are quantifier-free.
By induction on c, one shows:
Lemma 1 (Universally quantified). Let Q be essentially universally quanti-
fied and c be a quantifier-free statement. Then wp(c, Q) and vc(c, Q) are essen-
tially universally quantified.
There is one major problem with the definition of function wp: the substi-
tutions, such as C := C − {v} or r := r − (v1 , v2 ). When conceiving them as a
meta-operations, as is usually done, we see that substitutions would yield syntac-
tically ill-formed formulas. For example, reducing ([?] r C)[C := C − {v}] would
give ([?] r (C −{v})), which is not a valid concept expression. There are two ways
out of this difficulty: we could either relax our syntax and accept expressions of
the form ([?] r (C − {v})). This would induce a rather heavy change on the logic.
Alternatively, we can treat substitution as a constructor of our language. This is
the approach we have adopted, and therefore, substitutions appear as syntactic
elements in the definitions of Section 3.1. It remains to be seen (in Section 5.2)
how substitutions can be dealt with by proof methods of ALC.
5.2 Tableau Method
The core of the decision procedure for proving the verification conditions that
are obtained as described in Section 5.1 is a tableau calculus which combines
89
the traditional logical rules of a tableau calculus [19] with rules for progressively
eliminating the substitutions which are not part of the logic ALC.
As a consequence, and departing again from common practice in the DL
literature, our tableau procedure does not manipulate facts (in the sense of
Section 3.1), but formulas, i.e. Boolean combinations of facts. This extension
becomes necessary because elimination of substitutions generates complex for-
mulas. These could in principle be directly decomposed into sub-tableaux, but
such a procedure obscures both the presentation and the implementation.
Preprocessing: The tableau manipulates quantifier-free formulas in negation nor-
mal form (nnf ).
The formulas obtained from function vc do possibly contain quantifiers, but
as mentioned before, the formulas are essentially universally quantified. To get
rid of these quantifiers, we therefore perform the following steps:
– We convert the entry formula f to a prenex normal form, i.e. a form ∀x1 . . . xn .b
with quantifier-free body b.
– We drop the quantifier prefix; more precisely, we replace the bound variables
x1 . . . xn in b by free variables. This transformation preserves validity.
– We start the tableau with nnf (¬b). The procedure is a satisfiability check
that either produces an empty tableau (meaning that f is valid) or a model
of ¬b that is a counter-example of f .
In negation normal form, negations only occur in front of atomic concepts
(of the form ¬a, where a is an atomic concept). This invariant is maintained
throughout the tableau procedure.
5.3 Tableau Rules
In the following, we present a high-level description of the tableau procedure.
(The reader consulting the Isabelle theories will notice that the formalization is
on two levels: a set-based, relational version, aiming at proving essential prop-
erties such as soundness and completeness of the rules; and a list-based imple-
mentation. The formal proofs of these theories are not yet finalized.)
A tableau manipulates sets of branches (also called abox es - “assertional
boxes” in DL terminology). Each branch Γ is a set of formulas. We first concen-
trate on a set of rules aiming at decomposing formulas on a single branch. They
have the form Γ ֒− → Γ ′ , expressing that branch Γ is rewriten to Γ ′ . We write
Γ, f instead of Γ ∪ {f } for adding formula f to Γ . The rules are displayed in
Figure 6.
Let us comment on the rules: The structural rules conjC, disjCr, disjCl
(for concepts) and conjF, disjFr, disjFl (for formulas) should be clear. The
rule all allows to conclude y : C if x is only r-connected to elements of type
C, and there is an arc (x r y). The rule some inserts an arc (x r z) and a
membership z : C for an arbitrary z if it is known that x is r-connected to at
least one element of type C. The rule eq propagates an equality x ≡ y in the
branch, provided the equality is not x ≡ x.
90
(x : (C1 ⊓ C2 )) ∈ Γ not((x : C1 ) ∈ Γ and (x : C2 ) ∈ Γ )
conjC
Γ ֒−
→ Γ, (x : C1 ), (x : C2 )
(x : (C1 ⊔ C2 )) ∈ Γ (x : C1 ) ∈
/Γ (x : C2 ) ∈
/Γ
disjCr
Γ ֒−
→ Γ, (x : C1 )
(x : (C1 ⊔ C2 )) ∈ Γ (x : C1 ) ∈
/Γ (x : C2 ) ∈
/Γ
disjCl
Γ ֒−
→ Γ, (x : C2 )
(x : ([!] r C)) ∈ Γ (x r y) ∈ Γ (y : C) ∈
/Γ
all
Γ ֒−
→ Γ, (y : C)
(x : ([?] r C)) ∈ Γ for all y, not((x r y) ∈ Γ and (y : C) ∈ Γ )
some
Γ ֒−
→ Γ, (x r z), (z : C)
(x : (Cτ )) ∈ Γ nnf (push((x : C)τ )) ∈
/Γ
subst
Γ ֒−
→ Γ, nnf (push((x : C)τ ))
(x ≡ y) ∈ Γ x 6= y
eq
Γ ֒−
→ Γ [x := y]
f1 ∧ f2 ∈ Γ not(f1 ∈ Γ and f2 ∈ Γ )
conjF
Γ ֒−
→ Γ, f1 , f2
f1 ∨ f2 ∈ Γ f1 ∈
/Γ f2 ∈
/Γ f1 ∨ f2 ∈ Γ f1 ∈
/Γ f2 ∈
/Γ
disjFr disjFl
Γ ֒−
→ Γ, f1 Γ ֒−
→ Γ, f2
Fig. 6: Tableau rules
The rule subst is applicable for concepts with substitutions. As motivated in
Section 5.1, substitutions cannot be eliminated at once, but they can be removed
progressively, whenever the tableau prover hits on a fact of the form (x : Cτ ).
Note that the variable x was possibly not present in the original tableau with
which we have started the proof, but may have been introduced by a some-rule.
If we encounter such a situation, we push the substitution as far as possible. We
postpone the details to Section 5.5.
A branch Γ contains a clash (clash(Γ )) if either of the following holds:
– for x a variable, (x : ⊥) ∈ Γ
– for x a variable and a an atomic concept, (x : a) ∈ Γ and (x : ¬a) ∈ Γ
– for x, y variables, (x r y) ∈ Γ and (x (¬r) y) ∈ Γ
91
– for x a variable, (x 6≡ x) ∈ Γ
– ⊥∈Γ
5.4 Tableau Procedure
We can now formulate a depth-first-search function df s exploring a tableau. The
function takes a tableau (here implemented as a list of branches) and returns
a list of models. Initially, the tableau is just the formula [{f }] to be proved. If
the resulting list is empty, f is not satisfiable. Otherwise, the list contains an
element which is a model of f .
df s[ ] = []
df s(Γ :: Γs ) = if clash(Γ )
then df s(Γs )
else if reducible(Γ )
then df s({Γ ′ |Γ ֒−
→ Γ ′ }@Γs )
else [Γ ]
The procedure progressively eliminates all inconsistent branches (with clash(Γ )).
If a branch Γ is not inconsistent, but reducible (i.e. , there exists a Γ ′ with
→ Γ ′ ), then we expand the tableau and explore the new branches.
Γ ֒−
5.5 Eliminating Substitutions
The push function used in the subst rule of Figure 6 pushes substitutions into
formulas, “as far as possible”. The remaining tableau rules then decompose for-
mulas until substitutions hidden in subformulas become apparent and the subst
rule can be applied again. Intuitively speaking, this process decreases the “height”
of the substitutions in a formula, until they eventually disappear.
For a formula f , we define push(f ) as the formula f ′ which is the result of
the rewrite system spelled out in the following. Thus: push(f ) = f ′ iff f ∗ f ′ ,
where the rewrite relation is defined in the following. There are numerous
cases to consider, and we do not present all of them.
Substitution in formulas are pushed into subformulas:
– ⊥τ ⊥
– (¬f )τ (¬f τ )
– (f1 ∧ f2 )τ (f1 τ ∧ f2 τ )
– (f1 ∨ f2 )τ (f1 τ ∨ f2 τ )
Substitution in facts: Substitutions of individual variables f [x := y] are carried
out as expected. Otherwise, we procede as follows:
– (x : ¬C)τ x : (¬Cτ )
– (x : C1 ⊓ C2 )τ x : (C1 τ ⊓ C2 τ )
– (x : C1 ⊔ C2 )τ x : (C1 τ ⊔ C2 τ )
92
– For substitutions τ of the form a := a − {v} or a := a + {v}:
• (x : c)[a := a − {v}] (x : c) for a 6= c, and similarly for a := a + {v}
• (x : a)[a := a − {v}] (x : a) ∧ x 6= v
• (x : a)[a := a + {v}] (x : a) ∨ x = v
• (x : ([?] r C))[a := a − {v}] (x : ([?] r C[a := a − {v}])), and
similarly for the other combinations involving constructor [?] or [!] and
substitutions a := a + / − {v}.
– For substitutions τ of the form r := r − {(v1 , v2 )} or r := r + {(v1 , v2 )}:
• (x : c)[r := r − {(v1 , v2 )}] x : c, and similarly for r + {(v1 , v2 )}
• (x : ([!] r′ C))[r := r − {(v1 , v2 )}] (x : ([!] r′ C)) for r 6= r′
• (x : ([!] r C))[r := r − {(v1 , v2 )}]
ite ((x = v1 ) ∧ (v2 : (¬C[r := r − (v1 , v2 )])) ∧ (v1 r v2 ),
(x : (< 2 r (¬C[r := r − (v1 , v2 )]))),
(x : ([!] r C[r := r − (v1 , v2 )])))
Here, ite is for if-then-else: ite(a, b, c) = (a −→ b) ∧ (¬a −→ c).
Please note that the logic ALC cannot completely express the effect of
substitution, and we have to resort to the more expressive logic ALCQ,
which turns out to be complete for substitutions. Thus, the “then” branch
of the ite construct expresses that x is r-connected to less than 2 elements
of (¬C[r := r − (v1 , v2 )]). We have however not yet implemented tableau
rules for ALCQ, so we stick to the simpler logic in this presentation.
• (x : ([!] r C))[r := r + {(v1 , v2 )]
¬((x = v1 ) ∧ (v2 : ¬(C[r := r + (v1 , v2 )])) ∧ (v1 (¬r) v2 ))
∧(x : ([!] r (C[r := r + (v1 , v2 )])))
• Similar rules for existential quantification (x : ([?] r C)).
6 Conclusions
We have presented small-tALC, a framework for executing graph transforma-
tions and proving their correctness with a sound and complete calculus. One of
the distinctive features of the approach is its formal semantic basis. We are now
moving towards application, such as Sparql Query and Update in the knowl-
edge representation world, and model transformations as used in model-driven
engineering. The greatest challenge is the development of logics that are more
expressive than ALC but remain decidable. Even though a low proof-theoretic
complexity is not a major concern for program correctness proofs (these are
not executed on a large knowledge base), the concern changes when wanting to
execute programs efficiently on a large data set.
Acknowledgements We are grateful to María Espinoza who has helped us
explore the applicability of graph transformations to the RDF world [20].
93
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relative to nested conditions. MSCS 19(02) (2009) 245–296
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94
A Study of Bi-Objective Models for Decision Support in
Software Development Process
Vira Liubchenko1,
1
Odessa National Polytechnic University, 1 Shevchenko av.,
65044 Odessa, Ukraine
lvv@edu.opu.ua
Abstract. This paper is concerned with the bi-objective problem in search-
based software engineering for high-level decision-making. The paper presents
bi-objective models for next release problem and modularization quality
problem that characterized by the presence of two conflicting demands, for
which the decision maker must find a suitable balance. The complex nature of
such kind of problem has motivated the application of heuristic optimization
techniques to obtain Pareto-optimal solutions. In this case, limitation on the size
of the problem is reasonable.
Keywords. Search-based software engineering, bi-objective model, next release
problem, modularization problem.
Key Terms. Model, mathematical model, software engineering process.
1 Introduction
Search-Based Software Engineering (SBSE) has become a subfield of software
engineering characterized by growing of activity and research interest. SBSE seeks to
reformulate Software Engineering problems as ‘search problems’ [1] in which
optimal or near-optimal solutions are sought in a search space of candidate solutions,
guided by a fitness function that distinguishes between better and worse solutions.
It has been argued that the virtual nature of software makes it well suited for
Search-Based Optimization (SBO) [2]. This is because fitness is computed directly in
terms of the engineering artifact, without the need for the simulation and modeling
inherent in all other approaches to engineering optimization. This simplicity and
ready applicability make SBSE a very attractive option.
Traditionally SBSE has based on finding the optimal or near-optimal solution to
the problem with respect to a single objective. However, single-objective approach
often is incorrect because of existing of many incomparable objectives in the
95
framework of one problem. Incomparability of objectives makes inapplicable waiting
of the different objectives in order to combine them into a single weighted sum
objective.
This reason has caused applying of multi-objective approaches in SBSE and using
SBSE as a tool for decision support. To underpin the focus on decision support, SBO
problem should be formulated as multi-objective problems, to which a Pareto optimal
approach can be applied [3]. In Pareto optimal approaches, the outcome is a set of
candidate solutions, each of which cannot be enhanced according to one of the
multiple objectives to be optimized without a negative impact on another.
In this paper, we explore existing bi-objective approaches for high-level decision
support in software development process. The rest of the paper is organized as
follows. Section 2 briefly describes using of bi-objective models for Next Release and
Modularization Problems. Section 3 presents SBO on decision-making perspective.
Finally, section 4 draws the main conclusions.
2 Bi-Objective Models at the Early Stages of Software Development
Software engineers have been exploiting many different software development
methodologies that recommend different framework of stages. In this paper, we base
on the fact that high-level decision most often need support on requirement
specification and design stages, which present, more or less, in every methodology.
To explore bi-objective models at these stages, we use papers gathered in repository
of publications on SBSE [4].
2.1 Requirement Specification Stage
One of the core problems of requirement specification stage in incremental
methodologies is Next Release Problem (NRP). Decision maker determines which
features should be included in the next release of the product in order to satisfy the
highest possible number of customers and entail the minimum cost for the company
[3]. NRP is a form of cost-benefit analysis for which a Pareto optimal approach is
attractive.
In NRP a set of customers, C = {c1, ..., cm}, each customer has a degree of
importance for the company that can be reflected by a weight factor, Weight = {w1, ...,
wm}, where w 0,1 and j 1 w j 1 .
m
It is assumed that there is the set of independent requirements, R = {r1, ..., rn}, that
are targeted for the next release of an existing software system. Satisfying each
requirement entails spending a certain amount of resources, which can be translated
into cost terms, Cost = {cost1, ..., costn}.
Satisfaction of requirements provides value for the company. The level of
satisfaction for a given customer depends on the subset of requirements that are
satisfied in the next release of the software product. The requirements are not equally
important for a given customer. Each customer cj (10 if customer j has
the requirement i and 0 otherwise.
In the formulation of the bi-objective NRP, two objectives are taken into
consideration in order to maximize customer satisfaction (or the total value for the
company) and minimize required cost. Let the decision vector x x1,...,xn 0,1
determines the requirements that are to be satisfied in the next release. In this vector,
xi is 1 if the requirement i is selected and 0 otherwise.
The first objective function is considered for maximizing total value:
n m
Maximize xi w j value ri , c j .
i 1 j 1
The problem is to select a subset of the customers’ requirements, which results in
the maximum value for the company.
The second objective function is considered for minimizing total cost required for
the satisfaction of customer requirements:
n
Minimize costi xi .
i 1
In order to convert the second objective to a maximization problem, the total cost
is multiplied by -1. Therefore, the bi-objective model can be represented as follows:
n m
Maximize f1 x xi w j value ri , c j
i 1 j 1
. (1)
n
Maximize f 2 x costi xi
i 1
2.2 Design Phase
Software design usually includes low-level component and algorithm design and
high-level, architecture design. A high-level software engineering problem that is
most related to software architectures is Modularization Problem (MP). Decision
Maker finds the best grouping of components to subsystems. For that, structure of
software system is transformed into a directed graph G, the main question to be
answered is what constitutes a good partition of the software structure graph. The
goodness of a partition is usually measured with a combination of cohesion and
coupling.
Cohesion is a measure of the degree to which the components of a single
subsystem belong together. A high cohesion indicates a good modularization
arrangement because the components grouped within the same subsystem are highly
dependent on each other. A low cohesion, on the other hand, generally indicates a
97
poor modularization arrangement because the components grouped within a
subsystem are not strongly related.
The cohesion Ai of subsystem i with Ni components is defined as:
i
Ai ,
Ni2
where µi is the number of intra-edge dependencies (relationships to and from
components within the same subsystem), N i2 is the maximum number of possible
dependencies between the components of subsystem i.
Coupling is a measure of the connectivity between distinct subsystems. A high
degree of coupling is undesirable because it indicates that subsystems are highly
dependent on each other. Conversely, a low degree of coupling is desirable because it
indicates that individual subsystems are largely independent of each other.
The coupling Eij between subsystems i and j, each consisting of Ni and Nj
components respectively, is defined as:
0 if i j
Eij ij ,
if i j
2 Ni N j
where ij is the number of inter-edge dependencies (relationships to and from
components of subsystems i and j).
In the formulation of the bi-objective MP, two objectives expresses the tradeoff
between cohesion and coupling are taken into consideration in order to create highly
cohesive subsystems and penalize the creation of too many dependencies between
subsystems.
Given software structure graph G partitioned into k clusters, modeled partition of
software system into subsystems, we define MP as:
1 k
Maximize f1 x Ai
k i 1
k k 1 n k
. (2)
Maximize f 2 x ij E
2 i 1 j 1
3 SBO as Decision Support
SBO can be applied to situations in which the human will decide on the solution to be
adopted, but the search process can provide insight to help guide the decision maker.
This insight agenda, in which SBO is used to gain insights and to provide decision
support to the software engineering decision maker, has found natural resonance and
98
applicability when used at the early stages of the software engineering lifecycle,
where the high-level decisions made can have far-reaching implications.
Many of the values used to define a problem for optimization, particularly at the
early stages of the software development process, come from estimates. In these
situations, it is not optimal solutions that the decision maker requires, as much as
guidance on which of the estimates are most likely to affect the solutions. Therefore,
SBO is not merely a research program in which one seeks to ‘solve’ software
engineering problems; it is a rich source of insight and decision support.
Bi-objective problems stated above are NP-hard, and, therefore, cannot be solved
using exact optimization techniques for large-scale problem instances. That is why
metaheuristic search techniques are usually applied to find approximations of Pareto
optimal set (or front) for the bi-objective problem. Decision maker selects the solution
from the found set according to his (her) preferences.
Restriction on SBO approach connected with the point at which the problem
becomes too small. For NRP, limitation is a function of the number of requirements,
which should exceed about 20 requirements. By contrast, there is no number of
customers that is too small for the problem to be worthwhile. For MP, limitation is a
function of the number of components, which should exceed about 20 components.
4 Conclusion
Vital errors in software engineering such as too many requirements being realized in
release and poor quality of software architecture are caused by false intuition of the
decision maker. SBO can address this problem, it automatically scour the search
space for the solutions that best fit the human assumptions in the objective functions.
However, it has been widely observed that search techniques are good at producing
unexpected answers. Automated search techniques effectively work in tandem with
the human encapsulating human assumptions and intuition.
Future work will consider modification of SBO for including dependency
relationship between requirements in NRP, between components in MP, and
exploring the integrated model for both problems.
References
1. Harman, M., Jones, B.F.: Search based software engineering. Information and Software
Technology, 43(14), pp. 833--839 (2001)
2. Harman, M.: Why the virtual nature of software makes it ideal for search based optimization.
In: Proceedings of the 13th International Conference on Fundamental Approaches to
Software Engineering (FASE’10). LNCS, vol. 6013, pp. 1--12. Springer, Heidelberg (2010)
3. Durillo, J.J., Zhang, Y., Alba, E., Harman, M., Nebro, A.J.: A study of the bi-objective next
release problem. Empirical Software Engineering, vol. 16(1), pp. 29--60 (2011)
4. Repository of Publications on Search Based Software Engineering,
http://crestweb.cs.ucl.ac.uk/resources/sbse_repository/repository.html
99
5. Doval, D., Mancoridis, S., Mitchell, B.S.: Automatic Clustering of Software Systems using a
Genetic Algorithm. In: Proceedings of Software Technology and Engineering Practice, pp.
73--91 (1998)
100
Method of Evaluating the Success of Software Project
Implementation Based on Analysis of Specification Using
Neuronet Information Technologies
Tetiana Hovorushchenko1, Andriy Krasiy2
1
Khmelnitsky National University, Khmelnitsky, Ukraine
tat_yana@ukr.net
2
Khmelnitsky National University, Khmelnitsky, Ukraine
andriy-krasiy@yandex.ua
Abstract. The actuality and importance of skill to evaluate the possible success
of software project based on SRS were showed in this paper. The aim of
research is prediction of characteristics and evaluating the success of software
project implementation based on analysis of SRS. Method of evaluating the
success of software project implementation based on analysis of SRS using
neuronet information technologies was first proposed. This method provides the
prediction of success of software projects implementation, comparison of
software projects on the basis of SRS and choice of the best SRS of project.
Keywords: software requirements specification (SRS), software project, suc-
cess of project implementation, SRS indicators, project characteristics, integra-
tive indicator of project, the degree of success of the project implementation.
Key Terms: Model-Based Software System Development, Software Compo-
nent, Software System, Specification Process.
1 Introduction
Statistics of success of software projects implementation according to The Standish
Group International [1] showed that the rate of challenged projects (that late, over
budget, and/or with less than the required features) is the constant value (42-46%
projects). These statistics reflect the high rate of non-quality (the failed and the chal-
lenged) software projects in terms of interpretation of software quality [2].
As shown in [3], the errors of requirements formulation are 10-25% of all errors.
The analysis of errors of embedded and application software, which were made at the
stage of the requirements formulation, is given in [4]. In [5-7] the fact is confirmed,
that the causes of many incidents and accidents through software are in the SRS,
rather than in coding. In [6] the experiment is described, which showed that the
software versions written by different developers for the same requirements, contain
the joint errors associated with errors of SRS. These experimental statements leads to
101
the need to deepen of the SRS analysis. So the actual and important is the skill of
evaluation of the success of project implementation on the basis of SRS. The aim of
this research is the prediction of the characteristics and evaluation of success of
implementation of software project based on the SRS analysis.
The success of software project implementation is timely execution of software
project within the allocated budget and with realization of all necessary features and
functionality. It can be estimated at the design stage based on the predicted values of
the main project characteristics [8-10] - duration, cost, complexity, cross-platform,
usability and quality. Duration is the sequence of the project stages based on the
needs of project management. The relative duration is evaluated as compared to other
software projects. Cost is difficult to assess at the early stages because it is highly
dependent on the number of lines of code (the cost of one line is 0.5$). At the early
stages of the life cycle we can evaluate the relative cost (as compared to other pro-
jects). Complexity is determined by the number of interacting components, the num-
ber of connections between the components and the complexity of their interactions.
Cross-platform is the ability of software to run on more than one hardware platform
and/or operating system. Usability is effectiveness, profitability and satisfaction of
users by software project. Quality is the degree of compliance with the software
characteristics of requirements. From the determinations of characteristics it is clear
that none of them are part of other characteristic, that justifies this choice [9, 10].
Analysis shows, that the existing methods and tools [9, 10] of characteristics
determination are not suitable to evaluation of their values at the stage of
requirements formulation, since they focus on the ready source code. The known
methods (Using natural language processing technique, Using CASE analysis method,
QAW-method, Using global analysis method, O’Brien’s approach, Method to discov-
er missing requirement elicitation, Selection of elicitation technique, Comparison and
categorization of requirements elicitation techniques, Techniques for ranking and
prioritization of software requirements) and tools (OSRMT, Tools by LDRA, Sigma
Software, DEVPROM, CASE.Analytics) of SRS analysis and existing technologies of
risk management (SEI, SRE, CRM, TRM, FSI, ERM) [9-13] are not suitable for
quantitative evaluation of the project characteristics, because all are targeted to con-
trol over compliance with requirements of SRS, but none of them define the predicted
values of characteristics on the SRS analysis.
Then for prediction of success of software project implementation on the analysis
of SRS the task of research is development of method of evaluating the success of
software project implementation based on analysis of specification.
2 Method of Evaluating the Success of Software Project
Implementation Based on Analysis of Specification Using
Neuronet Information Technologies (MESSPI)
Method of evaluating the success of software project implementation based on analy-
sis of SRS consists of next stages: 1) neuronet prediction of characteristics of software
project based on the analysis of specification; 2) interpretation of the received relative
102
values of the software project characteristics; 3) evaluation of the degree of success of
the software project implementation; 4) testing of the stability and acceptability of
compensations of software project characteristics.
Let the software project is specified by the SRS [14] in the next formalized form:
SRS=, (1)
where R1 – the set of indicators of section1 of the SRS, R2 – indicators of section2,
R3 – indicators of section3, R4 – indicators of section4. Selection and possible values
of SRS indicators from the sets R1-R4 were detailed in [9].
The first stage of MESSPI is prediction of software project characteristics on the
SRS analysis, result of that is determining of the relative values of characteristics:
SCH={Cs,Dsp,Cx,Cp,Ub,Qs}, (2)
where Cs – software project cost, Dsp –duration, Cx –complexity, Cp – cross-
platform, Ub – usability, Qs – quality.
Some indicators of specification [9] affect the above characteristics, but equations
is not known, by which can calculate the characteristic value on the basis of the sets
of SRS indicators – all available formulas of characteristics evaluation is oriented to
ready source code [9, 10]. Hecht-Nielsen's theorem proves the possibility of solving
the task of representation of multidimensional function of arbitrary form on the
artificial neural network (ANN). Therefore, ANN will be used to implement of the
unknown functions of dependence of the project characteristics on SRS indicators. In
[9] the ANN was developed, which processes and approximates the set of SRS
indicators and provides the predicted quantitative values of characteristics - Fig. 1.
Selection and possible values of ANN inputs, equations for ANN functioning and
forming of ANN outputs (predicted relative values of the characteristics) were
detailed in [9], so this information is not represented in this paper.
ANN of characteristics prediction based on the SRS analysis was trained so that
all values of characteristics are the values of the interval (0, 1]. The value of each
characteristic nearly to 0 negative affects on the success of project implementation
(high cost, duration and complexity; low quality, usability, cross-platform). The value
nearly to 1 positive impacts on the success of the project implementation (low cost,
duration, complexity; high quality, usability, cross-platform).
Fig. 1. The concept of neuronet prediction of characteristics of software project based on the
analysis of specification
103
Let the ANN provided the following set of values of characteristics of project Sp:
SCHANN={CsANN, CxANN, DspANN, UbANN, CpANN, QsANN} (3)
The developers and customers are difficult to comprehensively assess the success
of software project implementation on the basis of the ANN's relative values of main
characteristics. Therefore, the second stage of MESSPI is the interpretation of the
received relative values of the project characteristics.
For this we introduce the integrative indicator of software project. Integrative in-
dicator IipSp – is the quantitative indicator of project implementation success based on
the set SCHANN. We cannot to establish mutual dependence of them and to determine
their impact on the integrative indicator of software project - these formulas and func-
tions are not available. Therefore, we assume that all six predicted characteristics are
equally important to the success of the project, and the integrative indicator of project
depends equally on all six characteristics. In the absence of formulas and functions
the simplest and the most obvious way of definition of integrative indicator of project
is the using of its graphic presentation (in the classic radar chart, the axes of which
there are six characteristics of the project - Fig. 2). Then the integrative indicator of
project is area of figure, which are shaped the predicted (by ANN) values of the pro-
ject characteristics. Because ANN predicts the values of 6 characteristics, the coordi-
nate system (Radar chart) will have 6 axes (the angle between the axes is 60°), and in
accordance the integrative indicator of project is area of the hexagon
CsANNCxANNDspANNUbANNCpANNQsANN highlighted thick line on Fig. 3.
Fig. 2. The coordinate system for IipSp Fig. 3. The graphical representation of IipSp and Iipmax
For calculation of integrative indicator IipSp we will divide the hexagon into six
triangles, will calculate the area of each triangle with two sides (value of characteris-
tics) and angle between them (60°) and will add the obtained values of triangles areas:
SCsOCx=½*CsANN*CxANN*sin60°=0.5*0.866* CsANN*CxANN, (4)
IipSp=0.5*0.866*(CsANN*CxANN+ CxANN*DspANN+ DspANN*UbANN+ UbANN*CpANN+
+CpANN*QsANN+ QsANN*CsANN) (5)
The order of hexagon axes was selected taking into account of features of ANN
training and for reasons of inability of compensation of the low values of some
characteristics by high values of other characteristics (as all six characteristics are
104
important for the software project). Formula (5) shows that pairwise multiplication of
the characteristics values can allow these compensations. Therefore, the upper part of
the coordinate system has three axes for characteristics Ub, Cp, Qs, and the lower part
consists of three axes for characteristics Dsp, Cx, Cs, for which the rule of ANN
training is: the value of characteristic nearly to 0 means high cost, duration,
complexity and low quality, usability, cross-platform. The junction of axes for
characteristics from different categories was selected in pairs exactly as low value of
cost (Cs→1) shall not compensate low value of quality (Qs→0), short value of
duration (Dsp→1) can not compensate low value of usability (Ub→0).
We will need also the maximum possible value of integrative indicator of project:
Iipmax – is the area of hexagon CsCxDspUbCpQs highlighted dotted line on Fig. 3.
ANN was trained so that maximum possible value of each characteristic – is 1. Then:
Iipmax=0.5*0.866*( 1*1+ 1*1+ 1*1+ 1*1+ 1*1+ 1*1)=2.598 (6)
By itself, the integrative indicator of project is uninformative to the developer and
customer due to the difficulty of interpretation of its value, therefore the third stage of
MESSPI is the evaluation of the degree of success of project implementation based on
the integrative indicator of project. The value Iipmax=2.598 – is the best value of inte-
grative indicator, then the degree PIip of success of project implementation is:
PIip=IipSp/Iipmax=IipSp/2.598=0.385*IipSp (7)
The value of the degree of success of the software project implementation nearly
to 0 indicates the low success of software project implementation.
As mentioned above, the compensation of values of the characteristics with the
same value of integrative indicator is not always correct. Then the fourth stage of
MESSPI is the testing of the stability and acceptability of characteristics compensa-
tions. If the hexagon CsANNCxANNDspANNUbANNCpANNQsANN (area of which is the
integrative indicator) will be convex, the characteristics of software project is
considered the stable, and their compensatory effects are acceptable (valid). We
introduce the indicator AceSp of stability and acceptability of compensatory effects of
the characteristics. This indicator will take the value “True”, if characteristics are
stable, their compensatory effects are acceptable (i.e. hexagon is convex).
Criterion of convexity of hexagon is the simultaneous fulfillment of two
conditions: 1) the same sign of sines of all angles of the hexagon; 2) the sum of all the
angles of hexagon is 720° (by theorem about sum of the angles of convex polygon).
Here are the steps to determine of the angles of the hexagon (by Fig. 3):
1) calculate the unknown third side for each triangle by law of cosines; 2) find one
unknown angles in each triangle by law of cosines; 3) find second unknown angle in
each triangle by theorem about the sum of angles; 4) find the angles of the hexagon.
After finding of the angles of the hexagon we should find sines of obtained angles
and compare their signs. And we should find the sum of the obtained angles and
compare this sum with 720°. If the sum of the angles of hexagon is 720° and sines of
angles have the same signs, then hexagon is convex, accordingly indicator of stability
and acceptability of compensatory effects of the characteristics AceSp=True.
105
3 Experiments
We performed experiments on the practical use of the MESSPI. For this we
considered four alternative software projects, developed by different teams of devel-
opers to solve the same task – development of support system (web-portal) for prac-
tices of students of IT-specialties. Each development team consists of three IT profes-
sionals: project manager, requirements engineer and web-developer. Specialists from
different teams had the same level of qualifications and the same experience in similar
projects: project manager and requirements engineer of each team previously worked
in three similar successful projects, web-developer of each team previously worked in
two similar successful projects. All four development teams represented the different
software companies of Khmelnitsky. Each development team had the equal oppor-
tunity to communicate with the customer for identification of customer requirements.
Three joint meetings of all developers of four teams and representatives of the cus-
tomer were organized. In addition, individual meetings of team representatives and
representatives of the customer took place. As a result of working together with cus-
tomer representatives all four development teams offered their SRS.
The sets R1-R4 of SRS indicators were formed for the each of four SRS and sub-
mitted for processing to the ANN. The results of ANN (predicted relative values of
the characteristics), the calculated by MESSPI integrative indicators and degree of
success of these projects implementation are in Table 1.
Table 1. Predicted relative values of characteristics, calculated integrative indicators and
degree of success of four software projects implementation
Characteristics and indica- Values for Values for Values for Values for
tors of software project Project1 Project2 Project3 Project4
Cost CsANN 0.8 0.22 0.39 0.59
Duration DspANN 0.9 0.19 0.41 0.57
Complexity CxANN 0.75 0.31 0.37 0.62
Usability UbANN 0.85 0.15 0.5 0.56
Cross-platformCpANN 0.87 0.21 0.47 0.57
Quality QsANN 0.89 0.17 0.49 0.61
Integrative indicator IipSp 1,847 0,113 0,501 0,894
The degree of success PIip 0.7111 0,0435 0.1929 0.3442
Thus, the results of Table 1 demonstrate that Project1 has the greatest predicted
degree of success of implementation (71%) and Project2 has the smallest predicted
degree of success of implementation (about 4%). Therefore the Project1 (SRS of Pro-
ject1) was proposed to the developer and the customer for solution of their task.
If we will not take into account the compensation of low values of some
characteristics by high values of other characteristics in the calculation of integrative
indicator of the project, there is a risk for the obtaining of following results. Let the
ANN gived certain values of characteristics for five different software projects. We
show these values and the corresponding values of integrative indicators in Table 2.
106
The data of Table 2 show that all five software projects have the same integrative
indicator IipSp=0.894, but have significantly different relative values of
characteristics. We need to check the convexity of the hexagons for all examined
software projects for determination of value of indicator AceSp - Table 3.
Table 2. Examples of compensation of characteristics for different software projects
Characteristics and indica- Values Values Values Values Values
tors of project for Pr.4 for Pr.5 for Pr.6 for Pr.7 for Pr.8
Cost CsANN 0.59 0.7 1 1 0.93
Duration DspANN 0.57 0.57 0.57 0.57 0.57
Complexity CxANN 0.62 0.62 0.62 0.62 0.62
Usability UbANN 0.56 0.56 0.56 0.403 0.56
Cross-platformCpANN 0.57 0.57 0.57 0.57 0.57
Quality QsANN 0.61 0.503 0.289 0.403 0.33
Integrative indicator IipSp 0.894 0.894 0.894 0.894 0.894
Table 3. Testing of the stability and acceptability of compensatory effects of the characteristics
for eight software projects
Values Pr.1 Pr.2 Pr.3 Pr.4 Pr.5 Pr.6 Pr.7 Pr.8
Sine of angle Qs + + + + + - + -
Sine of angle Cs + + + + + + + +
Sine of angle Cx + + + + + + + +
Sine of angle Dsp + + + + + + + +
Sine of angle Ub + + + + + + + +
Sine of angle Cp + + + + + + + +
Indicator AceSp True True True True True False True False
The testing of the stability and acceptability of compensations of characteristics of
software projects showed that for Project6 and Project8 the characteristics are
unstable, i.e. compensations of these characteristics are unacceptable.
4 Conclusions
This paper shows: the need of deepening of the SRS analysis; the dependence of
quality and success of software project implementation on the SRS; the actuality and
importance of the skill of evaluation of software project implementation success
based on the SRS; the need of support of the choice of the best SRS for the project.
The authors first proposed the method of evaluating the success of software
project implementation based on analysis of specification using neuronet information
technologies. MESSPI differs from the known methods (analysed in [8-13]) that pro-
vides the prediction of the success of software projects implementation based on only
SRS. The practical significance of the proposed method is the support in the
comparison of software projects on the basis of SRS, the choice of the best SRS of
107
project, and control for SRS quality also (SRS quality is very importance, as known
[14]). The proposed method is suitable only for software projects, for which SRS are
existing and available. This method helps to "cut off" the software projects with failed
SRS, because, as shown above, the software projects with failed requirements and
specifications can not be successfull at the implementation.
The authors have following perspectives for future researches: 1) increasing of the
veracity of ANN functioning for increasing of the MESSPI veracity; 2) selection of
variant component for ANN; 3) providing recommendations about that is necessary to
be changed in the SRS, that project became successful; 4) development of information
technology for prediction of characteristics and evaluation of success of software
project implementation based on the SRS analysis; this information technology
should support: the SRS indicators collection, the processing of this data by ANN, the
collection of the relative values of characteristics, the calculation of the integrative
indicator and the degree of success of the software project implementation, and test-
ing of the stability and acceptability of characteristics compensations.
References
1. The Standish Group International: CHAOS Manifesto – Think big, act small. Technical
report, CHAOS Knowledge Center (2013)
2. Bourque, P., Fairley, R.: Guide to the software engineering body of knowledge
(SWEBOK): Version 3.0. A project of the IEEE Computer Society (2014)
3. McConnell, S.: Code complete. Microsoft Press (2013)
4. Pomorova, O., Hovorushchenko, T.: The modern problems of software quality evaluation.
Radioeletronic and computer systems. 5, 319-327 (2013) [in Ukrainian]
5. Levenson, N.G.: Systemic factors in software-related spacecraft accidents. In: AIAA
Space Conference and Exposition, pp.1-11 (2001)
6. Levenson, N.G.: Software challenges in achieving space safety. Journal of the British In-
terplanetary Society. 62, 265-272 (2009)
7. Ishimatsu, T., Levenson, N., Thomas, J., Fleming, C., Katahira, M., Miyamoto, Y., Ujiie,
R.: Hazard analysis of complex spacecraft using systems-theoretic process analysis. Jour-
nal of Spacecraft and Rockets. 51, 509-522 (2014)
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best practices. Springer-Verlag Berlin Heidelberg, Berlin (2012)
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analysis of specifications. Computer-Integrated Technologies: Education, Science, Indus-
try. 66-76 (2014) [in Ukrainian]
10. Fenton, N.: Software metrics: A rigorous approach (3rd edition). CRC Press (2014)
11. Chen, A., Beatty, J.: Visual models for software requirements. MS Press, Washington
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12. Fatwanto, A.: Software requirements specification analysis using natural language pro-
cessing technique In: International Conference on Quality in Research, pp.105-110 (2013)
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14. IEEE 830-1998. Recommended practice for software requirements specifications (1998)
108
Calculation Method for a Computer’s Diagnostics of
Cardiovascular Diseases Based on Canonical
Decompositions of Random Sequences
Igor P. Atamanyuk1, Yuriy P. Kondratenko2
1
Mykolaiv National Agrarian University, Commune of Paris str. 9,
54010 Mykolaiv, Ukraine
atamanyukip@mnau.edu.ua
2
Petro Mohyla Black Sea State University, 68th Desantnykiv Str. 10,
54003 Mykolaiv, Ukraine
yuriy.kondratenko@chdu.edu.ua
Abstract. The canonical decomposition of sequence describing the change of
cardiograms is put in the basis of the method for a computer system of disease
diagnostics. Obtained criterion of the solution of the problem of electrocardio-
grams classification is considerably simpler than the known criterion of making
decision on the basis of the criterion of the maximum of density of distribution.
The transition from multi-dimension density distribution to producing of uni-
dimensional densities that allows to use random number of parameters of elec-
trocardiograms for diagnostics is offered to carry out. The results of numerical
experiment confirm the effectiveness of the offered method and high reliability
of the processes of identification of cardiovascular diseases identification on the
basis of its usage.
Keywords: calculation method, medical diagnostics, electrocardiogram, ran-
dom sequence, canonical decomposition.
Key Terms: computation, mathematical model.
1 Introduction
At present, cardiovascular diseases head the list among the most widespread and dan-
gerous diseases of modernity [1]. According to the data of the world Health Organiza-
tion the death rate because of heart diseases in Ukraine reaches 64%, in the USA heart
disease affects more than 800 000 people annually. At present the number of heart
diseases among capable of working population sharply increased (quite often the age
of the sick person with cardiac infarction doesn’t exceed 23-25 years).
As heart diseases belong to the diseases which course and results of treatment di-
rectly depend on timely detection and elimination of pathological deviations the relia-
ble diagnostics is the most important and primary task in the problem of cardiovascu-
lar diseases. As of today a great number of approaches [2-12] for the solving of the
109
given task with the usage of different mathematical methods including statistical
methods, methods of computational intelligence, fuzzy logic, neural network model-
ing algorithms and others are worked out.
Let us consider some related works concerning the methods for analysis of electro-
cardiograms using automated techniques, modern information technologies and com-
puter systems. For example, such investigations were started at the University of
Glasgow (Uni-G), United Kingdom more than 40 years ago and are continuing as
Uni-G ECG Analysis Program [13] based on development of different approaches, in
particular: methods for processing waveforms recorded in groups of three leads simul-
taneously, 12-lead ECG analysis program, optional approaches to computing the av-
erage QRS cycle including a simple mean, a weighted mean and a median beat,
rhythm analysis, Brugada pattern, neural networks, rule based criteria, software diag-
nostic criteria based on age, sex, race, clinical classification, drug therapy and so on.
A dynamic hybrid architecture is descripted in [14] for ECG data analysis, combin-
ing the fuzzy with the connectionist approach. The data abstraction is performed by a
layer of Radial Basis Function (RBF) units and the upcoming classification is carried
out by a classical two-layer feedforward neural network. For the evaluation a large
clinically validated ECG database is explored, but a more detailed description of the
input space using a larger number of RBF units does not grant sufficient improve-
ments.
Leiden ECG Analysis and Decomposition Software (LEADS) was developed [15]
at the Leiden University Medical Center, The Netherlands as a MATLAB program for
research oriented ECG/VCG analysis. LEADS focuses on the determination of a low-
noise representative averaged beat (QRST complex), in which multiple parameters
can be measured, paying special attention to the T wave. LEADS generates a default
selection of beats for subsequent averaging.
The paper [16] presents the current status of principal component analysis (PCA)
for ECG signal processing and describes the relationship between PCA and
Karhunen-Loeve transform.
Several ECG applications based on PCA techniques have been successfully em-
ployed, including data compression, ST-T segment analysis for the detection of myo-
cardial ischemia and abnormalities in ventricular repolarization, extraction of atrial
fibrillatory waves for detailed characterization of atrial fibrillation, and analysis of
body surface potential maps.
Advances in sensor technology, personal mobile devices, wireless broadband
communications, and Cloud computing are enabling real-time collection and dissemi-
nation of personal health data to patients and health-care professionals anytime. This
approach was proposed in [17] for creating an autonomic cloud environment for host-
ing ECG data analysis services.
A solution in [18] leverages the advance in multi-processor system-on-chip archi-
tectures, and is centered on the parallelization of the ECG computation kernel.
The article [19] reviewed time domain, frequency domain, premature complexes
detection, heart rate variability, and nonlinear ECG analysis based methods.
Several different approaches for ECG analysis are based on a chaos theory [20], a
combination of statistical, geometric, and nonlinear heart rate variability features [21],
110
a semantic web ontology and heart failure expert system [22], learning system based
on support vector machines [23], signal averaging method, multivariate analysis [24],
RPCA - recursive principal component analysis [25], nonlinear PCA neural networks
[26], cluster analysis, SPSA - simultaneous perturbation stochastic approximation
method [27], ABT - Amplitude Based Technique, FDBT - First Derivative Based
Technique, SDBT - Second Derivative Based Technique [28], Hilbert transform [29]
and so on.
At the same time each from above-mentioned methods has its disadvantages and
limitations. Just therefore the necessity of the working out of new effective methods
of medical diagnostics didn’t lose its actuality.
2 Statement of the problem
One of the most widespread methods of diagnostics and detection of cardiovascular
diseases is an electrocardiography, a method of graphic registration of the characteris-
tics of the electric field of a heart and their changes in the process of heart contrac-
tions. Electrocardiogram is characterized with a set of teeth by time and amplitude
parameters of which the diagnosis is done. Taking into account that changing of the
parameters of electrocardiogram has accidental character the problem of the classifi-
cation of the realization of random sequence (some disease or absence of a disease
correspond to every class) is the mathematical content of heart diseases diagnostics.
For the purpose of the increase of the reliability of the diagnostics of cardiovascular
diseases it is necessary to work out on the basis of the theory of random sequences the
method of electrocardiogram recognition with taking complete account of their sto-
chastic qualities.
3 Solution
The object of investigation is the random consequence
X X 1 , X 2 ,..., X 12 with twelve elements each of which corresponds to
some the most informative parameter of the electrocardiogram Fig. 1 (as appropriate
the number of parameters can be increased): X 1 is the width of the tooth P; X 2
is the height of the tooth P; X 3 is the interval P–Q; X 4 is the height of the tooth
Q; X 5 is the interval QRS; X 6 is the height of the first tooth R; X 7 is the
height of the second tooth R; X 8 is the height of the tooth S; X 9 is the interval
Q-T; X 10 is the height of the tooth T; X 11 is the duration of the first cycle of
the cardiogram; X 12 is the duration of the second cycle of the cardiogram.
111
Fig. 1. Teeth and intervals on the cardiogram
As the result of electrocardiography conducting some sequence of values
x i , i 1,12 about which it is known a priori that it is generated by one of the ran-
dom sequences X ( j ) i , i 1,12, j 1, J ( J 1 of diseases and normal state) is ob-
tained. It is necessary to define to which of these sequences exactly (to which of J
classes) relates to given realization. Formulated in such a way the problem of recogni-
tion completely comes to standard Bayes approach but during the usage of Bayes
criterion improbable (and that is why especially dangerous) diseases can not be rec-
ognized. Thereupon for solving of the problem of medical diagnostics the most ac-
ceptable is the criterion of the maximum of probability according to which during the
observation of the realization x x 1 , x 2 ,..., x 12 that hypothesis is taken
which meets the condition:
j* arg max f12 x / j , (1)
j
where f12 x / j , j 1, J is the relative density distribution of the symptoms x
provided that the realization belongs to the given class.
The problem of the recognition of random sequence realization comes to the de-
termination of the belonging of the realization x to one of J given distributions
f12 x / j , j 1, J .
112
Thus the following stage is the assessment of the unknown densities
f12 x / j , j 1, J that in its turn taking into account the great number of the results
of x i , i 1,12 observations is quite difficult and laborious procedure. Given prob-
lem in the context of linear relations is essentially simplified [30] during the transition
from sequence x i , i 1,12 to the analysis of the set of uncorrelated values
vi , i 1, I , which are determined from the canonical model of random sequence [31]
presentation:
i
X i V i , i 1,12, (2)
1
i 1
Vi X i V i , i 1,12, (3)
1
1
1
i M X X i D j j j i , 1, I , i , I . (4)
D j 1
i 1
Di M X 2 i D 2 i , i 1,12 , (5)
1
where i , , i 1, I is nonrandom coordinate function: 1, i 0 , if
i.
In this case the substitution of x for vector v taking into account
12
f I v / j f1 vi / j , j 1, J allows to put down the criterion of decision making
i 1
in the following form:
12
j* arg max f1 vi / j , j 1, J . (6)
j i 1
The problem of recognition thus comes to consecutive approximation of twelve
one-dimensional densities of distribution. The stochastic algorithm of diagnostics
becomes simpler essentially but the transition from the vector x to the vector v is
possible provided that the random sequences X i / j , i 1,12, j 1, J have only
linear relations. Taking down of the limitations of the random sequences
X ( j ) i , i 1,12, j 1, J normal distribution is possible as a result of the usage of
the corresponding nonlinear canonical decomposition [32-35]:
i 1 N 1
Vi( ) X i V( j )
( j)
i Vi( j ) ( ij ) i , i 1,12; (7)
1 j 1 j 1
113
D i i , i 1,12; (8)
i 1 N 2 1 2
D i M X 2 i D j
( j)
i ( j)
1 j 1 j 1
j i
1 N
h( ) i
1
M X X h i D j ( ) h i
( j) ( j)
D 1 j 1
(9)
1
D j
( j)
h(j ) i , 1, N , 1, i.
j 1
Taking into account different qualities of random sequences
X i / j , i 1,12, j 1, J parameters of the canonical decomposition (7)-(9) are
unique for each of the investigated sequences. The advantage of the decomposition
(7)-(9) usage is that their independence follows from noncorrelatedness Vi( N ) , i 1, I
as all stochastic relations of much lower order are removed from the given coeffi-
cients. Thus the same as in the previous case the conversion of the problem of recog-
nition from twelve measured space of the characteristics X 1 ,..., X 12 into the
space of the characteristics V ( N ) ,..., V ( N ) 1 12
of the same dimension simplifies the
procedure of the assessment of the densities of distribution
12
f12 v( N ) ,..., v( N ) / j f1 vi( N ) / j , j 1, J that comes to the approximation of
1 I
i 1
twelve unidimensional densities of distribution. The criterion of making decision
takes the following form
12
j* arg max f1 vi( N ) / j , j 1, J .
j i 1
(10)
The absence of the assumptions about the kind of the density distribution of the
random values V ( N ) ,..., V ( N ) comes to the necessity of the usage of nonparametric
1 12
methods for their description. The simplest and the most effective approach under
given conditions is the usage of nonparametric assessments of Parzen-type [36]:
dL1 g u ,
L
f L vi( N ) l (11)
l 1
where ul d 1 vi( N ) vi(,N
l
)
, vi(,N )
l , l 1, L are the realizations of the random value
Vi (N )
, g ul is a certain weigh function (kernel); d is a constant (coefficient of
blurriness).
114
The choice in the capacity of the function of the kernel of g u of steady density
distribution allows to write down the expression for the assessment of the density
distribution of Vi( N ) in the following form:
dL1 g v ,
L
f L vi( N ) l
(N )
i
l 1
where
0,5, v( N ) d v( N ) v( N ) d ,
i ,l i i,l
gl vi( N ) l 1, L;
(N ) (N)
0, vi vi,l d ,
d 0,5sup vi(,N ) (N) (N) (N)
l vi,l 1 , vi,l vi,l 1 , l 2, L.
l
The method of diagnostics of cardiovascular diseases on the basis of the offered
algorithm and criterion of making decisions presupposes the fulfillment of the follow-
ing phases:
Phase 1. Collection of statistic information about each investigated random se-
quence X ( j ) i , i=1, I , j=1, J ;
Phase 2. Calculation on the basis of the accumulated realizations xl( j ) i , i 1, I ;
l 1, L j ; j 1, J for the investigated sequences X ( j ) i , i=1, I , j=1, J discretized
moment functions M X l X h i ;
Phase 3. Forming for each sequence X ( j ) i , i=1, I , j=1, J the canonical decom-
position (7);
Phase 4. Obtaining on the basis of statistic information the assessments of one-
dimensional densities of the distribution of the random coefficients of the canonical
decompositions of the random sequences X ( j ) i , i=1, I , j=1, J ;
Phase 5. Decomposition of the recognizable realization by canonical expressions;
calculation of the values of one-dimensional densities of distribution of coefficients
formed as a result of decompositions; determination of the belonging of the realiza-
tion of a certain random sequence X ( j ) i , i=1, I (diagnostics of a disease) with the
*
help of a rule (10);
Phase 6. Entry of the recognized realization x ( j ) i , i=1, I into the base of statis-
*
tical data of the corresponding random sequence X ( j ) i , i=1, I .
*
115
The scheme of the functioning of the system of cardiovascular diseases diagnostics
is represented in Fig. 2.
In modern medicine more than one hundred different cardiovascular diseases are
classified [1]. Developed six-stage algorithm is tested on five the most widespread
diagnoses: “healthy heart” – is a random sequence X i /1 , i 1,12 ; “hypertrophy
of myocardium” - X i / 2 , i 1,12 ; “severe arrhythmia” - X i / 3 , i 1,12 ;
“stenocardia of the 2d functional class” - X i / 4 , i 1,12 ; “neurocirculatory dys-
tonia of light degree” - X i / 5 , i 1,12 .The check of the statistical hypothesis
about the independence of random coefficients of the canonical decomposition (7) on
the basis of the criterion 2 showed the validity of the hypothesis by N 3 for all
three sequences with the probability not less than PD 0,98 . Thus the decomposition
(7) with the corresponding set of coordinate functions h( ) i , h, 1,3, , i 1,12
modifies into the adequate model of the investigated random sequence
X i / j , i 1,12, j 1,3 . For example, in Table 1 values 1(1)
i , , i 1,12 for
X i / 3 , i 1,12 are represented.
Fig. 2. Scheme of functioning of the computer system of cardiovascular diseases diagnostics
Recognition of the diagnoses was done on the basis of 200 different cardiograms
for each disease. Comparative results of recognition of the diagnoses (a) on the basis
of the developed by the authors calculating method, (b) on the basis of neuronic net-
work [37] synthesized with the usage of Daubechies wavelet function of the 4th de-
gree and Levenberg-Marquardt algorithm (for training) and (c) on the basis of the
usage of fuzzy logic in medical diagnostics [3, 4] during the realization of the systems
of fuzzy logic inference of Mamdani-type are presented in Table 2.
Neuronic network that was used in calculating experiment (Table 2) has the fol-
lowing pecularities.
116
1. Expressions for the determination of approximation coefficients and detailing of
discrete wavelet transform are of the form [37]:
1
W j0 , k f x j0 ,k x ,
M x
1
W j, k f x j ,k x ,
M x
where j ,k x , j ,k x is a family of basic functions.
Table 1. Values of the coordinate function 1 i for random sequence
(1)
X i / 3 , i 1,12
2 3 4 5 6 7 8 9 10 11 12
1 0,14 1,46 0,12 0,92 1,49 0,06 0,22 3,06 -0,36 7,11 5,66
2 1 6,50 0,34 3,81 5,70 0,37 1,56 12,5 -2,41 28,72 22,1
3 0 1 0,08 0,63 1,01 0,04 0,15 2,13 -0,24 4,91 3,92
4 0 0 1 4,22 9,07 0,72 1,12 14,1 -0,18 33,40 25,3
5 0 0 0 1 1,22 0,20 0,29 3,02 -0,25 6,42 5,46
6 0 0 0 0 1 0,08 0,15 1,61 -0,14 3,79 2,79
7 0 0 0 0 0 1 0,24 2,70 -0,53 6,16 5,05
8 0 0 0 0 0 0 1 5,69 -0,50 11,17 9,52
9 0 0 0 0 0 0 0 1 -0,07 2,12 1,82
10 0 0 0 0 0 0 0 0 1 -6,08 -4,1
11 0 0 0 0 0 0 0 0 0 1 0,83
12 0 0 0 0 0 0 0 0 0 0 1
2. Outcoming signal of each of separate neuron of outcoming layer was forming as
1 K N
y k f wki f wij x .
M i 0
j 0
3. As activation function of each separate neuron continuous sigmoid bipolar func-
tion f x th x was being used.
In calculating experiment of the diagnostics of cardiovascular diseases on the basis
of the realization of the mechanism of fuzzy logic inference [3,4] the following input
parameters were used: x1 - age of the sick; x2 - double product of pulse on arterial
117
tension; x3 - tolerance to physical activity; x4 - increase of double product per one
kilogram of the body weight of the sick; x5 - increase of double product per one kilo-
gram of physical exertion; x6 - adenosinetriphosphoric acid; x7 - adenosine diphos-
phoric acid; x8 - adenylic acid; x9 - coefficient of phosphorilation; x10 - maximal
consumption of oxygen per one kilogram of the body weight of the sick; x11 - in-
crease of double product in the response for submaximal physical exertion; x12 -
coefficient of the ratio of lactic and pyruvic acid content.
Expressions for the determination of the diagnosis are of the form:
d f d x1 , y, z ,
y f y x2 , x3 , x4 , x5 , x10 , x11 ,
z f y x6 , x7 , x8 , x9 , x12 ,
where values d (diagnosis), y , z are determined with the help of the knowledge
base mentioned in the works of professor A. P. Rotstein [3,4].
Table 2. Results of the diagnostics of cardiovascular diseases (% of correct solutions)
Stenocardia of Neurocirculatory
Healthy Hypertrophy of Severe
the 2d function- dystonia of light
heart myocardium arrhythmia
al class degree
Method on the
basis of canoni-
100% 100% 100% 98% 97%
cal expansion
Method on the
basis of neural
89% 92% 94% 86% 83%
network
Method on the
basis of fuzzy
91% 90% 93% 91% 89%
logic
The results of numerical experiment confirm high effectiveness of the developed
calculating method in the comparison to the methods of artificial intelligence at the
expense of the usage of optimal parameters during the formation of the criterion of
making decision.
The choice of Daubechies function of the 4th degree from the existing limited set
of wavelet functions in the capacity of the parameter of neural network is not optimal
for solving of the problem of cardiovascular diseases diagnostics (usage of other func-
tions leads to the worsening of quality of problem solution [37]).
118
The results of the experiment on the basis of A. P. Rotstein’s approach [3, 4] indi-
cate that the absence of strict mathematical apparatus of fuzzy equation analysis
doesn’t allow to form optimal structure of fuzzy rules that naturally restricts the accu-
racy of cardiovascular diseases classification.
On the whole the basis of statistic data can be expanded by the way of the introduc-
tion of cardiogram information about wider class or about all existing types of cardio-
vascular diseases. This will allow to form on the basis of developed calculating meth-
od highly efficient information systems of cardiovascular diseases diagnostics for
their actual usage in medical cardiologic centers, clinics and diagnostic establish-
ments.
4 Conclusions
Therefore in the work the calculation method for a computer system of cardiovascu-
lar diseases diagnostics on the basis of the canonical decomposition of the random
sequence of electrocardiogram change is offered. The use of the mechanism of canon-
ical decompositions allowed to formulate the decisive rule of the maximum of the
combined density distribution in the form of the production of one-dimensional densi-
ties of distribution that gives the possibility to use for diagnostics random quantity of
electrocardiogram parameters. Besides canonical decomposition doesn’t impose any
essential limitations (linearity, stationarity, Markovian property etc.) on the class of
investigated random sequences. Thereby the offered approach to the solution of the
problem of cardiovascular diseases diagnostics allows to take into account the maxi-
mum stochastic characteristics of the electrocardiograms belonging to different cardi-
ovascular diseases. The given results of modeling show the high reliability of cardio-
vascular diseases diagnostics on the basis of the offered method.
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121
Synthesis of Time Series Forecasting Scheme Based on
Forecasting Models System
Fedir Geche1, Vladyslav Kotsovsky2, Anatoliy Batyuk3, Sandra Geche4, and
Mykhaylo Vashkeba1
1
Uzhhorod National University, Department of Cybernetics and Applied Mathematics,
Uzhhorod, Ukraine
(fgeche@hotmail.com, vashkebam1991@gmail.com)
2 Uzhhorod National University, Department of Information Management Systems,
Uzhhorod, Ukraine
kotsavlad@gmail.com
3 Lviv Polytechnic National University, Department of Automatic Control Systems, Lviv,
Ukraine
abatyuk@gmail.com
4 Uzhhorod National University, Department of Economic Theory,
Uzhhorod, Ukraine
sandra.geche@gmail.com
Abstract. This article is dedicated to the development of time series forecasting
scheme. It is created based on the forecasting models system that determines
the trend of time series and its internal rules. The developed scheme is
synthesized with the help of basic forecasting models "competition" on a certain
time interval. As a result of this "competition", for each basic predictive model
there is determined the corresponding weighting coefficient, with which it is
included in the forecasting scheme. Created forecasting scheme allows simple
implementation in neural basis. The developed flexible scheme of forecasting
of economic, social, environmental, engineering and technological parameters
can be successfully used in the development of substantiated strategic plans and
decisions in the corresponding areas of human activity.
Keywords. Trend, forecasting model, time series, functional, step of forecast,
autoregression, neural element, neural network.
Key Terms. MachineIntelligence, DecisionSupport, MathematicalModel
122
1 Introduction
At the present stage, for effective management of enterprises it is necessary to be
able to predict the major trends in social and economic systems, the main economic
indicators characterizing financial position and efficiency of the use of companies’
production resources.
Estimates and forecasts of the financial condition of the company make it possible
to find additional resources, to increase its profitability and solvency.
Problems of the analysis and the forecast of financial condition of the company by
means of corresponding indicators are an actual task, because on the one hand this is
the result of the company, on the other it defines the preconditions for the
development of the company. Qualitative forecast gives us an opportunity to develop
reasonable strategic plans for economic activity of enterprises.
Under market conditions, the adequate forecasting and capacity planning of
enterprises are impossible without working out economic and mathematical models
that describe the use of available resources during the operation of enterprises.
To determine strategies for enterprise development, calculation of forecasts of
economic indicators and factors of organizations plays an important role. If there is
reliable information about the company in the past, mathematical methods can be
applied to obtain necessary forecasts. These methods depend on the objectives and
detailed forecast factors; they also depend on the environment.
Various aspects of the theory, practice, and forecast of financial condition of a
company have been the subject of research of many domestic and foreign scientists,
such as Blank I.A [1], Heyets V.M. [2], Zaychenko Y.P. [3], Ivakhnenko V.M. [4],
Ivakhnenko O.G. [5], Yarkina N.M. [6], Tymashova L. [7], Stepanenko O.P. [8],
Tkachenko R.O. [9], Matviichuk A.V. [10], Hanke J.E. [11], Lewis C.D. [12], Box
G.E. [13].
When forecasting the indicators by which the financial position or efficiency of the
company’s production resources use are determined, it is impossible to point out a
single "the best" method of prediction because the internal laws (trends) of various
indicator systems are different and there arises the problem of choosing the method of
forecasting the studied indicator system.
Therefore, the development of new forecasting models of corresponding systems
of indicators is an actual and important problem.
The aim of the study is to develop an efficient scheme of time series prediction that
automatically (in the course of its training) adjusts to the appropriate system of
economic, social, environmental, and engineering parameters, and it can be
successfully used in the development of high-quality strategic plans in the branch of
economy, environment, and for forecast of different natural processes.
The research methodology includes the method of least squares, exponential
smoothing method, iterative techniques of minimization of functionals, and methods
of synthesis of neural-network schemes.
123
2 Synthesis of Forecasting Schemes of Time Series
Let v1 , v2 ,..., vt ,..., vn be a time series. Prognostic value v~t of the element vt at
the instant of time t can be written as follows [14-16]
v~t f (a1 ,..., ar , vt 1 ,..., vt k , t ) , (1)
where a1 ,..., ar are the model parameters, k is the depth of prehistory. To find the
parameters a1,...,ar , we constructed the functional
2
(2)
L(a1,..., ar ) vt v~t ,
n
t 1
which is usually to be minimized. Let a1* ,..., ar* are the values of parameters a1 ,..., ar
for which the functional L takes its minimum value. Then the prognostic value v~ n
of the model f with optimal parameters a1* ,..., ar* is determined as follows
v~n f (a1* ,..., ar* , vt 1 ,..., vt k , n ), (3)
where is the step of the forecast. Depending on the type of the function f with the
parameters a1* ,..., ar* , we have different optimal forecasting models of time series.
To build a predictive scheme, at the beginning let us consider the autoregression
method by means of which we define the optimal step of the prehistory k * for the
given time series vt with the fixed step of the forecast . In the autoregression
model, it is assumed that the indicator value vt at the instant of time t depends on
vt , vt 1 ,..., vt k 1 , where k is the parameter of the prehistory with fixed . The
prognostic value v~n by the autoregression method is found according to the
following model
v~n a1( )vn a2( )vn1 ... ak( )vnk 1. (4)
To determine the optimal values of the parameters at*( ) (t 1,2,...,k ) for a fixed
( t = t 0 ) , we minimize the functional
n 2
L(a1( ) ,...., ak( ) ) vt a1( )vt ... ak( )vt k 1 , (5)
t k
i.e. we solve the system of equations
124
L
0, t 1,2,..., k . (6)
ai( )
Let a1*( ) ,..., ak*( ) be a solution of the system (6). Then, according to (4) we have
v~t a1*( )vt a2*( )vt 1 ... ak*( )vt k 1, (7)
where t k .
It is obvious that the variable v~ t for a fixed value of 0 depends on the
parameter k (1 k n ) . To determine the optimal value of the prehistory
parameter k for 0 for the given time series v t , let us consider the variables
2
1 n
1 vt a1*( )vt ,
n t 1
vt a1*( )vt a2*( )vt 1 ,
2
1 n
2
n 1 t 2
n vn a1*( )vn ... an*()v1
2
Thus we obtain min δ1 , δ 2 ,..., δ n τ δ * . The variable k* determines the
kτ
optimal value of the prehistory parameter in the autoregression model for a fixed
0 .
After determining the k* for a fixed t 0 , consider the main base
forecasting models M1, M 2 ,...M q of time series with the fixed step of the forecast ,
i.e. models on the bases of which a new forecasting scheme are synthesized. Using the
results of the forecasting models mentioned above on the time interval
t n k* 1, n k* 2,, n , we draw the following table
125
Table 1. The Prognostic Values of Time Series
Forecasting Elements of Time Series vt
Models
vn k * 1
vn k * 2
vn
M1 v~ (1) *
n k 1
v~ (1) *
n k 2
v~n(1)
M2 v~ ( 2) *
n k 1
v~ ( 2) *
n k 2
v~n( 2)
Mq v~ ( q ) *
n k 1
v~ ( q ) *
n k 2
v~n( q )
In each column vn k * 1, vn k * 2 ,...,vn of Table 1, we can find the least
squared difference of the prognostic and the actual values of the corresponding time
series terms. Mathematically this can be written as following:
let j1 n k* 1 and
1 min (v j1 v~j(11) ) 2 , (v j1 v~j(12) ) 2 ,...,(v j1 v~j(1q) ) 2 ,
j2 n k* 2 and
2 min (v j2 v~j(21) ) 2 , (v j2 v~j(22) ) 2 ,...,(v j2 v~j(2q) ) 2 ,
………………………………………………………
jk * n and
k * min (vn v~n(1) ) 2 , (vn v~n(2) ) 2 ,...,(vn v~n(q) ) 2 .
Define the sets I1 , I 2 ,...,I k * as follows
126
I1 i 1,2,...,q1 (v j1 v (ji ) ) 2 ,
1
I 2 i 1,2,...,q 2 (v j2 v (ji ) ) 2 ,
2
I k * i 1,2,...,q k * (vn vn(i ) ) 2
and draw the table
Table 2. Parameters for Determining the Weighting Coefficients of the Model
Forecasting j1 j2 jk *
Resultant
Models Column
M1 a11 a12 a1k *
S1
M2 a21 a22 a2 k *
S2
Mq aq1 aq 2 aqk*
Sq
where
k* s , if s I ,
a ps s
0, if s I s ,
k*
S p a pj ,0 1,( p 1,2,...,q, s 1,2,...,k* ).
j 1
q
With the help of S p S p ( ) and S ( ) S p ( ) we determine the weighting
p 1
coefficients of the forecasting models M p ( p q) , with which these models are
included in the following forecasting scheme
S ( ) S ( ) S ( )
v~n S1( ) v~n(1) S2( ) v~n(2) ... Sq( ) v~n(q) . (8)
127
The coefficients of the forecasting models in the scheme (8) depend on the
parameter that determines the influence of the element vt upon the prognostic
value v~ . The more remote element v is from the prognostic point v~ , the less is
n t n
its influence on the prognostic value (0 1). In the case of 1 , all points of
time series vt are equivalent, i.e. in the model (8) the distance of the element vt from
the prognostic point v~ is not taken into account.
n
Synthesis of the predictive scheme (8) will be completed in the course of training its
concerning . For this purpose, we construct the functional
k*
S ( ) S qr ( ) ~ ( q) 2
L( ) (v ji S1( ) v~j(1) ... S ( )
v j ) , ( ji n k* i),
i i
i 1
and minimize it by varying the value . The interval (0,1] we divide into m equal
i
subintervals and find the value L( i ) at the points i
(i 1,2,...,m) . It is obvious
m
that m gives the accuracy of the finding the minimum of the functional L( ) . Let
m* min L(i ) . Then the forecast of time series we conduct according to the scheme
(8), substituting m* for .
3 Implementation of Forecasting Schemes of Time Series in
Artificial Neural Basis
The basis of all forecasting methods is an idea of extrapolation of patterns of the
development of the process, which was formed by the time when the forecast came
true for future period of time.
Let v1, v2 ,...,vt ,....,vn is time series. For the synthesis of artificial neural-network
forecasting scheme, there must exist a method (methods) of synthesis of neural
elements that implement appropriate forecasting models, on whose basis a neural
scheme should be constructed. For example, the following artificial neural element
with linear activation function implements the autoregression model
v~n w1( )vn w2( )vn 1 ... ...wk(* )vn k * 1 , with the
128
Fig. 1. Neuron of the Optimal Autoregressive Model
optimal step k* of the prehistory and the step of the forecast if
w1( ) a1*( ) ,...,wk * ( ) ak** a1*( ) ,...,ak*(* ) are optimal values of parameters of the
autoregressive model).
After the development of methods for the synthesis of neural elements that
implement the optimal forecasting models in the corresponding classes of models, to
predict the values vi (i 1,2,...,n) at instants of time t n , let us design the
following neural- network scheme
Fig. 2. Neuro-scheme for Time Series Prediction
All the blocks of the 1st layer contain the same number s of neurons, where each
neuron implements one of the forecasting models (autoregressive model, polynomial,
exponential, linear ones, Brown’s linear model, etc.). Neurons that implement the
same model in different blocks of this layer have the same serial number.
129
Each Block 2. m ( m 1,2,....,k ; k k* ) of the 2nd layer contains as much neurons
as in Block 1. m . In Block 2. m each neuron has two inputs and a weight vector (1,1),
where the value vn k m is given to the first input, and the prognostic value
v~n()k m,i is given to the 2nd input, which is the output signal of the іth neuron of
Block 1.m. Activation function of the іth neuron of Block 2. m is set as follows
~ ( )
exp( (vn k m v 2
. The neuron of the serial number i of Block 2. m is
n k m,i ) )
related to i th neuron of the 3rd layer in the following way: from the i th neuron of
Block 2. m to the m th input of the i th neuron of the 3rd layer there is given the signal
f m(,i) , where
~ ( )
1 , if i arg max(exp( (vn k m v 2
n k m , i ) ),
f m(, i)
0, otherwise.
Neurons of the 3rd layer have the linear activation function, and each of the
weighting coefficients of each neuron is equal to 1. At the output of the ith neuron of
( )
the 3rd layer for the fixed we obtain the number wi . The 3rd layer, except for
neurons with linear activation function, has one more BlokPROG containing exactly
as many neurons as a Block of the 1st layer contains. Neurons of this block implement
corresponding forecasting model with the depth and their serial numbers coincide
with the numbers of neurons of Blocks of Layer 1.
The 4th layer contains two linear neurons. The first neuron has s inputs, all its
weighting coefficients are equal to 1, and it has activation function
w1( ) w2( ) ... ws ( ) .
The second neuron of this layer has weighting coefficients w1( ) , w2( ) ,...,ws ( ) . If
the forecast result of the ith model of BlockPROG is denoted by , then at the
output of the second neuron of Layer 4 we have w1( ) v~n(1) ... ws ( ) v~n(s ) .
The 5th layer contains one neuron that has two inputs, a weight vector (1.1), and the
w ( ) v~ (1) ... ws ( ) v~n(s )
activation function v~n 1 ( ) n ( ) .
w1 w2 ... ws ( )
Blocks 2. m ( m 1,2,....,k* ) determine the most effective basic forecasting
models. At the output of the scheme we have a convex linear combination of the best
forecasting models.
4 Effectiveness of the Constructed Forecasting Scheme
Following types of errors are often used in the implementation of forecasting time
series forecasting
130
МАЕ – Mean Absolute Error
1 n
MAE vt v~t (9)
n t 1
where vt is the values of the time series at time t;
v~t predictable value vt .
The average absolute error of prediction (9) is an absolute measure of the quality
of forecast, estimating it independently of the other predictions. It's enough to set a
level of absolute error and compare the value of the specified error calculated by the
formula (9).
To compare the quality of forecasting, it is often used the average relative error
(MRE - Mean Relative Error) is often used
1 n vt v~t (10)
MRE ,
n t 1 vt
and the average square error (RMSE - Root Mean Square Error) is also used
vt v~t
n
2
RMRE t 1
, (11)
n
where vt are the terms of the time series, v~t are the prognostic values of vt . RMSE
and MRE are relative errors, i.e. they can be used to compare two (or more) different
time series prediction the best is the forecast whose value of MRE (10) or RMSE
(11) is less.
According to the average relative error criterion, the quality of the forecast of the
constructed predicting scheme is estimated by comparing its results with the results of
main forecasting models on base of which it is synthesized. To perform this, we use
data from the following Table 3 [17].
Table 3. The Original and Forecasted Volumes of Passenger Traffic
Under-
Automobile
Year Railway Sea River Aircraft ground
(coaches)1
railway
1980 648869 28478.4 24789 7801058 12492.4 430040
131
1981 653177 30705.6 27531.6 7794859 12720 473437
1982 656485 29362.2 26629.4 7874069 12728.7 515382
1983 668287 29690.2 26810.8 7876161 12711.6 520700
1984 687645 29228.8 24979.6 7998739 12777.8 551851
1985 695129 28660.6 23817.4 8076846 12616 602671
1986 734204 28681 21008.5 8230409 12797.5 598022
1987 717461 27567.3 18750.2 8383820 12670.4 590513
1988 711123 27961.5 20345.5 8552803 13065.3 634616
1989 704078 26524.3 20199.7 8382872 14299.6 648816
1990 668979 26256.7 19090.3 8330512 14833 678197
1991 537407 20786.5 18285.8 7450322 13959.6 595313
1992 555356 13139.5 11158 6464891 5669.3 610668
1993 501495 10497 8064.4 4795664 1947.4 644417
1994 630959 10358.2 6967.9 4039917 1673.3 684480
1995 577432 7817 3594.1 3483173 1914.9 561012
1996 538569 5044.6 2735.9 3304600 1724 536304
1997 500839 4311.3 2443.1 2512147 1484.5 507897
1998 501429 3838.3 2356.5 2403425 1163.9 668456
1999 486810 3084.3 2269.4 2501708 1087 724426
2000 498683 3760.5 2163.3 2557515 1164 753540
2001 467825 5270.8 2034.2 2722002 1289.9 793197
2002 464810 5417.9 2211.9 3069136 1767.5 831040
2003 476742 6929.4 2194.1 3297505 2374.7 872813
2004 452226 9678.4 2140.2 3720326 3228.5 848176
2005 445553 11341.2 2247.6 3836515 3813.1 886598
2006 448422 10901.3 2021.9 3987982 4350.9 917700
2007 447094 7690.8 1851.6 4173034 4928.6 931512
2008 445466 7361.4 1551.8 4369126 6181 958694
2009 425975 6222.5 1511.6 4014035 5131.2 751988
2010 427241 6645.6 985.2 3726289 6106.5 760551
2011 429785 7064.1 962.8 3611830 7504.8 778253
2012 429115 5921 722.7 3450173 8106.3 774058
2013 425217 6642 631.1 3343660 8107.2 774794
2014 424272.5 3490.2 453.8915 3059461.2 9308.8 816682.9
2015 414375.8 5373.2 406.4361 2645239.9 7243.7 876984.7
2016 425925.3 3847.1 369.0345 2641221.6 10609.4 972098.3
2017 420469.8 2975.1 233.0464 2395820.5 10870.7 1073108.1
2018 426849.1 3061.2 403.4616 2606148.8 12330.5 1205853.8
132
Table 4. Forecast Errors of Passenger Traffic according to MRE criterion
Forecasting methods Kinds of passenger traffic
Railway River Automobile
Step of the forecast
Autoregression method 0.0148 0.0115
0.0041
The method of least 0.7975 0.1680
squares with weights 0.015
Brown’s linear model 0.0358 0.0917 0.1478
Brown’s quadratic
model 0.0159 0.5516 0.086
Forecasting scheme 0.0039 0.0148 0.0115
Step of the forecast
Autoregression method
0.0045 0.0111 0.0233
The method of least
squares with weights 0.0048 0.0683 0.0595
Brown’s linear model 0.0585 0.0757 0.1482
Brown’s quadratic
model 0.0317 0.2295 0.0797
Forecasting scheme 0.0031 0.0108 0.0225
Having analyzed the data in Table 4, we see that the least average relative error
occurs in the constructed forecasting scheme. In the two cases (for 1 ), the error of
the scheme coincides with the error of autoregression method. Thus, in general, the
scheme developed in this work is the most effective among the methods on which it is
based. To obtain the average error (%) of the prediction methods for the given time
series in percentage, one should multiply by 100% the corresponding values of quality
from Table 4. The quality of the prediction methods of passenger traffic for the
forecast period (2014-2018) with the steps of the forecast 1 and 5 is shown in
the following charts
133
Fig. 3. Forecasting errors of prediction methods with the step 1 (in %)
Fig. 4. Forecasting errors of prediction methods with the step 5 (in %)
134
Note. The constructed forecasting scheme is flexible. This means that a new model
can be added to or excluded from basic models (on basis of which the predictive
scheme is constructed) at any time. It should be noted that the method of synthesis of
the very predictive scheme does not change.
Here are some results of the program implementation of developed forecasting
scheme for determining the share of road passenger transport in Ukraine to all other
types of transportation during time span since 1980 to 2013. Table 3 contains primary
data of passenger traffic volume (period 1980-2013) and projections of passenger
traffic (forecast period 2014-2018). On the base of this table it is evident that the
average share of road passenger transport in Ukraine was 51.85% over the above
mentioned period. Accordingly to the forecast this share will average 45.56% during
the prediction period 2014-2018. Thus, the role of road passenger transport in Ukraine
over the observable forecast period 2014-2018 is leading. Annual share of road
passenger transport in Ukraine during the prediction period is shown on the following
diagram:
Fig.5. The share of road passenger transport in Ukraine over the period (2014-2018)
To compare the dynamics of changes of the volume of passenger traffic in Ukraine
for different types of vehicles (rail, river, road) we construct the following diagram.
135
Fig.6. Dynamics of passenger traffic in Ukraine (2014-2018)
5 Conclusions
A flexible scheme for forecasting of economic, social, environmental, engineering
and technological indicators that can be successfully used in the development of
reasonable strategic plans and decisions in the corresponding fields of human activity
is worked out.
This forecasting scheme allows us to include new forecasting models of time series
or to exclude a model or groups of models from it at any instant of time.
As for the models which remain in the scheme, the competition between them is
made over a given period of time, and the final forecasting scheme represents a
convex linear combination of models -winners with corresponding weighting
coefficients.
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137
C-clause calculi and refutation search
in first-order classical logic
Alexander Lyaletski
Taras Shevchenko National University of Kyiv, Ukraine
lav@unicyb.kiev.ua
Abstract. The paper describes an approach to the construction of a
resolution-type technique basing on a certain generalization of the reso-
lution notion of a clause. This generalization called a conjunctive clause
(c-clause) leads to a possibility to introduce two different inference rules
and determine two c-clause calculi oriented to refutation search in first-
order classical logic both with and without equality. Using the connection
of these calculi with Robinson’s clash-resolution method, a simple way
for the proving of their soundness and completeness is given. Analogs of
some of the well-known resolution strategies for the calculi are suggested.
Besides, the treatment of Maslov’s inverse method in the resolution terms
is given. This research can be used in (e-)learning systems for the intel-
ligent testing of knowledge of trainees learning a mathematical subject.
Keywords: first-order classical logic, refutation search, calculus, sound-
ness, completeness, clash-resolution method, paramodulation, strategy
Key Terms: MachineIntelligence
1 Introduction
This paper is devoted to the description of special calculi intended for the es-
tablishing of the unsatisfiability of a formula F of a certain form or a set S of
such formulas in first-order classical logic maybe with equality. The calculi relate
to the class of refutation-search methods based on the ideas firstly presented in
Robinsin’s paper [1] on the well-known resolution method.
After the appearance of the resolution method, the main efforts of automated
theorem-proving community were concentrated on its development in the direc-
tion of the construction of its different modifications and strategies oriented to
increasing the efficiency of deduction search. All such attempts based on the use
of a clause being a well-formed expression of the resolution method leaving aside
the possibility of building efficient methods using modifications of the notion of a
clause, to which this paper is devoted. Besides, the problem of the interpretation
of the Maslov inverse method [2] in resolution terms is solved in it.
Our calculi completely are determined by their (resolution-type) inference
rules. The deducibility of a special expression Λ in such a calculus Π is equivalent
to the unsatisfiability of F or S. At that, Π is called a sound calculus, if the
138
deducibility of Λ implies the unsatisfiability of F or S; Π is called a complete
calculus, if the unsatisfiability of F or S implies the deducibility of Λ.
If we put certain restrictions on inferences of Λ in a calculus Π, these restric-
tions are said to determine a strategy for proof search in Π.
All the above-said takes place for the clash-resolution method [3] being called
the clause calculus below. It deals with clauses and contains the unique inference
rule – the latent class-resolution rule. The empty clause plays the role of Λ.
Let us stop on the way of the construction of an initial set of clauses for a
formula F (or a set S of such formulas) being investigated on unsatisfiability.
First of all, we can consider that F is a closed formula. Further, let us suppose
that F already is presented in Skolem functional form (for satisfiability), all
the quantifiers of which are omitted. Then, under the condition that all its
variables implicitly are bound by the universal quantifier, the following question
is reasonable: Can we refrain from the obligatory presentation F (or S) as a set
of clauses and develop a technique similar to the resolution one? Research in this
direction is described in what follows. At that, note that the papers [4] and [5]
are a starting point for the development of the approach presented here.
We usually give references to the original papers, which laid the foundations
for the research in a particular direction, although for the modern description of
most of them, one can turn to [6] or [7]. QED indicates the end of any proof.
2 Preliminaries
First-order classical logic with functional symbols and equality is considered.
The notions of terms, atomic formula, and formulas are assumed to be known.
A formula being the result of renaming of variables in a formula F is called a
variant of F . A literal is an atomic formula or its negation. For a literal L of
the form ¬A, its complementary L̃ is A. If L is an atomic formula A, then its
complementary L̃ is ¬A.
As it was said above, we restrict ourselves by the consideration of only closed
formulas F presented in Skolem functional form for satisfiability by means of the
elimination of positive quantifiers. That is, F may be considered as a formula
of the form ∀x1 . . . ∀xm G(x1 , , xm ), where x1 , , xm all the variables of F , and
G(x1 , , xm ) a quantifier-free formula. I. e. it can be assumed that in the case of
reasoning on satisfiability, one has to deal with only quantifier-free formulas, all
variables of which implicitly are universally bound.
We can reduce G(x1 , , xm ) to a formula D1 ∧ . . . ∧ Dn , where Di is a for-
mula presented in disjunctive normal form (DNF). As a result, we can make
investigation of the set {D1 , . . . , Dn } on unsatisfiability instead of making the
appropriate investigation of G(x1 , , xm ). This leads to the following notions.
If L1 , . . . , Lm are literals, then the expression L1 ∧. . .∧Lm (m ≥ 1) is called a
conjunct. An expression of the form C1 ∨. . .∨Cn , where C1 , . . . , Cn are conjuncts,
is called a conjunctive clause, or a c-clause (n ≥ 0).
A c-clause not containing any conjunct (that is, if n = 0) is called an empty
clause (or empty c-clause) and denoted by .
139
In what follows, any conjunct is considered to be the set of its literals and
any c-clause – the set of its conjuncts. Thus, in the case when any conjunct of
a c-clause contains exactly one literal, this c-clause can be considered as a usual
clause (see, for example, [1] or [6]).
The introduced definitions allow us to use all the semantic notions of first-
order classical logic for c-clauses and sets of c-clauses under the assumption
that every variable in any c-clause is universally bound. The empty clause is
considered to be an unsatisfiable formula.
Our main purpose is to prove that the inferring of in our calculi is equiv-
alent to the unsatisfiability of an initial set of c-clauses.
An inference from an initial set S of c-clauses in a calculi under consideration
is a sequence D1 , . . . , Dn , where every Di (i = 1, . . . , n) is either a variant of
an c-clause from S or a variant of a conclusion of a rule applied to some of the
c-clauses preceding Di . Therefore, our calculi uniquely are identified by their
inference rules. That is why the names of rules will serve as unique names of
the calculi under consideration. The deducibility of a c-clause C from a set S of
c-clauses in a calculus Π is denoted by S ⊢Π C.
The resolution method first was published in [1] in 1965. It contained the only
resolution rule of the arity 2. In [8], J.A.Robinson proposed its modification of
this rule under the name of the hyper-resolution. Its further generalization led
to the clash-resolution method [3]. The peculiarity of this generalization is that
it contains the only latent clash-resolution rule (denoted by RR below) that can
be applied to any finite number of clauses. The corresponding clash-resolution
method (being the clause calculus with the RR-rule) is sound and complete [3].
Let us give some necessary notations.
A substitution, σ, is a finite mapping from variables to terms that has the form
σ = {x1 7→ t1 , . . . , xn 7→ tn }, where variables x1 , . . . , xn are pairwise different
and for any i (1 ≤ i ≤ n), the term ti is distinct from xi .
A substitution σ is called a variant substitution if t1 , . . ., tn from σ are
only variables that are pairwise different. In this case, the inverse (one-one)
correspondence σ −1 exists and presents itself a (variant) substitution.
For an expression Ex and a substitution σ, the result of the application of σ
to the expression of Ex is understood in the usual sense; it is denoted by Ex · σ.
The composition of substitutions (as mappings) σ and λ is denoted by σ · λ.
It has the property that for any expression Ex, Ex · (σ · λ) = (Ex · σ) · λ.
For any set Ξ of expressions, Ξ ·σ denotes the set obtained by the application
of σ to each expression in Ξ. If Ξ is a set of (at least two) expressions and Ξ · σ
a singleton, then σ is called a unifier of Ξ. If Ξ1 , . . . , Ξn (n ≥ 1) are sets of
expressions and for a substitution σ, the set Ξi · σ is a singleton (i = 1, . . . , n),
then σ is called a simultaneous unifier of Ξ1 , . . . , Ξn .
It is known (see, for example, [6] or [3]) that in the case the existence of a
unifier σ of sets Ξ1 , . . . , Ξn , there exist such substitutions λ and σ ′ that Ξ1 ·
λ, . . . , Ξn ·· λ are singletons and Ξ1 · σ = (Ξ1 · λ) · σ ′ , . . . , Ξn · σ = (Ξn · λ) · σ ′ .
The substitution λ is unique up to renaming of its variables. It is called the most
general simultaneous unifier (mgsu) of Ξ1 , . . . , Ξn .
140
Obviously, we can consider that any mgsu σ has the idempotence property
that means that σ· σ = σ. This fact will often be used in what follows implicitly.
Robinson’s latent clash-resolution rule (RR). Let clauses C0 , C1 , . . . , Cq (q ≥
1) with mutually distinct variables be of the forms C0′ ∨ L1,1 . . . ∨ L1,r1 . . . ∨
Lq,1 ∨ . . . ∨ Lq,rq , C1′ ∨ E1,1 ∨ . . . ∨ E1,p1 , . . ., Cq′ ∨ Eq,1 ∨ . . . ∨ Eq,pq respectively,
where C0′ , C1′ , . . . , Cq′ are clauses and L1 , . . . , Lq , E1,1 , . . . Eq,pq literals. Suppose
that there exists the mgsu σ of the sets {L̃1,1 ,. . . ,L̃1,r1 , E1,1 ,. . . , E1,p1 }, . . .,
{L̃q,1 ,. . . , L̃q,rq , Eq,1 ,. . . , Eq,pq }. Then the clause C0′ · σ ∨ C1′ · σ ∨ . . . ∨ Cq′ · σ is
said to be deducible from C0 , C1 , . . . , Cq by the rule RR.
The RR-rule with two clauses as its premises will be denoted by RR2 .
The paper [3] contains the following result (see, also, [6]).
Robinson’s Proposition. An initial set S of clauses is unsatisfiable if and
only if the empty clause is inferred in the RR-calculus.
3 C-clause calculi for logic without equality
Below, we introduce two resolution-type rules in order to define two specific c-
clause calculi. These calculi have a number of similar properties. That is why
their proofs are detailed only for one of them. As to the other calculus, the
corresponding proofs for it can be obtained in the same way.
3.1 CR calculus
Let us start with the consideration of the calculus that is based on the analog
of Robinson’s rule RR.
Clash-resolution (CR). Let c-clauses D0 , D1 , . . . , Dq (q ≥ 1) pairwise without
common variables be of the forms D0′ ∨ K1,1 ∨ . . . ∨ K1,r1 ∨ . . . ∨ Kq,1 ∨ . . .
∨ Kq,rq , D1′ ∨ M1,1 ∨ . . . ∨ M1,p1 , . . ., Dq′ ∨ Mq,1 ∨ . . . ∨ Mq,pq respectively,
where D0′ , . . . , Dq′ are c-clauses and K1,1 , . . . , Kq,rg , M1,1 , . . . Mq,pq conjuncts.
Suppose that K1,1 , . . . , Kq,rq contain literals L1,1 , . . . , Lq,rq respectively and for
every j = 1, . . . , q, Mj,1 ,. . .Mj,pj contain literals Ej,1 ,. . .Ej,pj respectively such
that there exists the mgsu σ of the sets {L̃1,1 ,. . . ,L̃1,r1 , E1,1 ,. . . , E1,p1 }, . . .,
{L̃q,1 ,. . . , L̃q,rq , Eq,1 ,. . . , Eq,pq }. Then the c-clause D0′ · σ∨ D1′ · σ ∨ . . . ∨ Dq′ · σ
is said to be inferred from the nucleus D0 and electrons D1 , . . . , Dq by the CR-
rule. Besides, the q-tuple hD0 , D1 , . . . , Dq i is called a CR-clash and D0′ · σ ∨
D1′ · σ ∨ . . . ∨ Dq′ · σ its CR-resolvent.
Remark. If D0 , D1 , . . . , Dq are only clauses, the definitions of CR and RR
are coincides, which gives a simple way for proving some results relating to CR.
Proposition 1. The CR-rule is sound.
Proof. Since we implicitly consider every variable in any c-clause to be bound by
the universal quantifier, obviously it is enough to prove that a CR-resolvent is
the logical conclusion of its premises only in the propositional case. For this, it
is enough to check the validity of the propositional formula:
141
((D0′ ∨ (L̃1,1 ∧ K1,1 ′
) ∨ . . . ∨ (L̃1,1 ∧ K1,r ′
1
) ∨ . . . ∨ (L̃q,1 ∧ Kq,1 ′
) ∨... ∨
′ ′ ′ ′
(L̃q,1 ∧ Kq,r q
)) ∧ (D 1 ∨ (L 1,1 ∧ M 1,1 ) ∨ . . . ∨ (L 1,1 ∧ M 1,p1 )) ∧ . . . ∧ (Dq′ ∨
′ ′ ′ ′ ′
(Lq,1 ∧ Mq,1 ) ∨ . . . ∨ (Lq,1 ∧ Mq,p q
))) ⊃ (D 0 ∨ D 1 . . . ∨ D q ), where ⊃ is the
implication symbol, which can be made by applying induction on q. QED.
Let a c-clause D distinguished from be of the form K1 ∨ . . . ∨ Kn . Then
ρ(D) is the set {L1 ∨ . . . ∨ Ln : L1 occurs in K1 , . . . , Ln occurs in Kn }.
For , we suppose that ρ() contains and only it. S
If S is a set of c-clauses, then ρ(S) denotes the set D∈S ρ(D).
It is obvious that for any non-empty set S of c-clauses, ρ(S) is a finite non-
empty set and contains only clauses. Moreover, considering D as a formula, we
can produce ρ(D) my means of applying the following propositional tautology:
A ∨ (B ∧ C) ≡ (A ∨ B) ∧ (A ∨ C), where ≡ is the logical equivalence symbol.
Therefore, a set S is unsatisfiable if and only if ρ(S) is an unsatisfiable set.
Remark. According to the previous remark, we conclude that Robinson’s
clash-resolution technique is used when we are interested in the establishing of
the deducibility of from ρ(S) in the CR-calculus. Thus, for any finite set S of
c-clauses, it is true that S is unsatisfiable if and only if ρ(S) ⊢CR .
Lemma 1. Let D0 , D1 , . . . , Dq be c-clauses and A0 , A1 , . . . , Aq clauses such that
A0 ∈ ρ(D0 ), A1 ∈ ρ(D1 ), . . . , Aq ∈ ρ(Dq ). If for A0 , A1 , . . . , Aq , there is the CR-
clash hA0 , A1 , . . . , Aq i with A0 as a nucleus and A1 , . . . , Aq as electrons and A is
its CR-resolvent, then there exists the CR-clash hD0 , D1 , . . . , Dq i with D0 as a
nucleus, D1 , . . . , Dq as electrons, and D as its CR-resolvent such that A ∈ ρ(D).
Proof. Let us consider A0 , A1 , . . . , Aq from the lemma conditions. Let they be of
the form: B0 ∨ L1,1 ∨ . . . ∨ L1,r1 ∨ . . . ∨ Lq,1 ∨ . . . ∨ Lq,rq , B1 ∨ E1,1 ∨ . . .
∨ E1,p1 , . . ., Bq ∨ Lq,1 ∨ . . . ∨Lq,pq respectively, where B0 , . . . , Bq are clauses
and L1,1 , . . . , Lq,rq , E1,1 , . . . Eq,pq literals such that there exists the mgsu σ of
the sets {L̃1,1 , . . ., L̃1,r1 , E1,1 , . . ., E1,p1 }, . . ., {L̃q,1 , . . ., L̃q,rq , Eq,1 , . . ., Eq,pq }.
Then the clause B0 ·σ ∨ B1 ·σ ∨ . . . ∨ Bn ·σ is a CR-resolvent of the above-given
CR-clash.
Since A0 ∈ ρ(D0 ), D0 can be presented in the form D0′ ∨ K1,1 ∨ . . . ∨
K1,r1 ∨ . . . ∨ Kq,1 ∨ . . . ∨ Kq,rq , where D0′ is a c-clause and K1,1 , . . . , Kq,rg
conjuncts such that B0 ∈ ρ(D0′ ) and K1,1 , . . . , Kq,rg contain literals L1,1 , . . . ,
Lq,rq respectively.
Making reasoning in the similar way, we obtain that D1 , . . ., Dq can be
presented in the form D1′ ∨ M1,1 ∨ . . . ∨ M1,p1 , . . ., Dq′ ∨ Mq,1 ∨ . . . ∨ Mq,pq
respectively, where D1′ , . . ., Dq′ are c-clauses and M1,1 , . . . Mq,pq conjuncts such
that B1 ∈ ρ(D1′ ), . . . , Bq ∈ ρ(Dq′ ) and M1,1 , . . ., Mq,pq contain E1,1 , . . . Eq,pq .
In accordance with the definition of CR, this means that D0 , D1 , . . . , Dq form
a clash with D0 as a nucleus and D1 , . . . , Dq as electrons. For this CR-clash,
D0′ · σ ∨ D1′ · σ ∨ . . . ∨ Dq′ · σ is its CR-resolvent. Obviously, B0 · σ ∨ B1 · σ ∨
. . . ∨ Bn · σ ∈ ρ(D0′ · σ ∨ D1′ · σ ∨ . . . ∨ Dq′ · σ). QED.
Proposition 2. Let S be a set of c-clauses and B1′ , . . ., Bn′ an inference of
from ρ(S) in the RR-calculus. Then there exists an inference B1 , . . ., Bn of
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from S in the CR-calculus such that for every j (j = 1, . . . , n) Bj′ ∈ ρ(Bj ) and
if Bj′ is a variant of a CR-resolvent of the CR-clash hBi′r , . . ., Bi′1 i with Bi′r as
its nucleus, then Bj is a variant of a CR-resolvent of the CR-clash hBir , . . .,
Bi1 i with Bir as its nucleus (i1 < . . . < ir < j).
Proof. Let B1′ , . . ., Bn′ be an inference of from ρ(S) in the RR-calculus. It
is an inference of from ρ(S) in the CR-calculus
For each i = 1, . . . , n, assign a c-clause Bi to a clause Bi′ in the following way.
j = 1. The definition of an inference implies that B1′ is a variant of a clause
C ∈ ρ(S). That is there exists a variant substitution λ such that B1′ is C · λ.
Hence, we can select such a c-clause D in S that C ∈ ρ(D). Take D · λ as B1 .
Obviously, B1′ ∈ ρ(B1 ).
Suppose that j > 1 and we have c-clauses B1 . . ., Bj−1 that pairwise have no
common variables and satisfy the conditions: B1′ ∈ ρ(B1 ), . . ., Bj−1 ′
∈ ρ(Bj−1 ).
Two cases are possible.
(1) Bj′ is a variant of a clause C ∈ ρ(S). Proceeding in the same manner as in
the case of j = 1, we easily achieve the necessary renaming some of the variables
of D · λ in order the result Bj has no common variables with B1 , . . ., Bj−1 .
(2) Bi′ is a variant of a CR-resolvent C of a CR-clash hBi′r , . . ., Bi′1 i with
′
Bir as its nucleus (i1 < . . . < ir ). Accordantly to Lemma 1, we can construct
the CR-clash hBir , . . ., Bi1 i with Bir as its nucleus and D as its CR-resolvent,
for which C ∈ ρ(D).
Let λ be a variant substitution such that Bi′r is C · λ. Obviously, we can
select a variant B of D · λ not having common variables with B1 , . . ., Bj−1 and
satisfying the condition Bj′ ∈ B. Denote this B by Bj .
Let us consider B1 , . . . , Bn . Since Bn′ is and ρ() contains only , Bn is
the empty clause . Thus, accordingly to the construction of B1 , . . . , Bn , this
sequence is an inference of satisfying the conclusion of the proposition. QED.
Now, it is easy to obtain the soundness and completeness of the CR-calculus.
Theorem 1 (Soundness and completeness of CR-calculus). A set S of c-clauses
is unsatisfiable if and only if S ⊢CR .
Proof. The soundness of CR is provided by Prop. 1.
Completeness. If S is an unsatisfiable set of c-clauses, then ρ(S) is an un-
satisfiable set of clauses. The calculus RR is complete (Robinson’s proposition).
Hence, ρ(S) ⊢RR . Thus, S ⊢CR on the basis of Prop. 2. QED.
Let us consider an example of a deduction in the CR-calculus. Note that
all the examples in the paper are given only for propositional case since the
resolution-type technique under consideration uses the usual unification.
Example 1. Let U denote the following set of c-clauses: {(A ∧ ¬A) ∨ (B ∧ C) ∨
(E ∧ L), ¬B ∨ ¬C, ¬E ∨ ¬L}, where A, B, C, E, and L are atomic formulas.
The (minimal) inference of from U in CR is as follows:
1. (A ∧ ¬A) ∨ (B ∧ C) ∨ (E ∧ L) (∈ U ),
2. (A ∧ ¬A) ∨ (B ∧ C) ∨ (E ∧ L) (∈ U ),
3. (B ∧ C) ∨ (E ∧ L) (by CR from (1) as a nucleus and (2) as an electron),
143
4. (B ∧ C) ∨ (E ∧ L) (a variant of (3)),
5. ¬B ∨ ¬C (∈ U ),
6. E ∧ L (by CR from (5) as a nucleus and (3) and (4) as electrons),
7. E ∧ L (a variant of (6)),
8. ¬E ∨ ¬L (∈ U ),
9. (by CR from (8) as a nucleus and (6) and (7) as electrons).
Therefore, the set U is unsatisfiable.
3.2 IR calculus
Maslov’s inverse method (denoted by MIM here) and Robinson’s resolution
method (the calculus of clauses in our terminology) appeared approximately
at the same time: MIM – in 1964 [2] and RR – in 1965 [1].
After their appearance, the problem of the interpretation of MIM in the
resolution terms has arisen. This problem has attracted the attention of a number
of researchers in inference search (see, for example, [11] and [12]) also because
MIM was defined as a special calculus of so-called favorable assortments and its
description was made in the terms that did not correspond to traditional logical
terminology and resolution one applied at that time.
In [11], S. Maslov gave himself some MIM explanation in the resolution no-
tions for a restricted case. Later, after an attentive analysis of MIM, the author
of this paper “discovered” that MIM interpretation was preferable to do in the
terms of a special c-clause1 calculus [5], the enough description detailed of which
is given below. Also it was found that this calculus has an independent signifi-
cance. It echoes the CR-calculus and, at the same time, it differs from CR.
Inverse resolution (IR). Let c-clauses D0 , D1 , . . . , Dq (q ≥ 1) pairwise with-
1
out common variables be of the forms D0′ ∨ K1 ∨ . . . ∨ Kq , D1′ ∨ N1,1 ∨
1 ′ 1 1
. . . ∨ N1,p1,1 ∨ . . . ∨ N1,1 ∨ . . . ∨ N1,p1,r , . . ., Dq ∨ Nq,1 ∨ . . . ∨ Nq,pq,1 ∨
r1 r1
1
rq rq ′ ′
. . . ∨ Nq,1 ∨ . . . ∨ Nq,p n,rn respectively, where D0 , . . . , Dq are c-clauses and
1 rq
K1 , . . . , Kq , N1,1 , . . . , Nq,pn,rn conjuncts. Suppose that for every j (1 ≤ j ≤ q),
1 1
Kj contains literals Lj,1 , . . . , Lj,rj and Nj,1 , . . . , Nj,p , . . . , Nj,1j , . . . , Nj,pj j,r
r r
j,1 j
1 1 j j
contain literals Ej,1 , . . . ,Ej,p , . . . , Ej,1 , . . . , Ej,p respectively such that there
r r
j,1 j,r
j
1 1
exists the mgsu σ of the sets {L̃1,1 , E1,1 , . . . , E1,p 1,1
}, . . . , {L̃1,r1 , E1,1
r1
, ...,
1 1 rq rq
E1,p1,r }, . . . , {L̃q,1 , Eq,1 , . . . , Eq,pq,1 }, . . . , {L̃q,rq , Eq,1 ,. . . , Eq,pq,rq }. Then the
r1
1
c-clause D0′ · σ ∨ D1′ · σ ∨ . . . ∨ Dq′ · σ is said to be inferred from the nucleus D0
and electrons D1 , . . . , Dq by the IR-rule. Besides, the q-tuple hD0 , D1 , . . . , Dq i
is called its IR-clash and D0′ · σ ∨ D1′ · σ ∨ . . . ∨ Dq′ · σ its IR-resolvent.
Having the IR-rule, we can speak about the IR-calculus.
1
In 1989, V. Lifschitz independently introducing the notion of a c-clause under the
name of a super-clause improved such interpretation [13]. In [14], T. Bollinger ex-
tended Loveland’s model elimination method [15] to the case of c-clauses using the
name of a generalized clause for a c-clause.
144
The comparative analysis of IR and CR shows that the only difference be-
tween them is in the ways of the selection of cutting literals for their applications.
The following statement contains a more detailed explanation of this observation.
Lemma 2. If hD0 , D1 , . . ., Dq i is a CR-clash with D0 an its nucleus and D1 , . . .,
Dq as its electrons, then for any its CR-resolvent D, it is possible to construct
an IR-clash with D0 as its nucleus and certain variants of D1 , . . ., Dq as its
electrons such that for its some IR-resolvent D′ and a substitution τ , D = D′ ·τ .
Proof. If hD0 , D1 , . . ., Dq i is the CR-clash from the definition of CR-rule, then
the c-clauses D0 , D1 , . . ., Dq can be presented as D0′ ∨ K1,1 ∨ . . . ∨ K1,r1 ∨ . . .
∨ Kq,1 ∨ . . . ∨ Kq,rq , D1′ ∨ M1,1 ∨ . . . ∨ M1,p1 , . . ., Dq′ ∨ Mq,1 ∨ . . . ∨ Mq,pq
respectively, where D0′ , . . . , Dq′ are c-clauses and K1,1 , . . . , Kq,rg , M1,1 , . . . Mq,pq
conjuncts and moreover for literals L1,1 , . . . , Lq,rq , Ej,1 , . . .Ej,pj from K1,1 , . . . ,
Kq,rg , M1,1 , . . . Mq,pq respectively, there exists the mgsu σ of the sets Θ1 =
{L̃1,1 ,. . . ,L̃1,r1 , E1,1 ,. . . , E1,p1 }, . . ., Θq = {L̃q,1 ,. . . , L̃q,rq , Eq,1 ,. . . , Eq,pq } such
that D = D0′ · σ ∨ D1′ · σ ∨ . . . ∨ Dq′ · σ .
Let us take such variant substitutions λ1,1 , . . ., λ1,r1 ,. . ., λq,1 ,. . ., λq,rq that
D1 · λ1,1 ,. . ., D1 · λ1,r1 , . . ., Dq · λq,1 . . . Dq · λq,rq have no common variables with
D0 and each other. Considering λ−1 −1
1,1 , . . ., λq,rq as mapping graphs, construct the
−1
set λ1,1 ∪ . . . ∪ λ−1 q,rq . Obviously, it is a (variant) substitution. Let us denote it
by µ and the c-clause Dj′ · λj,k ∨ Mj,1 · λj,k ∨ . . . ∨ Mj,pj · λj,k by Djk .
Let us consider D11 , . . ., D1r1 , . . ., Dq1 , . . ., Dq q . Accordantly to their definition
r
−1
and the definition of µ, we have that Djk ·µ is the same as Djk ·λj,k and, therefore,
it is the same as Dj (j = 1, . . . , q; k = 1, . . . , rj ). Thus, we can select literals
1 1 1 1 rq rq
E1,1 , . . . ,E1,p 1
, . . . , E1,1
r1
, . . . , E1,p
r1
1
, . . ., Eq,1 , . . . ,Eq,p q
, . . . , Eq,1 , . . . , Eq,p q in
M1,1 · λ1,1 , . . ., M1,p1 · λ1,1 , . . ., M1,1 · λ1,r1 , . . ., M1,p1 · λ1,r1 , . . ., Mq,1 · λq,1 , . . .,
Mq,pq · λq,1 , . . ., Mq,1 · λq,rq , . . ., Mq,pq · λq,rq respectively, such that Ei,j k
· λ−1
i,k =
Ei,j · µ = Ei,j (i = 1, . . . , q; j = 1, . . . , pq ; k = 1, . . . , rq ).
k
Considering σ and µ as mapping graphs, we conclude that ζ = µ · σ ∪ σ is a
substitution. Because σ is the mgsu of the sets Θ1 , . . . , Θq , the definition of ζ and
the idempotence of σ imply that ζ is a simultaneous unifier of the sets of literals
1 1 1 1
{L̃1,1 E1,1 , . . . ,E1,p 1
}, . . . , {L̃1,r1 E1,1 r1
, . . . , E1,p
r1
1
}, . . ., {L̃q,1 Eq,1 , . . . ,Eq,p q
},
rq rq
. . ., {L̃q,rq Eq,1 , . . . , Ej,pq }. Therefore, there exists the mgsu θ of these sets, for
which ζ = θ · τ , where τ is a substitution.
As a result, we have that D0 , D11 , . . ., D1r1 , . . ., D1q , . . ., Dq q can form the
r
IR-clash with D0 as its nucleus and D11 , . . ., D1r1 , . . ., D1q , . . ., Dq q as its electrons
r
that produces the IR-resolvent D′ = D0′ · θ ∨ D1′ · (λ1,1 · θ) ∨ . . . ∨ D1′ · (λ1,r1 · θ)
∨ . . . ∨ Dq′ · (λq,1 · θ) ∨ . . . ∨ Dq′ · (λq,rq · θ).
Since θ · τ = ζ and ζ = µ · σ ∪ σ, it is obvious that D′ · τ = D. QED.
This result permits to “simulate” any inference in CR by an inference in IR.
Proposition 3. Let S be a set of c-clauses and B1 , . . ., Bn an inference of
from S in the CR-calculus. Then there exists an inference B1′ , . . ., Bm′
of
from S in the IR-calculus (m ≥ n) such that if Bj is a variant of a CR-resolvent
of an CR-clash with Br as its nucleus, then for some j ′ and r′ (j ′ ≥ j, r′ ≥ r),
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Bj′ ′ is a variant of an IR-resolvent of the corresponding IR-clash with Br′ ′ as its
nucleus; moreover, Bj = Bj′ ′ · τ for some substitution τ .
Proposition 4. The IR-rule is sound.
Proof. As in the case of the CR-rule, it is enough to establish the validity of
the following formula, “extracted” from the definition of IR-rule:
(D0′ ∨ (L̃1,1 ∧ . . . ∧ L̃1,r1 ∧ K1′ ) ∨ . . . ∨ (L̃q,1 ∧ . . . ∧ L̃q,rq ∧ Kq′ )) ∧ (D1′ ∨
1 1
(L1,1 ∧ M1,1 ) ∨ . . . ∨ (L1,1 ∧ M1,p 1,1
) ∨ . . . ∨ (L1,r1 ∧ M1,1r1
) ∨ . . . ∨ (L1,r1 ∧
′ 1 1
M1,p1,r )) ∧ . . . ∧ (Dq ∨ (Lq,1 ∧ Mq,1 ) ∨ . . . ∨ (Lq,1 ∧ Mq,pq,1 ) ∨ . . . ∨ (Lq,rq ∧
r1
1
rq rq ′ ′ ′
Mq,1 ) ∨ . . . ∨ (Lq,rq ∧ Mq,p q,rq ))) ⊃ (D0 ∨ D1 . . . ∨ Dq ). QED.
Theorem 2 (Soundness and completeness of IR-calculus). A set S of c-clauses
is unsatisfiable if and only if S ⊢IR .
Proof. The soundness is provided by Prop. 4.
Completeness. If S is unsatisfiable set, then S ⊢IR by Theorem 1. By Prop.
3, any inference of from S in CR can be transformed into an inference of
from S but already in the IR-calculus, that is S ⊢IR . QED.
Example 2. Let us consider the set U from Example 1 and construct the (mini-
mal) inference of from U in IR is as follows:
1. (A ∧ ¬A) ∨ (B ∧ C) ∨ (E ∧ L) (∈ U ),
2. (A ∧ ¬A) ∨ (B ∧ C) ∨ (E ∧ L) (∈ U ),
3. (B ∧ C) ∨ (E ∧ L) (by IR from (1) ac a nucleus and (2) as an electron),
4. ¬B ∨ ¬C (∈ U ),
5. ¬E ∨ ¬L (∈ U ),
6. (by IR from (3) as a nucleus and (4) and (5) as electrons).
We have again proved the unsatisfiability of U .
Draw your attention to the fact that this inference in IR is shorter than the
inference in CR from Example 1. This situation is more or less standard for these
calculi (see the section containing a comparison of CR and IR).
4 C-clause calculi for logic with equality
The CR- and IR-calculi admit equality handling based on a modification of the
paramodulation rule that was proposed in [9] for inference search in first-order
theories with equality (denoted by ≃).
We are needed in the following notions that provide us with a possibility to
reduce the establishing of the validity of the first-order statement with equality
to the search of the refutation of a certain set of c-clauses.
Let S be a set of c-clauses. Then S ≃ denotes the set of equality axioms for S
in the form of clauses, in which x, y, z, x0 , . . . , xp are variables (see, for example,
[6]): consists of the following (1) x ≃ x, (2) x 6≃ y ∨ y ≃ x, (3) x 6≃ y ∨ y 6≃
z ∨ x ≃ z, (4) xi 6≃ xo ∨ R̃(x1 , . . . , xi , . . . , xp ) ∨ R(x1 , . . . , x0 , . . . , xp ) for each
p-arity predicate symbol R occurring in S and for each i = 1, 2, . . . , p, (5) xi 6≃ xo
146
∨ f (x1 , . . . , xi , . . . , xp ) ≃ f (x1 , . . . , x0 , . . . , xp ) for each p-arity function symbol
f occurring in S and for each i = 1, 2, . . . , p.
A set S of c-clauses is called equationally unsatisfiable if and only if the set
S ∪ S ≃ is unsatisfiable.
Thus, in the case when we have deals with S requiring equality handling,
we must establish the equationally unsatisfiability of the set S, which can be
achieved by deducing the empty clause from S ∪ S ≃ . But such approach leads
to the extreme large growth of the searching space. For the optimization of such
growth, we use a modification of the paramodulation rule [9].
Paramodulation rule PP. Let we have two c-clauses D and D′ ∨ (K ∧ s ≃ t),
where D′ is a c-clause and K conjunct (possibly, empty). If there exists mgsu
σ of the set of terms {s, u}, where u is a term occurring in D at a selected
position, then the c-clause D′ · σ ∨ (D · σ)[t · σ] is said to be inferred from these
c-clauses by the rule P P , where (D · σ)[t · σ] denotes the result of replacing in
D · σ the term u · σ being at the selected position by t · σ. At that, the or-
dered pair h D, D′ ∨ (K ∧ s ≃ t) i is called a PP-clash (w.r.t. s ≃ t) with the
P P -paramodulant D′ ·σ ∨ (D·σ)[t·σ], nucleus D, and electron D′ ∨(K ∧s ≃ t).
The set S f of functionally reflexive axioms for a set S of c-clauses consists
of all the clauses of the form f (x1 , . . . , xp ) ≃ f (x1 , . . . , xp ), where f is a p-arity
function symbol occurring in S.
Adding P P to the CR- and IR-calculi, we get the calculi CR+PP and IR+PP
intended for inference search in first-order classical logic with equality.
Remark. If in the above-given definition, P P is applied to only clauses, we
have the usual paramodulation rule from [9] being denoted by P here.
Because of the completeness of the inference system “negative hyper-resolution
+ paramodulation” (see, for example, [6]), the following result takes place on
the basis that a set S of c-clauses is equationally unsatisfiable if and only if ρ(S)
is equationally unsatisfiable.
Robinson-Wos’s Proposition. A set S of c-clauses is equationally unsatis-
fiable if and only if ρ(S) ∪ {x = x} ∪ S f ⊢RR+P .
Taking into account the well-known result [10] about the completeness of
the system “resolution + paramodulation” without using functionally reflexive
axioms, we obtain the further reinforcement of Robinson-Wos’s Proposition.
Corollary. A set S of c-clauses is equationally unsatisfiable if and only if
ρ(S) ∪ {x = x} ⊢RR+P . Moreover, RR can denote the only binary rule.
Now, we have all the necessary for obtaining the results about the complete-
ness of the calculi CR+PP and IR+PP.
First of all, the following analog of Lemma 1 for the P P -rule is obvious.
Lemma 3. Let D and D′ ∨ (K ∧ s ≃ t) are c-clauses from the definition of
P P . If for C ∈ ρ(D) and C ′ ∈ ρ(D′ ), there exists the P P -clash hC, C ′ ∨ s ≃ ti
w.r.t. s ≃ t with a P P -paramodulant A, then there exists the P P -clash hD,
D′ ∨ (K ∧ s ≃ t)i w.r.t. s ≃ t with such a P P -paramodulant B that A ∈ ρ(B).
147
Using this lemma and Prop. 2 and 3, it is easy to obtain the following result.
Proposition 5. Let S be a set of c-clauses and B1′ , . . ., Bn′ an inference of
from ρ(S) ∪ {x = x} ∪ S f in the calculus RR+P. Then there exists an infer-
ence B1 , . . ., Bn of from S ∪ {x = x} ∪ S f in the calculus CR+PP (IR+PP)
such that: (1) if Bj′ is a variant of a resolvent of an RR-clash with Br′ as its nu-
cleus, then for some j ′ and r′ , Bj ′ is a variant of a resolvent of the corresponding
CR-clash (IR-clash) with Br′ as its nucleus and, additionally, Br′ ∈ ρ(Br′ ·τ ) for
some substitution τ ; (2) if Bj′ is a variant of a paramodulant of a P P -clash with
Br′ as its nucleus, then for some j ′ and r′ , Bj ′ is a variant of a paramodulant of
the P P -clash with Br′ as its nucleus and Br′ ∈ ρ(Br′ ·τ ) for some substitution τ .
This proposition, in fact, guarantees the completeness of the paramodulation
extensions of the CR- and IR-calculi as well as their methods and strategies, some
of which are given in the next section. Note that the soundness of such extensions
is provided by Prop. 1 and 4 and the obvious fact that P P -paramodulant is a
logical conclusion of the conjunction of all the c-clauses from {N, E} ∪ {N, E}≃ ,
where N is a nucleus and E an electron of a P P -rule application.
Theorem 3 (Soundness and completeness of CR+PP and IR+PP). A set S
of c-clauses is equationally unsatisfiable if and only if S ∪ {x = x} ⊢IR+P P
(S ∪ {x = x} ⊢CR+P P ). Moreover, CR (IR) can be the only binary rule.
Proof. The soundness of CR+PP and IR+PP is provided by the remark in
the preceding paragraph. Completeness takes place for CR+PP and IR+PP due
to Corollary and Prop. 5. The completeness of CR+PP with the binary CR-rule
is obvious. For proving the completeness of IR+PP with the binary IR-rule, it is
enough to note that any binary application of CR can be “decomposed” into r1
binary applications of IR (see the proof of Lemma 2 for the binary case). QED.
5 Methods and strategies for CR and IR
Prop. 5 gives a simple way for transferring most part of the methods and strate-
gies taking place for the usual clash-resolution (RR) to the ones for the CR- and
IR-calculi for classical logic both with and without equality. For the demonstra-
tion of how it is possible to do, let us consider the usual liner resolution and
positive and negative hyper-resolutions in their wording from [6].
Note that they are given for logic with equality. To obtain them for the
case without equality, it is enough to delete all parts concerning the P P -rule in
the definitions and wordings of the theorems given below. Also note that their
soundness is provided by the soundness of the rules CR, IR, and P P . That is
why a soundness proof is absent in corresponding theorems.
Linear strategy for CR2 +PP and IR2 +PP. It permits to apply CR2
(IR2 ) or P P to the pair of c-clauses when beginning with the second rule appli-
cation in an inference, any its c-clause is either a CR2 -resolvent (IR2 -resolvent)
or P P -paramodulant of the previous application of the rule CR2 (IR2 ) or P P ,
and the other c-clause is a variant of either a c-clause from an initial set S of
148
c-clauses or a c-clause that was deduced earlier.
Theorem 4 (Soundness and completeness of linear strategy for CR2 +PP and
IR2 +PP). A set S of c-clauses is equationally unsatisfiable if and only if there
exists an inference of from S ∪ {x = x} ∪ S f satisfying to the linear strategy
for CR2 +PP (IR2 +PP).
Proof. Completeness takes place due to the completeness of the usual linear reso-
lution with paramodulation [6], Robinson-Wos’s Proposition, and Prop. 5. QED.
Positive and negative hyper-resolution for CR2 +PP (IR2 +PP).
An atomic formula is called a positive literal. A literal of the form ¬A, where A
is an atomic formula, is a negative one.
A c-clause is called a positive (negative) if each its conjunct contains at least
one positive (negative) literal. Note that there are c-clauses being positive and
negative at the same time, for example, ¬A ∧ A.
A CR- or IR-clash hD0 , D1 , . . . , Dq i with D0 as a nucleus and D1 , . . . , Dq
as electrons is called positive (negative), if D1 , . . . , Dq are positive (negative)
c-clauses and the cut literals Lj,k in the definitions of CR or IR respectively are
negative (positive).
For logic without equality, positive (negative) hyper-resolution strategy for CR
and IR permits constructing inferences containing only the positive (negative)
hyper-resolution clashes with positive (negative) CR- or IR-resolvents.
In the case of logic with equality, we additionally permit to apply the P P -rule
only to positive nucleus and electron; moreover, a literal containing the selected
occurrence of the term u (see the definition of P P -rule) must be positive.
Theorem 5 (Soundness and completeness of positive and negative hyper-resolu-
tions with P P -rule). A set S of c-clauses is equationally unsatisfiable if and only
if there exists an inference of from S ∪ {x = x} ∪ S f satisfying to the positive
and negative hyper-resolution with CR- (IR-) and P P -rules.
Proof. Completeness. Since there exists an inference of from ρ(S)∪{x = x}∪S f
satisfying to the usual positive (negative) hyper-resolution and paramodula-
tion (see [6]), this inference can be transformed into an inference of from
S ∪ {x = x} ∪ S f satisfying to the positive and negative hyper-resolution with
CR (IR) and P P on the basis of Robinson-Wos’s Proposition and Prop. 5. QED.
Remark. In Theorems 9 and 10, the adding of functionally reflexive axioms
to the set S is the necessary condition for completeness. Examples demonstrating
this for clauses (when CR, IR, and RR are coincided) can be found in [6].
6 IR calculus and Maslov’s inverse method
Below, we give the description of MIM in the form of a special strategy for IR.
Maslov’s inverse method deals with so-called favorable assortments. In this
connection, we consider MIM as a calculus of favorable assortments that has
two inference rule: A and B. The A rule determines an initial set of favorable
149
assortments, while the B rule produces new favorable assortments from the al-
ready deduced ones. That is why we treat assortments as clauses and favorable
assortments as favorable clauses being produced by the α and β rules (see below).
If C is a conjunct L1 ∧ . . . ∧ Lr , where L1 , . . . , Lr are literals, then C̃ denotes
the clause L̃1 ∨ . . . ∨ L̃r .
Rule α. Let S be a set of c-clauses and S d = {C̃ : C is a conjunct from a
c-clause belonging to S}. If S α = {C : C = C ′ · σ ∨ C ′′ · σ, where C ′ , C ′′ ∈ S d
and C ′ and C ′′ contain literals L and L′ respectively such that there exists the
mgsu σ of {L̃, L′ }}, then any clause from S α is called a f avorable one deduced
from S by the α-rule.
Obviously, S α is a finite set if S is the same. Besides, each its (favorable)
clause contains both a literal and its complementary. That is why S is a unsat-
isfiable set of c-clauses if and only if the set S ∪ S α is unsatisfiable.
Rule β. Let S be a set of c-clauses, D ∈ S, D consists of q conjuncts, and
C1 , . . ., Cq be favorable clauses. If the IR-rule can be applied to D as a nucleus
and C1 , . . ., Cq as electrons, than the IR-resolvent of this application is called
a f avorable clause that is deducible from D, C1 , . . ., Cq by the β-rule.
Note that the requirement that the number of conjuncts in D ids equal to q
leads to the fact that any IR-resolvent of β-rule is a clause.
In these terms, MIM presents itself the following strategy for IR-calculus
called a MIM-strategy: First of all, we produce all the possible favorable clauses
applying the α-rule; then, we apply only the β-rule attempting to deduce .
The soundness of the MIM-strategy provides the soundness of IR-rule and
the above-given remark about S ∪ S α . As to completeness, the proof of it is
omitted here; we simply give the rewording of the main result for MIM from [2].
Theorem 6 (Soundness and completeness of MIM-strategy). A set S of c-clauses
that pairwise have no common variables is unsatisfiable if and only if there exists
an inference of from S satisfying to the MIM-strategy.
This result seams unexpected because of the requirement that D from the
definition of the β-rule must consist of exact q conjuncts. This apparent contra-
diction is explained by the fact that when using the MIM-strategy, we construct
S α containing clauses, the usage of which in an application of the β-rule can be
considered as a “latent” way for reducing the number of electrons.
The below-given example demonstrates some of the features of inferences
satisfying to the MIM-strategy.
Example 3. It is easy to see that for U from Example 1, U d = {¬A ∨ A, ¬B ∨ ¬C,
¬E ∨ ¬L, B, C, E, L}. As a result, U α = {¬A ∨ A ∨ ¬A ∨ A, ¬B ∨ ¬C ∨ B, ¬B ∨
¬C ∨ C, ¬E ∨ ¬L ∨ E, ¬E ∨ ¬L ∨ L}. We have the following MIM-inference:
1. (A ∧ ¬A) ∨ (B ∧ C) ∨ (E ∧ L) (∈ U ),
2. ¬B ∨ ¬C (∈ U ),
3. ¬E ∨ ¬L (∈ U ),
4. ¬A ∨ A ∨ ¬A ∨ A (by α-rule),
150
5. ¬B ∨ ¬C ∨ B (by α-rule),
6. ¬B ∨ ¬C ∨ C (by α-rule),
7. ¬E ∨ ¬L ∨ E (by α-rule),
8. ¬E ∨ ¬L ∨ L (by α-rule),
9. B ∨ E (by β-rule from (1) as a nucleus and (4), (5), and (7) as electrons ),
10 . C ∨ E (by β-rule from (1) as a nucleus and (4), (6), and (7) as electrons),
11. E (by β-rule from (2) as a nucleus and (9) and (10) as electrons),
12. B ∨ L (by β-rule from (1) as a nucleus and (4), (5), and (8) as electrons),
13 . C ∨ L (by β-rule from (1) as a nucleus and (4), (6), and (8) as electrons),
14. L (by β-rule from (2) as a nucleus and (12) and (13) as electrons),
15. (by β-rule from (3) as a nucleus and (11) and (14) as electrons).
We have proved the unsatisfiability of U at the 3rd time.
7 Comparison of CR- and IR-calculi
One can see that the obtained results on the CR- and IR-calculi “echo” each
other. In this connection, it is interesting to know is there any advantages of one
of them over the other? Moreover that Prop. 3 states that any inference of in
CR can be simulated by an inference of in IR with the same number of rule
applications. This section contains an answer on this question when comparison
is made w.r.t. inferences being minimal on the number of rule applications.
By ψ(Π, ∆, S), denote the number all the c-clauses in an inference ∆ of
a c-clause C from a set S in a calculus Π that are deduced by different rule
applications. The inference ∆ is minimal on the number of rule applications if
for any other inference ∆′ of a variant of C from S in Π, the inequality ψ(Π, ∆, S)
≤ ψ(Π, ∆′ , S) holds.
Let ∆ denote an inference of from S in CR. Using Prop. 3, it is easy to
construct an inference Γ of from S in IR such that ψ(IR, Γ, S) ≤ ψ(CR, ∆, S).
Thus, in the case when ∆min and Γmin denotes the minimal inferences on the
introduced characteristic, we have that ψ(CR, ∆min , S) − ψ(IR, Γmin , S) ≥ 0.
Let us make an attempt to find an upper bound for this difference restricting
us by the case when an initial set S contains only c-clauses without variables.
Let us consider an application of IR-rule to a nucleus c-clause D0 and electron
clauses D1 , . . . , Dn (n ≥ n) with an IR-resolvent D. Its attentive analysis
demonstrates that this (n + 1)-arity application can be slitted into n binary
applications of CR-rule in the following way: first we make a binary application
of CR to D0 and D1 , then to an obtained CR-resolvent and D2 , and so on. That
is we can split any n + 1-arity IR-application into n binary CR-applications in
such a way that for the result C of such CR-rule applications, C will contain all
or some of conjuncts belonging to D.
This observation leads to the following upper P bound for the difference given
above: ψ(CR, ∆min , S) − ψ(IR, Γmin , S) ≤ (mi − 2), where mi is the arity
of the ith CR-rule application in ∆min and the sum is taken over all of mi .
To demonstrate that this upper bound is achieved, let us take the sets Sn =
{(L1 ∧ E1 ) ∨ . . . ∨ (Ln ∧ En ), (A1,1 ∧ B1,1 ) ∨ . . . ∨ (A1,m1 ∧ B1,m1 ) ∨ L̃1 ∨
151
Ẽ1 , Ã1,1 ∨ B̃1,1 ∨ L̃1 ∨ Ẽ1 , . . ., Ã1,m1 ∨ B̃1,m1 ∨ L̃1 ∨ Ẽ1 , . . ., (An,1 ∧ Bn,1 ) ∨
. . . ∨ (An,mn ∧ Bn,mn ) ∨ L̃n ∨ Ẽn , Ãn,1 ∨ B̃n,1 ∨ L̃n ∨ Ẽn , . . ., Ãn,mn ∨ B̃n,mn
∨ L̃n ∨ Ẽn }, where L1 , . . ., Ln , E1 , . . ., En , A1,1 , . . ., An,mn , B1,1 , . . ., Bn,mn
are literals.
Below we give an inference ∆ of from Sn in the IR-calculus. (Thus, Sn is
an unsatisfiable set.)
⌈ (A1,1 ∧ B1,1 ) ∨ . . . ∨ (A1,m1 ∧ B1,m1 ) ∨ L̃1 ∨ Ẽ1 (∈ S),
| Ã1,1 ∨ B̃1,1 ∨ L̃1 ∨ Ẽ1 (∈ S),
| ...
⌊ Ã1,m1 ∨ B̃1,m1 ∨ L̃1 ∨ Ẽ1 (∈ S),
...
⌈ (An,1 ∧ Bn,1 ) ∨ . . . ∨ (An,mn ∧ Bn,mn ) ∨ L̃n ∨ Ẽn (∈ S),
| Ãn,1 ∨ B̃n,1 ∨ L̃n ∨ Ẽn (∈ S),
| ...
⌊ Ãn,mn ∨ B̃n,mn ∨ L̃n ∨ Ẽn (∈ S),
⌈ (L1 ∧ E1 ) ∨ . . . ∨ (Ln ∧ En ) (∈ S),
| L̃1 ∨ Ẽ1 (by IR from the 1st-block c-clauses with the 1st c-clause as a nucleus),
| ...
⌊ L̃n ∨ Ẽn (by IR from the nst-block c-clauses with the 1st c-clause as a nucleus),
(by IR from the (n+1)st block c-clauses with the 1st c-clause as a nucleus).
Using the ideas from [16], we can prove that ∆ is a minimal inference in IR
containing n + 1 rule applications with the arities m1 + 1, . . . , mn + 1, and n + 1.
Now, let us convert ∆ into an inference Γ of from Sn , but already in the
CR-calculus in the following way:
For each i (i = 1, . . . , n), let us replace the c-clause L̃i ∨ Ẽi by the sequence
of c-clauses (Ai,2 ∧ Bi,2 ) ∨ . . . ∨ (Ai,mi ∧ Bi,mi ) ∨ L̃i ∨ Ẽi , . . ., (Ai,mi ∧ Bi,mi )
∨ L̃i ∨ Ẽi , L̃i ∨ Ẽi that along with the all c-clauses form the i th block is an
inference of L̃i ∨ Ẽi in CR. Replace the empty clause by the sequence (L2 ∧
E2 ) ∨ . . . ∨ (Ln ∧ En ), . . ., . . . (Ln ∧ En ), , being an inference of in CR
since (L2 ∧ E2 ) ∨ . . . ∨ (Ln ∧ En ) is deduced from (L1 ∧ E1 ) ∨ (L2 ∧ E2 ) ∨
. . . ∨ (Ln ∧ En ) and (L1 ∧ E1 ) by the CR-rule, . . ., (Ln ∧ En ) is deduced from
(Ln−1 ∧ En−1 ) ∨ . . . ∨ (Ln ∧ En ) and (Ln−1 ∧ En−1 ) by the CR-rule, is
deduced from (Ln ∧ En ) and (Ln ∧ En ) by CR.
We have that Γ is an inference of from Sn in CR, for which ψ(CR, Γ , Sn )
P
= ( i=1 mi ) + (n + 1). Again using the ideas from [16], we can conclude that Γ
n
is a minimal inference in CR. Pn
Finally, we get ψ(CR, Γ , Sn ) − ψ(IR, ∆, Sn ) = (n − 1) + i=1 (mi − 1), that
is the upper bound is reachable.
8 Conclusion
The paper does not touch any practical aspects and is purely theoretical. Never-
theless, the author considers that it may be useful for researchers involved in the
implementation of intelligent systems, in particular, e-learning systems requiring
tools for proof search in classical logic at least for the following reasons.
152
The research demonstrates that the transition to c-clauses being the gener-
alization of the widely-used resolution notion as a clause gave the possibility to
construct the calculi possessing different properties in general and not worsening
such an important characteristic as the minimum number of rule applications
in comparison with the usual resolution methods. Although now it is difficult to
say that the “behavior” of provers based on these calculi will be better than the
“behavior” of the well-know resolution provers such as Vampire or Prover 9, we
may expect that more detailed analysis of the proposed approach will lead to
the further improvement of the traditional resolution technique. From this point
of view, MIM seems to be a more attractive method, possessing a number of
positive features not mentioned in the paper and requiring a separate study.
References
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In Russian.
153
Principles of intellectual control and classification
optimization in conditions of technological processes of
beneficiation complexes
Andrey Kupin1 and Anton Senko1
1
Department of Computer Systems and Networks, Faculty of Information Technologies,
Kryviy Rih National University, Partzyizdu str., 11,
50027 Kryviy Rih, Ukraine
kupin@mail.ru, antonysenko@gmail.com
Abstract. These theses contains realization of a typical technological
beneficiation complex for automation of control processes (in the context of
beneficiation of iron ore - magnetite quartzites). The hierarchy scheme of
intelligence control system for such complex combining principles of
neurocontrol, classification and optimal control has been shown. Results of
computer modeling of classification optimization process in the context of
actual indicators of magnetite quartzites concentration have been shown.
Keywords. Intellectual control, classification optimization, beneficiation
technology, iron ore, magnetite quartzites
Key Terms. Intelligence, Control System, Model, Classification
1 Introduction
Nowadays the problem of intellectual control of technological processes is considered
rather actual. Thus necessity of constant improvement of manufacture, increase of
competitiveness, minimization of technological environmental impact demands
application of complex automation systems is based on modern information
technologies (IT) and intelligent control systems (ICS) [1].
Let's consider the complex of technological processes of iron ore beneficiation
(magnetite quartzites). As the object of control such complex is characterized by
sufficient complexity (multichanneling, nonlinearity, non-stationary, illegibility and
incompleteness of information along with great value of transport delay of output
parameters, presence of noise and disturbance, presence of recycles on the majority of
stages, etc.) [2]. Taking into account these properties, statement of a problem and
154
potential approaches to their decision such complex can be considered as typical [3-
4].
Works of [2-10] are of great importance for the development of intellectual control
theory of beneficiation technology objects. At the same time, despite of considerable
quantity of research and development, existing systems of automation do not always
meet modern requirements and do not provide the effective decision of difficult tasks
in actual conditions in beneficiation process line.
2 Review of existing decisions and task setting
Taking into account multidimensionality, illegibility and incompleteness of
technological information on all levels of control it is necessary to use ICS to support
operators’ (controllers, technologists and other) decision making and increase their
quality [1]. The further task setting of intellectual control of a process line (a section)
can be also conditionally represented by means of classical cybernetics chart "black
box" (Fig. 1). Accordingly, for controlling the beneficiation process set of vectors X,
U, Y, V on the basis of can be formed as follows.
V 1 , 2 , 3 ,..., n
v
g d0
SECTION
C1 C2 C3
I stage II stage III stage
Q0 Q1 Q2 Q3
Internal d1 Internal d2 Internal
variables: pp 1( 1) variables: pp 2( 2) variables: d3
1 2
Pm 1 ε1 Pm 2 ε2 Pm3 pp 3( 3),βk
Вm 1 ρk1 Вm 2 ρk2 Вм 3 ρk3
ρs1 ρs2 ρs3 3, k
В k1 В k2 В k3
ε 3, ε k
Вs 1 Вs 2 Вs 3
х1 х2 х3
х
Fig. 1. Process line (section) of concentrating as the object of intelligence control
In Fig. 1 such notations are taken: i 1...N r is a number of industrial variety of
ore; Nr is quantity of industrial varieties; i is estimated raw ore grade;
i is specific gravity of every variety of ore; i is an index or a group of
indices that characterize physical and chemical properties of ore (for example, density
of corresponding varieties of ore, strength, grindability, etc.); g g i is index that
155
characterizes mineralogical and/or morphological properties of ore (for example,
averaged size of magnetite dissemination in ore after varieties); d0 is averaged ore
coarseness before beneficiation; Q0 is an ore consumption on the first stage of
beneficiation; j 1...N s is number of beneficiation stage; Ns – is quantity of stage;
Q Q j , is processing output of each stage; C C j is circulation load; d d j
is averaged product coarseness; is a solid content in pulp;
Pm Pm j
Bm Bm j , Bk Bk j , Bs Bs j are consumption of water to the mill, classifier and
is a pulp density in the process of
magnetic separation respectively; k k j
classification; is a pulp density before magnetic separation;
s p j
pp pp j j is an estimated grade in the industrial product; х х j is loss
of a commercial component in tails; k is a quality of concentrate; j is an
output of useful component in an industrial product; k is an output of useful
component in concentrate; j is an extraction of useful component in an
industrial product; k is an extraction of useful component in a concentrate.
Thus distribution of state vector on input and output indexes is conditional enough
because most parameters on output, for example, of the first stage will be input for the
second, etc.
For further application of multidimensional model such as Fig. 1 (for example, for
decision of identification tasks or synthesis of automated control systems of
beneficiation TP) with using artificial intelligence technology a number of typical
neural network structures that will be offer by the author here.
3 The hierarchy scheme of intelligence control system for such
complex combining principles of neurocontrol, classification and
optimal control
The results of tests of such intelligent systems have proved the possibility of their
application in the beneficiation TP. At the same time, to ensure their operation it is
necessary to determine the values of settings and / or trends in their paths. Further
studies have shown that the determination of the required setting values it is necessary
to carry out by combination of the following [7]:
1. Classification control, that is founded on the basis of permanent accumulation of
technological parameters history database (DB), their grouping on certain signs
(clustering) and determination of value of setting for the measure of similarity to the
current values of vectors: input, output and internal parameters[8, 9].
2. Optimal control, which requires the design of general purpose functionality for
the system and the application of global optimization methods [4, 10].
Main advantages of the classification approach are their potentially high fast-acting
due to the use of well-known methods of clustering and patterns recognition (for
example, neural networks classification). The disadvantage is low accuracy (the
156
chosen decision is not necessarily optimal, and even quasioptimal). Also, application
of the approach does not always guarantee the result. In particular, this may be due to
such cases:
at the beginning of the system operation, when the database of technological
situations parameters is quite small;
in the case when necessary (similar) combination of parameters (cluster) has not
been met yet in the process of exploitation of ICS;
in changing of flowsheet, regime map, presence of considerable disturbance of
properties of primary raw material (ore, its amount and correlation of mineral
varieties, etc.).
On the one side, optimization approaches in the case of multidimensional goal
function are also characterized by disadvantages that are caused by:
the difficulty of obtaining a sufficiently adequate mathematical model of TP [4],
which is typical for most inertial processes (in particular, the beneficiation);
the bad conditionality of optimization task (presence of great amount of local
extremums) that appears in the case of application of well-known identification
methods of the multidimensional systems (regressive models, Wiener–Hopf
equation, synergetic and self-organizations, artificial neural networks and others in
particular) and greatly limits the application of well-known methods of
multidimensional optimization;
slow convergence rate of computing process during optimization in large number
of cases.
On the other hand, in the case of the possibility of designing the mathematical
model and a good choice of hill climbing algorithm (method) it is possible to solve
control task, which allows to define a really optimal (or quasioptimal) settings, with
certain limitations. Taking into account well-known advantages and disadvantages of
the above-mentioned approaches for the implementation of multichannel ICS of TP of
iron-ore beneficiation the approach based on combination of classification and
optimization algorithms has been offered. Structure of multichannel hierarchical ICS
of TP of beneficiation complex based on the system of coupling of neurocontrol,
classification and optimization methods is shown in Fig. 2.
In Fig. 2 such notations are taken: OCij is a control object (channel), j its number
(j=1,…,ki; ki is an amount of control channels), i is a number of the stage for local TP
(for example, fragmentation, classification, magnetic separation, etc., i=1,…,Ns; Ns is
amount of the stages of beneficiation TP); NCij – intelligence neurocontroller of OCij;
Vij is a vector of disturbing influences for OCij; Yij – a vector of output characteristics
of OCij; Uij is a vector of control influences (actions) of OCij; Xij is a vector of
informative parameters about the state of OCij; Ysij is a vector of settings of output
characteristics of ОCij; TP*i is the complex of all local TP of the certain stage; V*i is a
vector of main influences of disturbing of TP*i; Y*i is a vector of output characteristics
of ТP*i; X*i is a vector of information parameters about current stat of TP* complex i;
Y*si is a vector of tasks (settings) for output characteristics of TP*i; NE*i –
neuroemulator (predictive mathematical model or predictor) for TP of the
corresponding stage.
Three main control levels 1) of local regime parameters (ore and/or water
consumption, pulp density, etc.); 2) quality indices (content of useful component,
157
output, exception, etc.); 3) complex of TP (fragmentation, classification, magnetic
separation) are divided in the structure.
First stage of beneficiation TP
V11 V*1
U 11 Y11
OC11 Y*1
TP*1
X11
NC11 X*1
Control
Y11, X11, V11, U11 system of
First control channel first stage of
Y s11 beneficiation TP
of iron ore
V1k 1
Y * s1 Y *1
U 1 k1 Y1 k1 NE*1
OC 1 k
1
X 1k 1
N C1k Y1k 1 , X 1k 1 , V1k 1 , U 1k 1
1
Control channel (k1) Y s1k 1
for TP of first stage
Y *s n
Last stage (n) of beneficiation TP
Y *n
Block of optimization of functioning of complex TP ore-concentrating factory
Choice of general Choice of method of
criterion of optimization realization of intellec-
of TP of beneficiation tual control of TP:
- classification;
- optimization.
Fig. 2. The structure of combined multichannel ICS of TP of magnetite quartzites
beneficiation (classification-optimal control)
So, for example, for a complex of TP of the first stage (supposing that for TP of
fragmentation i=1, k1=2): the first channel (OC11) is the correlation of "ore-water"; the
second channel (OC12) is the mill productivity output (at unloading); V11={coarseness
of grading (averaged coarseness) of input product}; V12={physical and chemical and
158
mechanical properties of ore}; Y11, Y12={ coarseness of grading (averaged
coarseness) of industrial product, productivity after the industrial product, output of
the prepared class}; U11={mill water consumption }; U12={ ore input productivity};
X11={content of solid in the middle of the mill}; X12={all regime indices of mill
work}. Similarly the formalization for other TP of the first stage (classification,
magnetic separation) is carried out. Then the resulting characteristics for a complex of
TP (all stages) as a whole are formed as follows: V*1=V11V12 ( is the operation of
logical combination of vectors); Y*1={quality of industrial product by quality of
useful component, productivity on the output stage}; X*1=X11X12.
The idea of the approach is in application of combined algorithm with combination
of classification and optimal control approaches in order to ensure the acceleration
decision-making process in multichannel ICS of TP of magnetite quartzites
beneficiation. The main features of the implementation of such a system are as
follows [1, 7].
The intellectual analysis of current state of control object is carried out constantly
at the end of the next step of discrete time by the top level of the system on every
stage of beneficiation in the block of optimization of beneficiation complex operation.
The determining of settings (tasks) for the control systems of the corresponding stages
(middle level) is carried out on the basis of a coherent analysis of indexes of all
beneficiation stages. At the same time, in contrast to existing approaches, decision-
making process (definition of the necessary settings) in the system (Fig. 2) can be
occurred through intelligent classification (classification control) or global
optimization (optimal control). Algorithms for the implementation of corresponding
computational procedures will be given in the future.
On the middle level control of TP complex for separate stages is carried out. For
this purpose the level is given the value of optimal settings from a top level and it
determines a task (proves these settings) for the regulators of all local TP and their
corresponding channels of control of every beneficiation stage. From the other side
middle level systems collect primary information about the state of every channel
(control actions, outputs, disturbing) from the subsystems of the bottom level, carry
out its primary processing, prediction of values of input and output indexes of the
stage using of neuroemulator (NE*і). Certain data are also passed on the top level for
decision making and determination of optimal settings for the purpose of the
coordinated control of all stages and complex of beneficiation TP as a whole.
The bottom level of the system controls separate local TP of each stage. For this
purpose the level contains the number of control channels. Each channel has its own
inverse neuroregulator that recreates the inverse dynamics of the process. The task of
work of such regulator is maintenance of necessary value of settings, that is
determined at the top level of the system and given from the corresponding control
subsystem of the certain stage (id est. middle level). In turn, the bottom level
subsystem passes information about the state of each channel (indexes of control
influences, value of output and information signals, disturbance) to the middle level
system at first and then to the top level.
159
1. Desired Output and Actual Network Output
170
150
130 (U3)
Output (В3, t/h)
110 (U2)
BM3(U1)
90 BK3(U2)
70 BC3(U3)
50 (U1)
30
10
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Exemplar
2. Desired Output and Actual Network Output
240
220
200
Output (Q3, t/h)
180 Q3*
160 Q3
140
120
100
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Exemplar
4. Desired Output and Actual Network Output
67
66,5
66
65,5
Output (βK , %)
65
βK*
64,5
βK
64
63,5
63
62,5
62
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Exemplar
Fig. 3. Results of computer modeling of classification optimization process in the
context of actual indicators of magnetite quartzites concentration
160
4 Conclusions
For the hierarchy scheme of ICS of beneficiation technological complex on the basis
of combination of principles of neurocontrol, intelligence classification and global
optimization contingency approach at forming limit cluster of certain "special
technological situations", that allows to control TP automatically in real-time mode,
determine and propose corresponding control influences has been offered.
The conducted researches, results of computer modeling (Fig. 3) and industrial
tests [1, 5-7] proved that application of neural networks schemes on the basis of
inverse models and neuroemulators as regulators of separate channels of beneficiation
TP has a sufficient dynamics (reasonable time of settings exercise on condition of its
presence), the possibility of the proper disturbance rejection at 10% level and
operation on the conditions of nonlinear limitations (changes of controller parameters)
on the basis of satiation principle. Thus, the task of this work is the verification of
possibilities of classification strategy for reliable determination of optimal values of
current parameters of TP (in the form of the relevant tasks or setting for controllers),
that will provide stable work of local regulators in the above-mentioned terms.
References
1. Kupin, A.I.: Intellectual identification and controls in the conditions of processes of
concentrating technology. The monograph. Kyiv: Korneychuk's Publishing house (2008)
2. Scheiner, B.J., Stanley, D.A., Karr, C.L. Emerging computer techniques in the minerals
industry. Littleton, CO: Society for Mining, Metallurgy, and Exploration, Inc. (1993)
3. Wills, B.A. Automatic control in mineral processing . Mining Mag. No 3, pp. 316--320
(1987)
4. Maryuta, A.N., Kochura, E.V. Economic - mathematical methods of optimum control of the
enterprises. Dnepropetrovsk: Science and education (2002)
5. Kupin, A.I. Neural identification of technological process of iron ore beneficiation.
Proceedings of 4th IEEE Workshop on Intelligent Data Acquisition and Advanced
Computing Systems Technology and Applications (IDAACS’2007). Dortmund, pp. 225--
227 (2007)
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concentrating technology is on the basis of application of neural networks. Metallurgical and
Mining Industry, No4, pp. 51--55 (2014)
7. Kupin, A.I. Application of neurocontrol principles and classification optimisation in
conditions of sophisticated technological processes of beneficiation complexes.
Metallurgical and Mining Industry, No6, pp. 16--24 (2014)
8. Scheiner, B.J., Stanley, D.A., Karr, C.L. Control of liquid level via learning classifier
system. Proceedings of The Applications of Artificial Intelligence VII Conference. No1095,
pp. 78-85 (1989)
9. Krasnopoyasovsky, А.S. Information synthesis of intellectual control systems. Sumy:
Publishing house SumSU (2004)
10.Morkun, V.S., Tron V.V. Ore preparation multi-criteria energy-efficient automated control
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No5, pp. 4--7 (2014)
161
A Composite Indicator of K-society Measurement
Kseniia Ilchenko1,2, Ivan Pyshnograiev1,2
1 World Data Center for Geoinformatics and Sustainable Development,
Peremohy av. 37, 03056 Kyiv, Ukraine
2 National Technical University of Ukraine „Kyiv Polytechnic Institute“,
Peremohy av. 37, 03056 Kyiv, Ukraine
{ilchenko, pyshnograiev}@wdc.org.ua
Abstract. The development of K-society theories leads to necessity of finding
an approach of measuring the progress of each country. The paper presents the
composite model which based on OECD and UN methodology. The hierarchy
model consists of three dimensions and 14 indicators and gives a possibility to
calculate K-society Index for 87 countries. The analysis of the results presents
country’s current rating and dynamics. The data for Top-20 countries, the last
twenty countries and North America are introduced in the paper. K-society
Index for Ukraine is described in details. The future state’s strategy can be
based on K-society measurement.
Keywords: MathematicalModeling, Knowledge, Methodology,
DecisionSupport.
1 Introduction
The fundamental concept of sustainable development requires the review of the
classic studies about the world. Knowledge as a higher value of informational process
forces the progress in sustainability. Also, the knowledge is one of the factors of
production in modern economy. That is why, the theory about knowledge-based
economy and society becomes wide shared among scientists. For example, knowledge
society is described as sustainability concept by N. Afgan and M. Carvalho [1]. M.
Kulin studies learning and knowledge influence as a factor of global competitiveness
[2], the impact of knowledge for society is the main focus of G. Bohme and N. Stehr
research [3]. Thus, the theoretical aspects of Knowledge society are well-studied.
At the same time, the questions about applied evaluation of knowledge in a country,
comparison of different countries and knowledge dynamics research are still open.
Taking into account the complex character of knowledge, it can be presented as the
set of indicators which are gathered in a hierarchy model.
Therefore, the main idea of the research is to draw out a composite indicator for
measurement knowledge as a sophisticated category with a purpose of country
development analysis.
162
2 K-society as a New Mode of the World Developing
Classic economic theory presents three factors of production that are used in a
production process, which leads to finished goods. These three basic resources are
land, labor and capital. Nowadays this fundamental approach was divided into several
complex theories that include additional factors of production, for example,
technological progress, human capital and social capital. Basically, those resources
can be aggregated into one category – knowledge. More than this, knowledge and
information become the most significant factors of production and form the basis for
new technological mode.
Knowledge society (K-society) is widespread concept, but scientists still
investigate its nature [4]. The mass production of knowledge changes the economy in
global world in quite short terms. However, this process is dissimilar in different
countries.
The research of K-society is undertaken by all developed countries for more than
40 years but there are still a lot of controversial question. First of all there is no
agreement about terminology. Such terms as “K-society”, “Informational society”,
“Technogeneous society” serve the purpose of science communication in this topic.
The term “K-society” was used by M. Zgurovsky to mean a where institutions and
organizations give possibilities to people and information to develop without any
barriers and open opportunities for mass production and mass usage of all kind of
knowledge in global scales. Therefore, the development of technologies is an
important part of K-society, but not the main purpose. Thus, the term
“Technogeneous society” doesn’t describe these processes in full measure.
The question about links between K-society and information society is more
complicated. The first one is based on definition of knowledge, the second one uses
information as a basic category. The development of new computing technologies has
not influenced to significancy of common paradigm, but the possibility to get, safe,
analyze and transfer knowledge was changed cardinally. That led to increasing
velocity of information circulation. Moreover, it is difficult to divide information and
knowledge. But in the purpose of this research it is assumed that knowledge includes
information, and it is a product of information processing.
According to theoretical research the concept of K-society is ambiguous. On the
one hand it is a philosophic theory, which has no practical meaning, on the other hand
it is the set of instruments and methods for providing sustainable development of
modern society [5]. In accordance to the second opinion K-society proclaims the
active usage of knowledge, which is the main asset.
The main accent is education, which forms a human capital and guarantees the
access to information. But the measurement of educational level cannot give a
complete picture of knowledge in society. Therefore, K-society must be formalized
more manifold system of indicators. Likely, such system includes the description of
current situation in economy, perspectives and information transactions. It is obvious
that the development of model for describing K-society is a nontrivial issue.
163
3 Methodology
According to the UNO methodology, the index of K-society should be based on
three dimensions: Assets, Advancement and Foresightedness [6]. The first one
describes the level of education, especially, among young people, and the
development of information streams. These two main directions include such
indicators as: expected schooling, proportion of young people, the diffusion of
newspapers, the Internet, main phone lines and cellular phones. The second
dimension represents human and informational resources, which are indicated by
public health expenditure, research and development expenditure, military
expenditure, pupil/teacher ratios in primary education, and a proxy of the “freedom
from corruption” indicator. The last dimension shows the external influence on K-
society dynamics in the state. This dimension consists of low child mortality rates,
equality in income distribution (GINI Index), protected areas as percentage of a
country’s surface, and CO2 emissions per capita indicators. This approach was
officially accepted for approximately 45 countries in 2005.
Taking into account the existent basic specification of the main categories, it
becomes possible to continue this research in terms of current informational mode.
Thus, new hierarchical model for K-society measurement should be built.
Therefore, it is necessary to clarify the approaches for drawing out this model. The
OECD presented methodology and user guide on constructing composite indicators
[7]. According to this, there are several obligatory steps in models’ creation.
Firstly, the full understanding of processes that can have influence on K-society
needs to be represented in theoretical framework. This step concludes with the
number of selection criteria. As referred to listed above, the framework is based on
UN model.
Secondly, the very important step is data selection. It includes the availability and
quality data checking. In addition, the question about strengths and weaknesses of
indicators must be resolved. Not least important is to find the reputable source for
each data set. Theoretically, all data must be provided by international world-known
organizations.
In view of these two steps the UN approach has some disadvantages that are
caused by following reasons. On the one hand, last ten years have brought significant
changes in informational development. As a result of this process some of indicators
lost their relevance. On the other hand, not all data sets are still gathered by
authoritative organizations. That is why the original model needs revision and
modernization.
Thirdly, the modeling needs complete data sets. Thus, the problem of empty cells
that usually appears after the data selection requires imputation of missing data. The
various kinds of methods for working with complex models are established in World
Data Center for Geoinformatics and Sustainable Development [8]. Therefore, the
recommendation for this case is to augment the empties by previous period
information.
The step includes multivariate analyses. This phase gives the possibility to double
check the starting hypothesis about the set of indicators. The significance of sampling
should be checked. Other important question is to evaluate relations between
indicators. That is why the elements of principal components analysis and cluster
164
analysis influence the final decision about model structure. This step identifies
statistically similar indicators. Thus, the additional explanation of internal relations or
model’s rebuilding can be required. As a result of this issue the model can be
amplified by additional explanation.
Taking into account the miscellaneous nature of indicators the next step is
normalization. There are more than ten typical approaches to its implementation. It is
necessary to underline that there is no goal to make the estimation more complex. For
this reason, the standardization is the optimal variant for this step. The formula of this
type of normalization is as below:
Valuenorm = (Value – Valuemin)/( Valuemax - Valuemin) . (1)
In case when it is necessary to represent the inverse coupling this formula converts
to:
Valuenorm =1 - (Value – Valuemin)/( Valuemax - Valuemin) . (2)
As a result, all indicators values lie in interval from 0 to 1.
To express the theoretical framework and relations underlined at the previous
stages, the sixth step includes finding out the way of indicators aggregation and their
weights establishment. For instance, the model’s hierarchy is constructed.
Each dimensions’ index consists of several indicators and can be presented as the
average value of its components. In the same manner K-society Index equals to the all
dimensions indices aggregation.
At the next step uncertainty and sensitivity analysis emphasize the reasons of the
differences between results of using variety of aggregation, imputation and
normalization methods. This step identifies all possible sources of uncertainty and
determines what sources have more influence to the overall score.
Eighthly, detecting dominant and critical indicators for objects or their groups
provides the information about the levels of influence for the assessed system. It is
also very important for policy making problems.
Then, for modeling results validation developed index is compared to others that
describe the phenomenon of similar nature. The comparison base consists of well-
known indices that authoritative organizations and institutions provide. Thus, two
indices were chosen for purposes of final analysis: Fragile State Index [9] and Index
of Economic Freedom [10].
Finally, the last step is to present the results in a clear and accurate manner. That is
why visualization is the part of this algorithm. It is necessary to choose the correct
tools that provide total understanding of the obtained results. Thus, the final step of
modeling becomes the element of a decision making support system.
Taking into consideration the UN approach and OECD methodology the new
model was drawn out. The indicators, data providers and data sources are presented in
Table 1.
165
Table 1. List of indicators
Type of
Indicator Institution Source
influence
UNESCO
School life
Institute for http://www.uis.unesco.org Positive
expectancy
Statistics
School enrollment, http://data.worldbank.org/indica
World Bank Positive
secondary (% net) tor/SE.SEC.NENR
Internet http://www.itu.int/en/ITU-
subscriptions per ITU D/Statistics/Pages/stat/default.a Positive
100 inhabitants spx
Main phone http://www.itu.int/en/ITU-
subscriptions per ITU D/Statistics/Pages/stat/default.a Positive
100 inhabitants spx
Cellular http://www.itu.int/en/ITU-
subscriptions per ITU D/Statistics/Pages/stat/default.a Positive
100 inhabitants spx
Gov’t Health
World Health http://apps.who.int/gho/data/?th
Expenditures (% of Positive
Organization eme=main
total gov’t exp)
UNESCO
R&D expenditure
Institute for http://www.uis.unesco.org Positive
as % of GDP
Statistics
Military
expenditures (% of SIPRI http://www.sipri.org/ Negative
GDP)
Pupils per teacher http://data.worldbank.org/indica
World Bank Negative
in primary school tor/SE.PRM.ENRL.TC.ZS
Corruption Transparency http://www.transparency.org/re
Positive
perception International search/cpi/overview
Child mortality
(children under 5 http://data.worldbank.org/indica
World Bank Negative
years per 1000 tor/SH.DYN.MORT
births)
http://data.worldbank.org/indica
Gini Index World Bank Negative
tor/SI.POV.GINI
Terrestrial and
marine protected http://data.worldbank.org/indica
World Bank Positive
areas (% of total tor/ER.PTD.TOTL.ZS
territorial area)
CO2 emissions
http://data.worldbank.org/indica
(metric tons per World Bank Negative
tor/EN.ATM.CO2E.PC
capita)
Data for 87 countries were gathered and complemented in the process of model
development. Thus, the results of estimations are described in the next paragraph.
166
4 Results
According to the algorithm each of the dimensions were counted based on their
components. It is necessary to mention that it gives the possibility to measure Assets,
Advancements and Foresightedness as separate indices. Such evaluation brings an
opportunity to additional comparison of countries in terms of the dimensions. But in
accordance with the main purpose of the research the K-society Index has to be
measured. That is why the procedure of linear convolution is implemented twice.
Collected data give a possibility to provide the calculations for period from 2008 to
2013.
The results for 2013 year show that the Top 10 countries for K-society Index
consists of Switzerland, Denmark, Netherlands, Sweden, Slovenia, France, Austria,
New Zealand, Japan and Finland. The values for the final index and three dimensions
are presented in Table 2.
Table 2. Top 10 countries by K-society Index 2013
The Assets The Advancement The Foresightedness KS Rank
Index Index Index Index
Switzerland 0,801 0,827 0,780 0,803 1
Denmark 0,758 0,794 0,785 0,779 2
Netherlands 0,764 0,757 0,789 0,770 3
Sweden 0,722 0,809 0,766 0,766 4
Slovenia 0,670 0,642 0,949 0,754 5
France 0,789 0,636 0,792 0,739 6
Austria 0,703 0,749 0,765 0,739 7
New Zealand 0,744 0,737 0,711 0,731 8
Japan 0,719 0,777 0,687 0,728 9
Finland 0,692 0,773 0,722 0,729 10
The analysis of representatives shows that Top 10 involves high-developed countries
with sustainable economic, ecological and social conditions. The variance between
the first and the last states from the list described above equals to 0,074. Moreover,
the gap between top possible value of the index, and the value for Switzerland is
0,197.
The last 10 countries of the ranking for 2013 year are presented in following table
(Table 3).
The last one, Nigeria, has a high level of Fragile States Index, which is caused by
alert meaning of such indicators as Demographic Pressure, Group Grievance, Uneven
Economic Development, State Legitimacy, Public Services, etc. Even more, the
conflict barometer, which is counted by HIIK [11], shows that this country has the
value 5. That means the existence of the war in Nigeria.
According to the same sources Pakistan is under the inter-ethnic violence and
conflict with India that were classified as limited war and violent crisis. Also the
problems with Demographic Pressure, Refugees, Group Grievance, State Legitimacy
167
Human Rights, Security Apparatus, etc. exist in the state. Moreover, the situation,
described by Fragile States Index, is even worse than in Nigeria.
Table 3. Last 10 countries by K-society Index 2013
The Assets The Advancement The Foresightedness KS Rank
Index Index Index Index
Paraguay 0,280 0,359 0,569 0,402 78
Senegal 0,145 0,432 0,633 0,403 79
India 0,278 0,327 0,589 0,398 80
Madagascar 0,133 0,334 0,543 0,337 81
Gambia 0,145 0,359 0,455 0,320 82
Kenya 0,206 0,249 0,492 0,315 83
Ethiopia 0,052 0,284 0,637 0,324 84
Mozambique 0,183 0,260 0,494 0,312 85
Pakistan 0,107 0,182 0,578 0,289 86
Nigeria 0,074 0,304 0,433 0,270 87
The next one is Mozambique. In accordance to the Fund for Peace methodology
the state’s current pressure assessment is “Very High Warning”. The more dangerous
indicators are: Demographic Pressure, Uneven Economic Development, Economy
and Public Services.
Ethiopia is in a group of countries, which have “alert” status. The greatest
problems of Ethiopia are Social and Economic Fields, External Intervention and
Factionalized Elites. Such tendency has been continuing since 2009.
Kenya has a limited war, which is connected with inter-ethnic violence. In addition
this state is 18 from 178 countries in Fragile States Index. The problems with Political
and Military, Social and Economic fields lead to high negative rating.
The next country is Gambia. It has growing tendency from stable to very high
warning assessment in Fragile States Index.
India is the neighboring country for Pakistan. Thus, problems with conflicts, which
were described above, also concern India. Furthermore, India has to worry about
Demographic Pressure, Group Grievance, Uneven Economic Development and
Security Apparatus. The less number of problems gives India higher value of K-
society Index. The fact of common knowledge is that India tries to develop IT sphere.
But it seems that it is not enough for building K-society.
Senegal has stable, very high warning assessment since 2006. The long-term
tendencies show that the situation in the country becomes more and more dangerous.
Madagascar is near Senegal in rating and the common tendencies almost the same,
except the reduction of Group Grievance and Refugees. Such situation has been
occurred since 2008. However, Paraguay is the only country from the bottom part of
the rating that has been increasing in Fragile States Index in terms of improving
situation.
This analysis shows that K-society Index reflects much more information than IT
or science alone. It correlates with current political and economic situation in the
country. Moreover, it is impossible to build K-society in unsustainable environment.
168
It is essential to discover the relations between K-society Index and other well-
known indices. Fig. 1 shows the correlation between Fragile States Index and K-
society Index.
Fig. 1. Correlation between Fragile States Index and K-society Index
It describes high linear relation between indices. Thus, it is an additional proof of
state instability influence to knowledge establishment.
Fig. 2. Correlation between Economic Freedom and K-society Index
Probably, more interesting results were obtained from K-society Index and
Economic Freedom relations. Fig. 2 shows that the economic component is not
fundamental for processes in K-society. The truth is that economy is rather important.
The results of the research show that K-society can be unequal in neighboring
countries. Also there is no dependence between the leading positions in the world and
absolute success in K-society creation. For instance, the comparison of Mexico, USA
and Canada is a good illustration of mentioned above thesis (Fig. 3).
The graph illustrates the North America countries’ values. The first place has
Canada. The USA shows almost the same tendency but with lower score. Both
countries have falling K-society Index tendency in 2012-2013. It is noteworthy that
Mexico’s tendency corresponds to others but the values of index are much lower on
all period of research.
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Fig. 3. K-society Index for Mexico, USA and Canada
The challenging issue is to find out Ukraine’s situation with K-society
development. Ukraine had good infrastructure, science and educational bases but it is
necessary to clarify it is still competitive or not in the international area.
The first step in this direction is to compare Ukraine with neighboring countries.
Taking into account that all neighbors are from post-Soviet area, this sample is
congeneric. Thus, the results in the index form should describe the Ukrainian success
in K-society development. In addition, the qualitative information about neighbors
gives a possibility to verify calculations. The existence data let to find values of index
for Poland, Russia, Moldova and Hungary. The dynamics of K-society Index for these
countries and Ukraine is introduced on one graph. This approach allows
demonstrating the differences obviously (Fig. 4).
Fig. 4. K-society Index for Ukraine’s neighbors
Firstly, it is necessary to mention that Russia confirms the significant fall of index’
values in 2012-2013, that USA and Canada showed. Secondly, two countries,
Hungary and Poland, have almost equal dynamics of index’ values. Ukraine shown
higher estimations than Moldova and Russia in 2008 and outstripped those countries
until 2012. The situation was changed in 2013 when Ukraine got lower position than
Moldova. In general, Ukraine takes the 40th place from 87 countries in 2013. Its value
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of K-society Index equals to 0,546. It is to be recalled that the value for Switzerland is
0,803.
It is useful to discover the components of index for Ukraine to define the weak part
of it. Fig. 5 illustrates the Assets, Advancement, Foresightedness and K-society
Indices’ dynamics from 2008 to 2013.
Fig. 5. Ukraine’s values of K-society Index and its components
In the purpose of this analysis all components are described by places rating. This
gives the opportunity to show relative measures and ranking. The Advancement
dimension shows the worst values in all period. Thus, let’s consider from what
indicators this dimension consists of. Obviously, Ukraine has a great problem with
freedom from corruption indicator. In addition, research and development
expenditures, pupil/teacher ratios in primary education and public health expenditure
are lower than generally accepted (for example, in Europe) norms. This issue can be
an opportunity to significant development of K-society in future. Accordingly, these
fields need to be modernized and get all possible funding for improving the situation.
Thuswise, this analysis shows the preconditions of strategic planning and decision
making in Ukraine in case it is necessary to reach the leading countries. The last
hypothesis is based on the fact that the leaders in K-society Index are the most
developed countries.
5 Conclusions
In paper it was shown that K-society is a probable next mode of economy
development that leads to changes in institutional and organization structure inside
each country and over the world.
K-society is a complex category, which can be considered as a strategy goal for
country. Therefore, it needs to be measured in quantitate form. The analysis of
existence approaches shows that it is possible to use OECD methodologies for
creating composite indices and UN methodology for K-society Index. The
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improvement and combination those two sources give the base for model of K-society
Index.
The K-society Index was drawn out as a combination of three dimensions and 14
indicators. The values of index were calculated for 87 countries that provide all
necessary information.
The analysis of results shows that there is no direct dependence between K-society
development and the country leadership in the world.
The situation for Ukraine was analyzed deeply. Firstly, Ukraine has lower meaning
of index than it’s neighbor countries Moldova, Poland, Hungary. Secondly, the less
developed dimension is “Advancement”. Thus, the strategy of its extension must be
provided.
Some common tendencies were found for all countries. The index decreased
rapidly its value in 2008. The values of index have high correlation with Fragile State
Index and Economic Freedom.
References
1. Naim Hamdija Afgan, Maria G. Carvalho. The Knowledge Society: A Sustainability
Paradigm. Cadmus. Volume 1. Issue 1 (2010)
2. Michael Kuhn, Massimo Tomassini, P. R. J. Simons. Knowledge Based
Economy: Knowledge and Learning in European Educational Research (2006)
3. Gernot Bohme, Nico Stehr. The Knowledge Society: The Growing Impact of Scientific
Knowledge on Social Relations. Springer Science & Business Media (1986)
4. UNESCO World Report: Towards Knowledge Societies. UNESCO, France (2005)
5. Understanding Knowledge Societies in Twenty Questions and Answers with the Index of
Knowledge Societies. New York: UNPAN (2005)
6. Understanding Knowledge Societies. Department of Economic and Social Affairs, United
Nations, New York (2005)
7. Handbook on Constructing Composite Indicators: Methodology and User Guide.
Organization for Economic Co-Operation and Development, France (2008)
8. World Data Center for Geoinformatics and Sustainable Development, http://wdc.org.ua/
9. Fund for Peace: Fragile State Index, http://ffp.statesindex.org/
10. Terry Miller, Anthony B. Kim, Kim R. Holmes: Highlights of the 2014 Index of Economic
Freedom: Promoting Economic Opportunity and Prosperity. The Heritage Foundation, New
York (2014)
11. Conflict Barometer 2013. Heidelberg Institute for International Conflict Research,
Germany, №22 (2013)
172
Implementing Manufacturing as a Service:
A Pull-Driven Agent-Based Manufacturing Grid
Leo van Moergestel1 , Erik Puik1 , Daniël Telgen1 , and John-Jules Meyer2
1
HU Utrecht University of Applied Sciences, Utrecht, the Netherlands
{leo.vanmoergestel, erik.puik, daniel.telgen}@hu.nl
2
Utrecht University, Utrecht, the Netherlands
J.J.C.Meyer@uu.nl
Abstract. User requirements and low-cost small quantity production
are new challenges for the modern manufacturing industry. This means
that small batch sizes or even the manufacturing of one single prod-
uct should be affordable. To make such a system cost-effective it should
be capable to use the available production resources for many different
products in parallel. This paper gives a description of the requirements
and architecture of an end-user driven production system. The end-user
communicates with the production system by a web interface, so this
manufacturing system can be characterized in terms of cloud comput-
ing as the implementation of manufacturing as a service, abbreviated to
MaaS.
Keywords: agile manufacturing, agent technology, MaaS
Key Terms Industry, Infrastructure, Machine Intelligence.
1 Introduction
At the HU Utrecht University of Applied Sciences, an agile manufacturing system
has been developed that is capable of so-called multiparallel production of small
batches or even one single product. The need for such a manufacturing system
comes from the fact that nowadays the demand for custom end-user specified
products is increasing. Internet is offering a method to involve the end-user
directly into the production. Also the possibilities of additive manufacturing by
using 3D printers offers new ways to set up a manufacturing infrastructure with
the focus on the manufacturing of small quantities.
This paper will focus on the interface to connect the end user to the produc-
tion process. Before going into detail, the manufacturing system itself will first
globally be described.
In the next section details about the basic design considerations are given.
Because the implementation is based on agent technology, a short description of
what an agent is, will be given. The architecture and the connection with the
end-user will be the treated next. Finally, the results, related work, discussion
and a conclusion will end the paper.
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2 Global description of the manufacturing system
Every product to be made starts its life as a software entity, that contains the
information what should be done to make the product. This software entity is a
so-called software agent.
2.1 Agents
A common definition of an agent given by Wooldridge and Jennings [13] is:
Definition (agent). An agent is an encapsulated computer system or com-
puter program that is situated in some environment and that is capable of flexi-
ble, autonomous action in that environment in order to meet its design objectives
or goals.
The manufacturing system that has been designed is based on a group of
cooperating agents. A system with two or more agents is called a multiagent
system (MAS). In our design the following properties of agents are important:
– goal: an agent is designed to reach a goal. If reaching the goal is complex,
subgoals can be defined as states to be reached to finaly come to the end-goal.
– action: an action is what the agent can do.
– plan: to reach a goal or subgoal the agent builds or receives a plan. Normally
a plan consists of a list of actions to reach a goal or subgoal within a certain
role.
– role: agents can have different roles. In a multiagent system these roles play
an important part in the way agents cooperate.
– behaviour: closely related to the role is the behaviour. This the set of actions
that an agent will perform in a certain role.
– belief: a belief is what the agent expects to be the case in the environment.
In multiagent technology other aspects can also be important, but the prop-
erties mentioned here are specific for the manufacturing system presented in this
paper. The main reason for choosing agent technology is that it offers a natu-
ral decomposition of responsibilities and tasks to be completed in this complex
manufacturing system. It also means that if one agent fails, other agents can
continue to fulfil their own goals and even take over actions or tasks from the
failing agent.
2.2 The manufacturing grid
The infrastructure of the manufacturing system consists of cheap reconfigurable
production machines that we will call equiplets. These equiplets are capable to
perform one or more production steps. The set of steps an equiplet can per-
form depends on its front-end. An equiplet can be reconfigured by changing
its front-end. The equiplets are placed in a grid arrangement. In conventional
mass production, a line arrangement is used because for all products the same
sequence of production steps should be followed. However in our case every prod-
uct can have a different path along the equiplets, so a grid arrangement is more
natural offering multiple mostly shorter paths in case of an arbitrary sequence
of equiplets to be visited.
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2.3 Agent-based manufacturing
The equiplet-based manufacturing description will have its focus on the MAS
where the equiplet agent is the representative of the equiplet. An equiplet agent
will publish its capabilities. This means it will announce its production steps. It
will wait for products to arrive to actually perform the production steps.
The product agent has several roles. It starts with planning the path along
the equiplets for the production. Next, it will schedule the production. After
successfully scheduling, it will guide the product along the equiplets. At every
equiplet it will instruct the equiplet agent what step or steps to perform. It will
log the results of a production step and also update a globally shared knowledge
base that can be consulted by other product agents to check the reliability of a
certain equiplet for a certain step with certain parameters. Having the respon-
sibility for the manufacturing of a product, the product agent is also the entity
that should recover from errors during manufacturing. If there is a failure on
a certain equiplet, depending on the type of failure (recoverable or severe) the
product agent will try to plan the required step on an alternative equiplet for
the same reason as why one would not prefer to hire a plumber who previously
made mistakes resulting in a flood. By putting the information about the failure
(step type and parameters) in a shared knowledge base, the product agents will
learn as a group about the reliability of the equiplets for certain steps.
When the product is finished, the product agent can also have a role in other
parts of the life cycle of a product, being a software entity that knows a lot about
the product and the actual production. To achieve these roles, the agent could
be embedded in the product itself, but being accessible in cyberspace is also a
possibility.
3 System architecture
In this section a description of the system architecture as well as the constraints
on our type of production will be presented.
In figure 1 the layered software architecture is given. Only one product agent
and one equiplet agent is depicted and the modules in the lower layer of the
equiplet depend on the front-end that has been connected to the equiplet. In
this case an equiplet with the pick and place capabilities and vision modules
is used in this example. For the MAS layer Jade [1] was used as a platform.
Jade is a widely accepted Java-based multiagent environment. The inter-agent
communication is implemented by using blackboards. A blackboard is a software
entity where agents can publish information that will be available to other agents.
The software for the equiplet is based on ROS. ROS is an acronym for Robot
Operating System [10]. ROS is not really an operating system but it is middle-
ware specially designed for robot control and it runs on Linux. In ROS a process
is called a node. These nodes can communicate by a publish and subscribe mech-
anism. In ROS this communication mechanism is called a topic. This platform
has been chosen for the following reasons:
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Product
Agent
Blackboard MAS
Equiplet
Agent
Equiplet
Node
Database ROS
Pick & Place Vision
Node Node
Gripper Motors Camera LINUX
Fig. 1. Layered architecture
– Open source, so easy to adapt, compliant with a lot of open source tools.
– Wide support by an active community.
– Huge amount of modules already available.
– Nodes that are parts of ROS can live on several different platforms, assumed
that a TCP/IP connection is available.
At the lowest layer in figure 1 is a Linux platform running modules that com-
municate with the underlying hardware. Linux is a stable, portable and versatile
platform. In the next section we will take a closer look at the implementation of
this architecture in combination with a web interface.
Our production model is based on trays that will carry the product to be
built. These trays are transparent boxes, so equiplets with a camera can inspect
them both from the top and the bottom. In the latter case the workplace of an
equiplet should also be transparent, which is the case for the equiplets built so
far. The trays are marked with a unique QR-code. During the first production
steps the trays are filled with all the components required to make the product.
This way a kind of construction box is generated. This means that for all steps
to come, the components are available. This is a big advantage over a situation
where logistic streams of components within the grid should be taken care of.
The disadvantage is that parallel production of sub-parts in complex production
paths is not possible. However for the proof of concept this is not a big problem
and solutions can be found where the sub-parts are first manufactured in parallel
and added to the construction box. Of course within our conceptual model other
production models could be used, but the examples given here are based on this
model.
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4 Connecting the end-user
To use the manufacturing grid, a webserver has been added to allow end-users to
construct products to be made by the grid. This is why it can not happen that a
product is requested that does not fit within the capabilities of the manufacturing
grid, because the grid itself is offering the webinterface for designing the product.
If a product can be made using the webinterface, the grid will be capable to make
it. This web interface will be called WIMP as an acronym for Web Interface
Managing Production. The addition of a web interface as shown in figure 2
Web Web Multiagent Manufacturing
browser server system grid
End-user
Fig. 2. Combination with webinterface
fits neatly in the concept of agile and lean manufacturing [11], where the end-
user plays a prominent role in the production itself. The end-user specifies the
product that will be tailor-made to his or her requirements. This pull-driven
type of manufacturing will not lead to overproduction and waste of material.
The architecture of the software of the manufacturing system is depicted
in figure 3. In this figure blackboards are abbreviated by BB. A web server
Webbrowser Webserver
HTML5
Javascript Tomcat
Timeserver Java application
Time process
BB-planning Jade Product Agent
BB-steps
BB-logfile Jade Equiplet Agents
Equiplet 1 Equiplet 2 Equiplet 3 ...
Fig. 3. Combination with webinterface
publishes a website where a customer can design his product. This could be a
new product if the steps to produce it are within the capabilities of the equiplets
in the grid. The webserver will be responsible to offer only those production step
possibilities that are present in the grid. By pushing a submit button, a server-
side program will create and activate a product agent. This agent will start to
177
plan the production path and communicate with the available equiplet agents
to create the product. A more technical picture showing the distributed nature
of the system is given in figure 4. The numbered components in figure 4 are:
Grid control system Webserver
4
5 Gateway Tomcat
server server 3
6 Product 2
agent
JADE
Equiplet Web
agent 1 browser
Client PC
7
Knowledge Collective
DB DB
Grid information system
Fig. 4. Different platforms and their relations
1. The client PC as used by end-user. The end user can use any HTML-5
enabled browser.
2. Connection to the Tomcat server is established via a web socket.
3. The Tomcat server on which the website is hosted. The server can be placed
on the grid server, but it can also be located somewhere else.
4. A connection between the gateway server and the Tomcat server is made
through a (Java) socket.
5. The gateway server is responsible for spawning a product agent in the jade
container. The gateway server acts as a gateway to the outside world, imple-
mented to be able to spawn agents.
6. The Jade container of the grid contains all agents. Agents can communicate
with the Tomcat server as will be explained in more detail further on in this
paper.
7. The grid information system is a server where the databases and blackboards
reside. These are the systems where shared and individual knowledge will be
stored.
Agents have to be able to report back to the user. In order to do so, a software
solution was implemented to allow them to send information over a socket. In
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order to keep the connection alive, a heart-beat system has been developed. This
is not shown in detail in figure 4, but the realisation will be described in the next
sections.
4.1 Communications with the web interface/Tomcat server
Once a product agent is created through the web interface, the agent will create
a socket behaviour. This socket behaviour is the way for a product agent to
communicate with the server and thus to the web interface. To check whether or
not the server is still alive and reachable a heart message is sent. If this message
is not answered with a beat message it is assumed that the server is down. This
is how the socket behaviour is used and implemented: The socket behaviour is
used for the communication with the web interface and extends the Jade Waker
behaviour which means it will become active after a certain amount of time.
At the time of writing the wake up period for the socket behaviour is set at
5 seconds. This means that every 5 seconds the socket behaviour will become
active and check if it is connected to the WIMP server. If it is connected it
will check if there are data in the buffer; if any it will process the data. If the
buffer is empty or if all data is processed the socket behaviour will go idle and
will become active once the Waker behaviour is fired again after 5 seconds. The
socket behaviour can also be used to write messages to the WIMP server even
if the socket behaviour is not active, this is because it will be executed within
the action method of another behaviour.
The heartbeat behaviour was created to eliminate a problem we were having
with the socket behaviour. The problem encountered was the socket behaviour
being unable to see if the socket connection is still alive, if it is not closed
properly. The socket behaviour will only know if the connection is closed when
either the client closed it properly or when the socket behaviour is trying to
write on the socket when it is closed. Because we can receive commands from
the WIMP server, we need to be sure the connection is active. If the connection
is closed, but the socket behaviour is not aware of this, that would mean that the
socket behaviour simply cannot receive messages from the WIMP server. And
since the socket behaviour does not know the socket is closed, it will not try to
reconnect. The heartbeat behaviour sends a heart message every 5 seconds and
sets a timeout timer for 15 seconds. After sending a heart message the heartbeat
behaviour expects a response within 15 seconds from the WIMP server. The
response should be a beat. If it does not receive a response message within 15
seconds it will report to the socket behaviour that the connection is no longer
active and will tell the socket behaviour to reconnect. If it is not possible to
reconnect immediately, the socket behaviour will try to reconnect every time it
becomes active.
4.2 WIMP capabilities
At the client side a web-browser receives a web-page in HTML5 format with
embedded JavaScript and will display a graphical environment where a product
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can be designed. This is the user interface of what has been called the WIMP. At
this moment 4 typical product design web interfaces are implemented in WIMP:
1. Pick and place: 2D ball in cradle placement.
2. Paint pixels: pixel-based picture.
3. Pick, place and stack: simple 3D design.
4. Inspection of 3D printing object in STL-format.
A simple example of the pick and place interface is shown in a screen-shot in
figure 5. A case with compartments of a certain dimension specified by the user
Fig. 5. Case with coloured balls in the webbrowser
is to be filled with coloured balls. The end-user selects a ball of a certain colour
and moves the ball to an empty compartment.
An example of a sceenshot of the paint design interface is given in figure 6.
On a canvas, a pixel-based painting using a combination of several colours can
be made.
Fig. 6. A simple paint example
The WIMP software is also capable to build three-dimensional structures.
It has some built-in intelligence. For example if a user wants to add a part
at a place where adhesive is needed to keep it in place, it will warn the user
180
if he / she did not select the adhesive option for the placement of this part.
This part of WIMP is only a basic implementation and in future development
Fig. 7. A 3D structure
all kinds of special provisions should be added. For example when gluing two
objects together several points of special interest arise. First of all the location
of the objects you want to glue is very important. If the object is glued onto
an existing structure it is possible that the existing structure will tip over. The
structure must be stable enough and strong enough to support the new object.
To determine if those conditions are met you have to know the material of
the current structure, how much it weighs, and several other factors. Another
important aspect of gluing objects is the type of adhesive. Not all materials can
be glued together and not all types of adhesive can be used in combination with
all materials. During manufacturing the objects that will be glued must be held
together. This must be done until the adhesive is dry. Some adhesive types need
heat to function properly, other types can be hardened by using UV-light.
Fig. 8. View of an STL-image
At the client side a product is described by JSON. JSON, or JavaScript
Simple Object Notation is a popular alternative to XML. XML was the de-facto
standard before the existence of JSON. Until HTML 5, you needed to include
libraries to encode and decode JSON objects. Now, the JavaScript engine that
comes with HTML 5 has built-in support for encoding/decoding JSON objects.
For every part placed on the design grid in the webbrowser, the parttype (ball, or
block), colour (red, blue, green, yellow) and position (coordinates on the design-
181
grid) is entered in this JSON information. It is also possible to choose whether
or not to use adhesive. By clicking the submit button, the JSON information
is transferred to the webserver. Every action described in this information is
related to and translated into a production step. In figure 9 the internal structure
of a production step information block is given. A unique ID is followed by a
capability. This is the step action required and will be tied to an equiplet capable
to perform this step. The parameters give extra information about the object the
action has to work on. For example in a pick and place action, the parameters
will specify the coordinates of the final positions and the object that has to move
to that position.
ID Capability Parameters
Fig. 9. Components of a step object
4.3 Webserver and Tomcat-driven Java application
The web page presented to the client is presented by a Tomcat web server.
Tomcat is designed to support Java Servlets. This means that Tomcat is capable
to start a Java program at the server the moment the client sends a request
for a product. This Java program is capable of spawning a product agent in
the Jade environment. To do this a Gateway is used in the Jade environment
to achieve this functionality. This newly spawned agent will also receive the
JSON information about the product to be made. From this information, the
needed product steps are generated by the product agent. An overview of the
connection sockets is shown in figure 10. Every product agent is capable to
receive information from the Tomcat server using the Gateway Server. Every
product agent can also directly send information to the Tomcat Server. This
will create the possibility to inform the end-user in realtime about the progress
of the production.
Product agent The product agent is created and its goal is to produce the
product. Therefore it has to fulfil its sub-goals. The first sub-goal is planning
the production path. This means: selecting the equiplets involved, inquire if the
steps are feasible and finally scheduling the production. The next sub-goal is to
guide the product along the production path and to inform the equiplet about
the step or steps to perform. For every step, data aquisition of the production
data is possible and should be carried out by the product agent. It depends on
the equiplet agent what information will be made available.
Blackboard and timing The blackboard system as described in the architec-
ture was implemented as actually three separate blackboards (see figure 3). This
182
Socket A
Socket B
Socket C
Socket D
Gateway Server Tomcat Server
Socket D
Agent D Socket C
Agent C Socket B
Agent B Socket A
Agent A
Fig. 10. Socket connections between product agents and the user interface
has to do with the fact that the performance of the system could be better and
also the read and write access permissions become more clear. The BB-steps
blackboard is used by the equiplet agents to announce its production steps. This
information is under normal circumstances read-only for the product agents. The
BB-planning blackboard is read and written by the product agents and a timing
process. The information on this blackboard is the planning of timeslots or time
steps for every equiplet, and a load of every equiplet.
To synchronise all agents, a timeserver has been added to the system. The
scheduling is done by the product agents. Every newly arrived product agent
tries to schedule itself in a way that it will not exceed its deadline. If it fails, it
will ask other product agents with a later deadline to temporally give up their
scheduling. Next it will try to generate new schedules for all involved agents.
If successful, the new schedule will be adopted. If the scheduling fails the old
schedules are restored and the new agent reports a scheduling failure.
The third blackboard in figure 3 (BB-logfile) is used to build a knowledge
base about the performance of the individual equiplets and is shared among the
product agents. Successful and unsuccessful steps are reported in this blackboard
by products agents. This blackboard serves as an extra check when the product
agent is planning the set of equiplets to be used for a certain product. The higher
the failure rate of a certain equiplet, the more it will be avoided by the product
agents. This failure rate can be reset after repair or adjustment of an equiplet.
Equiplet agent The equiplet agent is also implemented as a Jade agent and
it is the interface to the underlying software and hardware. It depends on the
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front-end of the equiplet what modules are available. The equiplet agent is also
the interface to the product agent. Both types of agents live in Jade containers
and can communicate with each other. The communication between the product
agents and the equiplet agents as well as other product agents is FIPA-based.
FIPA is an acronym for Foundation for Intelligent Physical Agents and the foun-
dation developed a standard for inter-agent communication. The Jade platform
is FIPA-compliant. For the implementation of the blackboard, Open BBS has
been chosen. This Java-based blackboard was easy to integrate in the Jade en-
vironment; it was open-source and tests proved that it performed well enough
for our grid.
The equiplet agent will translate the production steps in front-end-specific
sub-steps. A pick-and-place action is composed of movements and control of a
vacuum pincer to pick the objects involved. The movements and commands are
sent to the ROS-layer that will control the hardware and the commands are
actually carried out by the connected hardware.
5 Results
The research done so far for this agent-based production system had several
milestones. The first milestone was the proof of concept given by a simulation
of the multiagent system as described in [5]. In that system the product agents
planned their production path along equiplet agents that used timing delays
to mimic the production steps. The equiplet agent was not combined with the
equiplet hardware. The next milestone was the implementation of a reliable and
fast scheduling algorithm as described in [6]. The third step was integrating
the MAS with the ROS-based equiplet in the system, so the integration with
real equiplet hardware has been accomplished [12]. The latest step is described
in this paper. A web front-end has been built to specify the product to be
produced. At this moment the given 2D examples can be executed on the three
available equiplets. So the total chain from design to production is working. In
figure 11 a design in the paint application of WIMP is made. In figure 12 the
result of this product is shown. Though this example still is very simple, it shows
that the multiagent system is working to our expectations. The 3D example is
already implemented at the MAS level and ROS level. The equiplet front-end
to perform these steps is under development as a glue dispenser and an extra
degree of freedom (rotation capability around the z-axis) of the pick and place
robot is needed. However using a dummy equiplet (as in the earlier developed
simulation) shows that the software is working to our expectations. This also
includes an error recovery system.
6 Related work
The concept of using agents for production is not new. Among others a multiagent-
based production system has also been developed by Jennings and Bussmann
[3][4]. Jennings and Bussmann introduce the concept of a product agent, in their
184
Fig. 11. WIMP paint design
terms workpiece agents, during the production. Their system focuses on relia-
bility and minimizing downtime in a production line. This approach is used in
the production of cylinder heads in car manufacturing. The roles of the agents
in this production system differ from our approach. This has to do with the fact
that Jennings and Bussmann use agent technology in a standard pipeline-based
production system and the main purpose was to minimise the downtime of this
production system. Their agents do not perform individual product logging and
only play a role in the production phase. In our approach the product logging
is done by the product agent for every single product and could be the basis
of the other roles of the product agent in other parts of the life cycle. In the
model presented by Jennings and Bussmann the workpiece agent is not so much
involved in production details as the product agent in our model. Another big
difference is also that our model is end-user driven.
In the field of agent-based production there are several other important pub-
lications. Paolucci and Sacile[8] give an extensive overview of what has been
done. Their work focuses on simulation as well as production scheduling and
control. The main purpose to use agents in [8] is agile production and making
complex production tasks possible by using a multi-agent system. Agents are
also introduced to deliver a flexible and scalable alternative for MES for small
production companies. The roles of the agents in their overview are quite di-
verse. In simulations agents play the role of active entities in the production. In
production scheduling and control agents support or replace human operators.
185
Fig. 12. Resulting product on the equiplet
Agent technology is used in parts or subsystems of the manufacturing process.
We on the contrary based the manufacturing process as a whole on agent tech-
nology and we have developed a production paradigm based on agent technology
in combination with a manufacturing grid. This model uses only two types of
agents and focuses on agile multiparallel production. The design and implemen-
tation of the production platforms and the idea to build a manufacturing grid
can be found in Puik[9]. After production the product agents can be embedded,
if possible, in the product itself. In [7] the role of product agents in the whole
life cycle of a product is discussed.
The term industrial internet [2] is used to describe the possibilities of inter-
connected machinery, sensors and devices that can be used to enhance production
and solving emergent problem on the fly. Research in this field is related to our
research. The approach we used however is purely based on the aforementioned
cheap reconfigurable equiplets. The introduction of agent technology opens pos-
sibilities that go beyond the production phase, as the product agent can play an
important role in other parts of the life cycle of a product.
7 Discussion and future work
The production approach described here is also applicable to a hybrid system
containing human actors as parts of the production system. In this situation
186
human workers take the position of the equiplets. The production steps for a
certain product should be translated to human-readable instructions and humans
perform the actual production steps. In that model the equiplet agent carries out
this translation so the MAS layer is still intact. This approach is useful in the
situation where the production tasks are too complicated for an equiplet to be
performed, but it can also help in the situation where a new equiplet front-end
has to be developed.
Standard mass production always has the risk of overproduction, especially
when new products arrive from other sources offering better performance or a
lower price. In the concept of lean manufacturing, this kind of waste should
be avoided by so-called pull-driven production. This means that a product will
only be made if an end-user is asking for it. This is exactly what has been
accomplished in the manufacturing system described in this paper.
For transport of the products between equiplets, automated guided vehicles
(AGV) are being developed. However, the use of AGVs is not implemented yet,
but the transport between equiplets can be seen as a step needed in the sequence
of steps to make a product. This means that from the point of view of the product
agent, an AGV is just another equiplet, offering the product transport step fitting
in the total sequence of steps needed for manufacturing the product. There is
a difference however. The AGV is reserved for a whole sequence of steps, while
equiplets are reserved for just a single step or a set of steps if these steps are
consecutive and can be realised by the same equiplet.
8 Conclusion
In this paper we described a real production system that has been built as a proof
of concept. All software used is based on open standards. Further research on
the manufacturing of products with a higher complexity must be done, however
the basic techniques for the implementation proved to work.
The grid is capable to produce several different products in parallel and every
product has its own unique production log generated by and embedded in the
product agent. This product agent can play an important role in the other parts
of the life-cycle of the product. When a product will be disassembled the product
agent carries important information about the sub-parts of the product. This can
be useful for recycling and reuse of sub-parts.
References
1. Bordini, N., Dastani, M., Dix, J., Seghrouchni, A.E.F.: Multi-Agent Programming.
Springer (2005)
2. Bruner, J.: http://radar.oreilly.com/2013/01/defining-the-industrial-internet.html
(2013)
3. Bussmann, S., Jennings, N., Wooldridge, M.: Multiagent Systems for Manufactur-
ing Control. Springer-Verlag, Berlin Heidelberg (2004)
4. Jennings, N., Bussmann, S.: Agent-based control system. IEEE Control Systems
Magazine (Vol 23 nr.3), 61–74 (2003)
187
5. Moergestel, L.v., Meyer, J.-J., Puik, E., Telgen, D.: Decentralized autonomous-
agent-based infrastructure for agile multiparallel manufacturing. ISADS 2011 pro-
ceedings pp. 281–288 (2011)
6. Moergestel, L.v., Meyer, J.-J., Puik, E., Telgen, D.: Production scheduling in an
agile agent-based production grid. IAT 2012 proceedings pp. 293–298 (2012)
7. Moergestel, L.v., Meyer, J.-J., Puik, E., Telgen, D.: Embedded autonomous agents
in products supporting repair and recycling. Proceedings of the International Sym-
posium on Autonomous Distributed Systems (ISADS 2013) Mexico City pp. 67–74
(2013)
8. Paolucci, M., Sacile, R.: Agent-based manufacturing and control systems : new
agile manufacturing solutions for achieving peak performance. CRC Press, Boca
Raton, Fla. (2005)
9. Puik, E., Moergestel, L.v.: Agile multi-parallel micro manufacturing using a grid
of equiplets. IPAS 2010 proceedings pp. 271–282 (2010)
10. Quigley, M., Gerkey, B., Conley, K., Faust, J., Foote, T., Leibs, J., Berger, E.,
Eheeler, R., A., N.: Ros: an open source robot operating system. Open-Source
Software workshop of the International Conference on Robotics and Automation
(ICRA) (2009)
11. Shingo, S.: A Study of the Toyota Production System. Productivity Press (1989)
12. Telgen, D., Moergestel, L.v., Puik, E., Meyer, J.: Requirements and matching soft-
ware technologies for sustainable and agile manufacturing systems. INTELLI 2013
proceedings pp. 30–35 (2013)
13. Wooldridge, M., Jennings, N.: Intelligent agents: Theory and practice. The Knowl-
edge Engineering Review (10(2)), 115–152 (1995)
188
ICT and e-business development by the Ukrainian
enterprises: the empirical research
Nataliia Medzhybovska
Odessa National Economic University, Odessa, Ukraine
nmedzh@oneu.edu.ua
Abstract. This paper presents the results of the research about the level of
information and communication technology (ICT) implementation by the
Ukrainian enterprises. We studied different Web-sites and made more detailed
research about ICT implementation at the Odessa industrial enterprises. The
conclusion is made that the state of Odessa e-commerce market does not
correspond to the current state of ICT development, nor to the needs of the
information society development in our country. The research of industrial
enterprises shows insufficient use of the advantages, which can brings the
effective use of ICT. Most businesses, despite the relatively high level of
technical equipment, automate only a part of routine operations. Most
administrative functions are performed by traditional methods, using only e-
mail. Thus, the Ukrainian enterprises are facing an urgent task of the most
effective use of available human and ICT potential to improve their
performance and competitive position at the market.
Keywords: Industrial enterprises, business partners, information and
communication technology, e-business, e-commerce, Web-site, intercompany
interaction, electronic information interchange.
Key Terms. Development, industry, research.
1 Introduction
Nowadays e-business in Ukraine relates mostly to online retail shopping and to
searching of relevant information and slightly extended to intra- and intercompany
interaction. Moreover, the benefits of e-business are not used by all business sectors
in Ukraine. The most developed in terms of Internet penetration are banks, large retail
chains, high-tech enterprises, enterprises in leisure activities and entertainment, etc.
Unfortunately, the industry – the main and leading sector of material production in
Ukraine – lags in the context of the use of e-business tools to improve the efficiency
and competitiveness of domestic enterprises.
The paper is organized as follows. Section 2 elaborates on theoretical
underpinnings, and presents an overview of the related works. Section 3 provides the
research methodologies and the empirical results. Section 4 concludes.
189
2 Related works
International researches show that “there is a growing amount of evidence from
developed and developing countries that the adoption of ICTs by enterprises helps
accelerate productivity grows, which is essential for supporting income and
employment generation. More widespread adoption of ICTs in the productive sectors
of developing countries should also accelerate innovation and thus enhance the
competitive position of developing countries” [1].
A considerable amount of researches identify the benefits that brings the use of e-
business tools for industrial enterprises. Researchers stated that “the potential of B2B
e-commerce is not captured by merely automating document printing and mailing
operations of transactions, but by encompassing all trading steps and collaboration
between business partners. Firms need to realize the importance of cross-firm process
integration and make determined efforts to integrate B2B e-commerce in critical
business processes” [2]. Several studies concern to barriers to the implementation of
B2B e-business solutions [3], the conditions necessary for their successful adaptation
[4] and others.
Importantly, many researches confirm the fact that e-business in B2B is less
developed compared with e-business in B2C. Scientists comprehend the reasons for
this situation in the differences between B2B and B2C markets. For example,
Harrison et al. identified 10 reasons, including more complex decision-making unit
and associated with it increased rationality of buyers, the complexity of production,
the limited number of buying units, far fewer behavioral or needs-based segments,
importance of personal relationships, long-term purchases or at least purchases which
are expected to be repeated over a long period of time, etc. [5]. Wright has identified
the following features of B2B: decision-making structure is complex and the process
involves a lot of people; decision-making could be delayed, depending on the
purchase value; rational reasons for ordering; high value of product/service, contacts,
projects and consulting; the final consumer probably will not be a decision-maker;
since the process time increases, suppliers have the access to decision-makers [6].
In our opinion, the sufficient reason for backlog of e-business development by the
Ukrainian industrial enterprises is also the backwardness of the employees who do not
tend to improve their skills in the ICT field, fear of change and therefore limitation
themselves to existing business practice. On the other hand, the advance of B2C
sector in this area can be explained by the voice of customers who do not satisfied by
the old methods of obtaining information and traditional relationships. In other words,
the B2C sector is forced to respond to the market needs for maintaining its
competitiveness. This need for B2B sector in Ukraine as well as for internal and
intercompany automation, in our view, has not formed yet.
190
3 The Research
3.1 The methodologies used for e-business development research
This section presents the methodologies for the evaluation of e-business and ICT in
use maturity in Ukraine on the example of the Odessa enterprises. The study was
conducted in two directions.
Within the first direction, we examined the large number of enterprises in Odessa
region. These companies were divided into the two groups: the industrial enterprises
and companies in other business fields. We analyzed all industrial enterprises listed at
the Odessa official site http://www.odessa.ua (in total 161 companies). Enterprises of
other business areas were chosen randomly using the Internet handbook “World Gold
Page. All Odessa” at www.mercury.odessa.ua and partly on the Odessa official site
(total 664 companies).
Companies were chosen from different fields of business, they have different forms
of ownership, scope of activities, etc. Choice of the specific number of companies in
each area were dependent on its scale and popularity in Odessa and Odessa region.
Odessa is a major business center in Ukraine, therefore the study of the level of ICT
in use maturity at the Odessa enterprises is quite representative for Ukraine.
The purpose of this study is the investigation of these companies’ presence in the
Internet and a comparison between industrial enterprises and companies of other
spheres of activity. We understand that having a Web-site does not fully indicate the
involvement in e-commerce and/or e-business, but it is minimal and necessary
condition for this purpose. In this context, we determine not only the existence of
Web-site, but also make a detailed study of different kinds of Web-pages for named
companies.
The second direction is represented by a detailed study of the level of ICT use and
e-business development at the 12 industrial enterprises in Odessa, including 5
engineering companies, 3 food processors, 2 enterprises of fabricated metal products,
1 cable plant and 1 plant for the plastic products production. Research was made on
the basis of employees’ survey data and state statistical observation (form № 1-ICT
“Information and communication technologies and e-commerce in enterprises”).
On the basis of these documents, 18 indicators have been allocated, characterizing
the level of ICT in use maturity and e-business development at the enterprise.
On the basis of the expert survey were identified the levels of: achievement of the
objectives of information systems; the Internet use; duties automation; achievement of
automation benefits. These indicators were determined based on the frequency of
positive respondents’ answers to the questionnaire.
Part of transactions with suppliers / customers / other organizations that are
implemented via electronic information interchange (EII), as well as the part of
functions that are provided by Web-site, were determined on the basis of form № 1-
ICT. In this case we also used the frequency of positive answers to the relevant
questions of the state statistical observation.
It should be noted that we use the term of “electronic information interchange”,
which assumes the use of computers and communication tools to transmit
information. It includes exchange of information through the enterprise Web-site /
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Web-portals including publication of information, upload / download documents, e-
mails; automated data interchange systems, which exchange data in real time over a
coherent structure, format and data transmission standards with minimal or no human
intervention (XML, EDIFACT, etc.).
The author believes that this term adequately reflects the whole spectrum of
transactions, which is mentioned in the relevant paragraphs of 1-ICT form.
Answers to questions of form № 1-ICT allow also to define the part of products
which are sold via computer networks; part of material resources purchased via
computer networks; availability of personal computers for administrative staff and
employees; part of personal computers connected to the Internet. These parameters
were defined as the quotient between the corresponding data.
The quality of the Internet connection is also determined on the basis of form № 1-
ICT. The answers to this question are qualitative, so it is necessary to transform them
to the quantitative form. For this reason we conducted the survey of the ICT
professionals regarding the weights for different variants of Internet connection. It
was found that the most relevant criteria for assessing the level of Internet connection
is the connection speed, because of other communication quality parameters such as
the level of support, the stability of the signal response to faults, etc. depend on the
quality of a particular ISP, not on the way the Internet connection. For further
calculations we used the arithmetic mean value of the respondents' answers. For each
company it was compared with the maximum possible/progressive method
(combination of methods) of Internet connection.
Availability of LAN, wireless LAN access, intranet and extranet were evaluated on
the basis of answers to the relevant questions of form № 1-ICT. Answer “Yes” is set
to 1, answer “No” is set to 0.
Assessment of the ICT in use maturity e-business development at the industrial
enterprises on the above parameters was carried out using a software package for
statistical analysis “Statistical Package for the Social Sciences” SPSS.
3.2 Comparative analysis of e-business development
The results of comparison of e-business adoption between Odessa industrial
enterprises and enterprises of other business fields are following.
The research shows that from 161 industrial enterprises only 64 have the Web-site
(40%), that indicate an insufficient level of e-business implementation in Odessa
industry. We are sure that high quality Web-site can become a gateway for industrial
enterprises to attract new business partners, conduct competitive procurement,
provide the comprehensive information about its products, offer secure and controlled
communication with business partners, etc. From the other hand, 329 companies from
the 2nd group (50%) have its own Web-site.
In both cases, Web-sites often provide information in Russian language (for
industrial enterprises – 89% that have Web-site, for companies in other fields – 93%).
Publication information in Ukrainian is at 23% and 20% of Web-sites respectively, in
English – 41% for both groups. Obviously, multilingual information is essential for
companies interested in attracting a great number of customers and business partners.
192
We discovered the following methods of communication with companies
employees through Web-site. For industry each has phone number, 72% contain the
mailing address, 87,5% – email address (20 of them hosted on free hosting, that
indicate a lack of attention to the positive reputation in the e-commerce market), chat,
feedback service and sms are not popular (8%, 27% and 8% respectively). For
companies in other business fields phone number presented at 94% of Web-sites, e-
mail address – at 78%, mailing address – at 53%, feedback service – at 23%, chat – at
8%, sms – at 4%. It is logical that availability of free channels of communication for
B2B sector is not as critical as for B2C e-commerce, but the presence of multiple
communication channels is helpful. Furthermore, in this case it is important that
communication channels are personalized (e.g., the purchasing issues should be
addressed directly to the sales department, proposals from suppliers – to the
procurement department, etc.). Moreover, such requests should be fixed in order to
monitor the timeliness and completeness of its accomplishment.
The following results describe the quality of information presented at the
companies’ Web-sites. Complete information about the products is available at 90%
of industrial Web-sites, partial – at 8%, no product information – at 2% of Web-sites.
Complete information about the products is available at 76% of Web-sites of other
business fields companies, partial – at 23%, no information available – at 1%. These
figures clearly show lack of attention of Ukrainian enterprises to the use of Internet as
a cheap and convenient channel for information dissemination. We believe that
information about the company's products should be presented at the Web-site with
the required level of detail, in some cases – with the drawings and specifications. The
companies Web-site is also should have the full information about the enterprise and
provide standard contracts forms, business rules, etc.
Further, the research found that industrial enterprises do not use social networking.
We believe that social networks should be used by companies to maintain personal
contact with business partners and to create the specific professional communities.
The data regarding the presence of other business fields companies in social networks
are the following: the Facebook pages have 8% of firms, accounts in Twitter – 5%, in
YouTube – 4%. Moreover, for B2C companies and consumer goods’ producers the
social networking is critical for increasing the loyalty of existing and attracting new
customers.
We also investigated the availability of information about the companies which do
not have Web-sites, on the popular Ukrainian Internet portals such as Prom.ua,
Businessua.com, Ua.all.biz. We proceeded from the assumption that if the company
does not have a Web-site, it should have an account at the niche portals to implement
at least the minimum presence in the Web.
The research shows the following data: at the Prom.ua we found 9% of the
industrial enterprises, which do not have own Web-site, at the Businesua.com – 3%,
at the Ua.all.biz – 26%. There are no information at these portals for 64% of industrial
enterprises which do not have its own Web-site.
For companies of other business areas the data is following: 3% of companies
which do not have Web-site, we found at Prom.ua, 0,6% – at Businessua.com, 6% –
at Ua.all.biz. The information about 90% of companies which do not have their own
Web-site, we didn’t find at these portals.
193
Thus, the example of Odessa enterprises shows the unsatisfactory level of e-
business development for both groups of enterprises. Moreover, it is the obvious gap
in the e-business development by the industrial enterprises as compared to businesses
of other fields. Many enterprises do not have their own Web-site, most of these
companies do not even presented at the most famous Ukrainian portals. Companies
that have Web-sites show its insufficient quality. Furthermore, the industry did not
use the resources of social networking for disseminating information and supporting
its business partners loyalty.
3.3 Research of the ICT development at the industrial enterprises
Evaluation of the ICT in use maturity at the Odessa industrial enterprises of the
chosen sample allowed to make following important conclusions.
On average, the surveyed enterprises use information systems to achieve 2,4±0,2
purposes from 6, and the most popular purpose to use information systems is
improving the access to information (78% of enterprises).
Internet in the surveyed companies is used to perform an average of 4,1±0,4 duties
from 11. The most popular direction of Internet usage are message and document
transfer to business partners (79% of enterprises), to employees and superiors (67%)
and search for suppliers (62%).
On average, the surveyed enterprises automate 1,9±0,3 duties from 8. The leader
among the responses is reporting (45% of enterprises).
Automation of duties allow to realize an average 4,0±0,4 purposes from 13 at the
surveyed enterprises. The most commonly implemented objectives are speeding the
paper documents preparing (84% of enterprises) and its transfer to employees and
superiors (67%), reducing its number (79%).
Electronic information interchange with suppliers implemented by 5 enterprises
from 12. These enterprises use EII on average 6,0±0,2 transactions with suppliers
from 7, and all enterprises use EII for the transferring orders to suppliers, receiving
electronic invoices and product information from suppliers.
Electronic information interchange with customers is implemented on the same 5
companies from 12. They realize an average of 5,9±0,2 transactions with customers
from 7, and all these companies send electronic invoices and information about its
products to customers.
Electronic information interchange with other organizations is executed by all
enterprises. On average, they realize via EII 5,5±0,2 operations with other
organizations from 7, with the most popular such as: obtaining banking and financial
services (94% of enterprises), information from government agencies (90%),
documents from government agencies (85%), returning of completed forms to
government institutions (81%), sending or receiving data to/from government
institutions (79%), sending payment orders to financial institutions (60%).
Level of EII with other organizations for all enterprises significantly exceeds the
level of EII with suppliers and customers. From our point of view, this situation is
caused by the availability of the relevant proposals and realized possibilities from the
government institutions and banks/financial institutions (receiving and returning of
194
electronic documents, executing the administrative procedures, submitting proposals,
using the Internet banking, etc.).
Web-site is available for 6 companies from 12, and it provides on average 2,3±0,4
functions from 6. All Web-sites contain product catalog or price list, but only one
company realizes all features listed in the form № 1-ICT.
Although five companies in the study group show the automation of certain
procurement and marketing functions, this automation is very limited and is
implemented mainly by sending e-mail notifications to some business partners.
An indirect proof of this fact is the almost complete lack of material resources and
finished products, which are purchased/sold via computer networks. Only one
company 75% of its products realize through computer networks. Other company
only a very small amount of its production sold this way (0.001081%), and a small
part of material resources purchased via computer networks (0.01328%). Therefore,
we have no reasons to report about mass and systematic electronic sales and
procurement for the study group of enterprises.
An interesting analysis of the ICT equipment level for the study group of
enterprises. Thus, the availability of personal computers for administrative staff
indicates the gap in the level of company computerization. One company has this
value higher than 5, three of them – near 1, but two – less than 0,1, others – near 0,5.
The study also shows the gap between enterprises in PCs availability for employees.
These values vary between 0,022 and 0,572.
It should be noted that industrial enterprises have different level of Internet
connection (four of them – 100%, five – near 70%, three – only near 30%). Five
enterprises apply the most advanced methods of Internet connection, including mobile
communications, which increases the efficiency and timeliness of information transfer
and processing, but four companies use broadband Internet connection with maximum
speed 24 Mbit/s and three still use outdated analog modem or an ISDN connection.
Almost all companies have local computer network, 5 of them use a wireless LAN
access. Two companies have internal computer network (intranet) and extend it for
the business partners (extranet). In other words, they have the technical ability for
intra- and intercompany collaboration.
Thus, the results of this research do not allow us to state the mass implementation
of ICT and e-business by the Odessa industrial enterprises. In most businesses,
despite the relatively high level of technical equipment, only a part of routine
operations are automated. Most administrative functions are performed by traditional
methods, using only e-mail.
4 Conclusions
During the conducted research, we attempted to study, firstly, the level of e-business
development by the Odessa enterprises of industry and other spheres of activity, and
secondly, the level of ICT usage at the Odessa industrial enterprises.
Based on this research we can make several important conclusions:
1. The state of Odessa e-business market does not correspond to the current level
of ICT development, nor the needs of the building the information society in our
195
country. More than half of the companies do not have its own Web-sites, they are
poorly represented in social networks and in niche portals on relevant topics. Detailed
research of existing Web-sites showed its low quality. Web-site content and quality of
its services, including on-line ordering and payment, secure communication, etc.
require radical restructuring.
Comparative analysis of presence in Internet of industrial enterprises and
companies of other fields of business showed the significant lag of industrial
enterprises in terms of providing the information and interaction with customers and
business partners. Thus, an urgent task for the Ukrainian enterprises is the most
effective implementing of e-business tools into a business practice.
2. Research of the ICT equipment of the industrial enterprises showed its
insufficient use, and failure to obtain the benefits that bears its effective
implementation. Automation covers mostly routine paper operations, they have a very
primitive mode of electronic communication with business partners and employees
(often only e-mails), e-procurement and e-sales are not implemented at all, although
the level of technical equipment and Internet connection are relatively high.
3. The most unfavorable situation is in the field of intercompany electronic
interaction of the enterprise with its customers and business partners. The study shows
almost complete absence of electronic procurement and sales. Some enterprises
realize only electronic information interchange, but only with those organizations that
have provide relevant technical and other possibilities for this purpose (government
organizations, banks/financial institutions).
Summarizing, we can note unsatisfactory use of the ICT benefits and e-business
development by the Odessa enterprises.
It should be noted that this study is only the first attempt to analyze the situation in
the field of adaptation of e-business tools and ICT by the Ukrainian enterprises, so
allow only to formulate the challenges in this business field. Future research should
be conducted on a regular basis with the justification of representativeness (typicality)
of selected companies. It also should study the companies from all regions of Ukraine,
separating them by industry, type of ownership, size, etc. Also limitation of this
research is the resistance of most businesses for detailed study of their activity.
References
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Geneva: United Nations Conference on Trade and Development (2006)
2. Claycomb, C., Iyer, K, Germain, R.L.: Predicting the level of B2B e-commerce in industrial
organizations. In: Industrial Marketing Management, vol. 34, pp. 221--234 (2005)
3. Janita, I., Chong, W. K.: Barriers of B2B e-Business Adoption in Indonesian SMEs: A
Literature Analysis. In: Procedia Computer Science, vol. 17, pp. 571--578 (2013)
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organizational capabilities and market opportunities. In: Electronic Commerce Research and
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196
Geospatial intelligence and data fusion techniques for
sustainable development problems
Nataliia Kussul1,2, Andrii Shelestov1,2,4, Ruslan Basarab1,4, Sergii Skakun1, Olga
Kussul2 and Mykola Lavreniuk1,3
1.
Space Research Institute NAS Ukraine and SSA Ukraine
(nataliia.kussul, serhiy.skakun, andrii.shelestov,
basarabru)@gmail.com, nick_93@ukr.net
2.
National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine
olgakussul@gmail.com
3.
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
4.
National University of Life and Environmental sciences of Ukraine
Abstract. Knowledge on spatial distribution of land cover and land use is
extremely important for solving applied problems in many domains such as
agriculture/food security, environmental monitoring, and climate change.
Geospatial data including satellite imagery play an important role since it can
provide regular, consistent and objective information. Identifying geospatial
patterns and quantifying changes that occur in space and time require special
techniques to be exploited. These techniques are associated with the area of
geospatial intelligence and deal with multi-source data fusion and exploitation
of advance intelligent methods. This paper presents the use of these techniques
for processing archived and up-to-date satellite imagery for large-scale land
cover and crop classification in Ukraine. The main purpose of this paper is to
not only show potential of geospatial intelligence, but to pay attention of
educators to this extremely important area.
Keywords. Geospatial intelligence, land cover, crop mapping, image
processing, satellite imagery, big data.
Key Terms. HighPerformanceComputing, MachineIntelligence,
InformationTechnology, Intelligence, Data.
1 Introduction
Geospatial information is a very important source of data for distributed systems
development, education, decision making and competitive business. Due to regular
acquisition of satellite data all over the world for the last couple of decades as well as
new communication, navigation and crowdsourcing techniques, it has become
possible to monitor the current state of the large territories development, estimate
trends, analyze available scenarios for future development and manage things to
provide sustainability. The approach is based on modern IT, namely geospatial
197
intelligence [1] and data fusion [2] techniques. By geospatial intelligence we consider
all aspects of geospatial data processing including intelligent methods and
technologies to fuse/integrate data and products acquired by multiple heterogeneous
sources using machine learning techniques and emerging big data and geo-
information technologies. In this paper we exploit geospatial technique to address two
important applications for Ukraine, in particular land cover/land use mapping and
crop mapping. The purpose is to not only show the potential of geospatial
intelligence, but to pay attention of the educators to this powerful IT and bridge the
gap between market needs for such specialists and professionals.
Ukraine is one of the main crop producers in the world [3], so agricultural
monitoring is a very important challenge for Ukraine. One of the most promising data
sources to solve the underlined tasks at large scale is remote sensing data, namely the
satellite imagery [4-12]. This is mainly due capabilities to timely acquire images and
provide repeatable, continuous measurements for large territories. At present, there
are only coarse-resolution satellite imagery (500 m spatial resolution), that has been
utilized to derive global cropland extend, e.g. GlobCover, MODIS [13]. But, low-
resolution maps always underestimate or overestimate certain land cover or crop type
areas. Also several global land cover maps have been made using higher resolution
data such as from Landsat-series satellites [14-15], but they are not accurate enough at
regional level for Ukraine. Therefore, creation of global products, such as land cover
maps and crop maps, based on high resolution satellite images (at 30 m) is very
important task for sustainable economic development of Ukraine. This paper presents
the results of regional retrospective high resolution land cover mapping and large
scale crop mapping for Ukrainian territory using multi-temporal Landsat-4/5/7/8
images and also some supporting data and knowledge obtained during our own
investigations [7-8]. The main results of the work were obtained within EC-FP7
project “Stimulating Innovation for Global Monitoring of Agriculture and its Impact
on the Environment in support of GEOGLAM” (SIGMA).
2 Objective of the study and data description
The paper covers two different studies: retrospective land cover mapping and crop
mapping. These two problems are solved using the same geospatial intelligence
approach that encompasses the use of advanced machine learning techniques. In
particular, we use a combination of unsupervised and supervised neural networks to
first restore missing values in multi-temporal images, and then to provide a supervised
classification with an ensemble of multilayer perceptrons (MLPs). One of the
advantages of this approach is possibility for automatic processing taking into account
of large amount of satellite imagery that need to be processed.
At the first study, we used atmospherically corrected Landsat-4/5/7 products to
produce land cover maps for land cover change detection. This was performed for all
territory of Ukraine and required processing of about 500 Landsat scenes to cover it
completely for three decades: 1990s, 2000s and 2010s. Also, we manually formed
training and test sets for supervised classification using the photo interpretation
198
method. Train and test sets were created with uniform spatial distribution over the
territory of interest and proportional representation of all land cover classes, namely
artificial surface, cropland, grassland, forest, bare land and water.
Fig. 1. Location of Ukraine and JECAM test site in Ukraine (Kyiv oblast, marked with bold
boundaries.
The second study is the pilot project on large scale crop mapping for JECAM test
site [16] in Ukraine for 2013 (Fig. 1). The Joint Experiment for Crop Assessment and
Monitoring (JECAM) is an initiative of GEO Agriculture Monitoring Community of
Practice with the intent to enhance international collaboration around agricultural
monitoring towards the development of a “system of systems” to address issues
associated with food security and a sustainable and profitable agricultural sector
worldwide (http://www.jecam.org). The JECAM test site in Ukraine was established
in 2011 and covers administrative region of Kyiv oblast with the geographic area of
28,100 km2 with almost 1.0 M ha of cropland. For large scale crop mapping over the
study region we used two data sources – remote sensing images acquired by
Operational Land Imager (OLI) sensor aboard Landsat-8 satellite and data acquired at
ground surveys. We used Fmask algorithm for clouds detection and masking [17].
Ground surveys were conducted in June 2013 to collect the knowledge about crop
types and land cover types (Fig. 2) over the interested area. In this study we used
European LUCAS nomenclature as a basis for land cover / land use types.
3 Method and results
The main scientific challenges for geospatial intelligence problem solving are
geospatial data fusion and correct interpretation of geospatial information. To address
them for big data satellite monitoring problems we propose the novel approach, based
on combination of three machine learning paradigms for geospatial information
analysis: big data segmentation, neural network classification and data fusion. Data
fusion is performed at the pixel and at the decision making levels. During
preprocessing stage, Landsat-4/5/7 and Landsat 8 scenes were merged to multi-
channel format for each path, row and date. First, we restore cloudy pixels from time-
series of images using self-organizing Kohonen maps [18] and after provide
199
classification based on the time-series of restored images available for the certain year
and required area. Classification was done by using an ensemble of neural networks
(MLPs). The method of pixel and decision making level data fusion is proposed in
[16].
Table 1. Accuracy comparison of Land Cover30-2010 and GlobeLand30-2010
Product Land Cover30-2010 GlobeLand30-2010
Class UA, % PA, % UA, % PA, %
Artificial 100 87.8 79.5 3.4
Cropland 93.5 96.2 99.4 85.3
Forest 95.4 96.2 89.9 95.9
Grassland 81.4 71.2 34.4 60.5
Bare Land 91.7 96.4 0.4 57.1
Water 99.5 99.6 96.6 99.9
Overall accuracy, % 94.7 89.7
Fig. 2. The land cover map of Ukraine for 2010 year (and also land cover maps of Kyiv oblast
for 2010, 2000 and 1990 years).
To estimate the accuracy of land cover classification for Ukrainian territory, we
used two approaches: accuracy assessment on independent test (testing) set and
comparison of the class areas in land cover with official statistics. The overall
classification accuracy achieved in this study was approximately 95%. Accuracies for
each individual class were more than 70%. The lowest classification accuracy was for
grassland, because it is difficult to separate grassland from some of spring crops. We
also compared (Table 1) our result, taken for Ukraine with global land cover map
GlobeLand30-2010 at 30 m resolution. The overall classification accuracy of our land
cover map was 5% higher than GlobeLand30-2010. Also accuracy of grassland from
200
our maps was +10% (producer accuracy, PA) and +45% (user accuracy, UA) [19]
better than GlobeLand30-2010. Our final land cover map is shown at Fig. 2.
Table 2. Classification results
No Class PA, % UA, %
1 Artificial 100.0 97.9
2 Winter wheat 95.7 91.8
3 Winter rapeseed 93.5 99.4
4 Spring crops 40.6 34.6
5 Maize 90.5 86.8
6 Sugar beet 94.9 89.6
7 Sunflower 84.1 85.4
8 Soybeans 69.7 77.1
9 Other cereals 70.9 78.0
10 Forest 96.9 92.9
11 Grassland 91.0 89.0
12 Bare land 86.7 99.0
13 Water 100.0 98.1
3.1 Large scale crop mapping
The use of multi-temporal Landsat-8 imagery and an ensemble of MLP classifiers
allowed us to achieve overall accuracy of slightly over 85% (Table 2) which is
considered as target accuracy for agriculture applications.
Target accuracy of 85% was also achieved for winter wheat, winter rapeseed,
maize and sugar beet. For the spring crops, sunflower and soybeans the accuracy is
less, than 85%. Soybeans is the least discriminated summer crop with main confusion
with maize. In particular, almost 61% of commission error and 71% of omission error
was due to confusion with maize. All non-agriculture classes including forest and
grassland yielded PA and UA of more than 85%. The final classification map is
shown in Fig. 3.
Comparison of official statistics and crop area estimates derived from Landsat-8
imagery for Kyiv region described at the Table 3.
201
Fig. 3. Final crop map obtained by classifying multi-temporal Landsat-8 imagery.
Table 3. Comparison of official statistics and crop areas derived from Landsat-8 imagery
Class no. Class Crop area: Crop area: Relative
official Landsat-8 error, %
statistics, x derived, x 1000,
1000, ha ha
2 Winter wheat 187.3 184.5 -1.5
3 Winter rapeseed 46.7 59.9 28.3
5 Maize 291.7 342.4 17.4
6 Sugar beet 15.5 11.2 -27.9
7 Sunflower 108.2 117.6 8.7
8 Soybeans 145.9 168.5 15.5
4 Application in education process
As well as geospatial intelligence is one of the emerging areas of data science, we
actively use it in education process. Developed approach to land cover and crop
mapping is actively used for education purposes. We incorporate these topics
(geospatial intelligence methods and developed software) into a master and PhD
program of “Ecological and economic monitoring” specialization at the National
University of Life and Environmental Sciences of Ukraine with the main focus on big
geospatial data processing and satellite data analysis.
Also we are actively trying to implement project based education, involving
students into scientific projects . Some methods of data fusion are included into
laboratory works on intelligent computations. Master and PhD student fulfill their
qualification diplomas within international projects. According to our experience
more attention should be paid on geospatial data processing and intelligent
202
computations within Bachelor programs on Computer Science in Life Science
universities.
5 Conclusions
This paper presents a novel approach for satellite monitoring based on big
geospatial data analysis. The main idea of the proposed geospatial intelligence
approach is the use of supervised neural networks in order to classify multi-temporal
optical satellite images with the presence of missing data. A supervised classification
was performed with the use of ensemble of MLP classifiers to create such global
products as retrospective land cover and crop maps for the whole territory of Ukraine.
Proposed approach allowed us to achieve the overall classification accuracy of 95%
for three different time periods (1990, 2000 and 2010) and improve quality of maps
comparing to other land cover maps available for Ukraine at 30 m spatial resolution,
namely GlobeLand30-2010. The same approach was successfully applied for the
JECAM test site in Ukraine for large area crop mapping.
Now geospatial intelligence is a hot topic in big data analysis, but we observe the
lack of experts in the area. Therefore, we would like to pay attention of the IT
educators to the gap and build a roadmap to fill it.
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(March 1986)
204
Risk Assessment of Use of the Dnieper Cascade
Hydropower Plants
Andriy Skrypnyk1, OlhaHoliachuk1
1
National University of Life and Environmental Sciences of Ukraine
avskripnik@ukr.net, olia_ailo34567@ukr.net
Abstract. In this article we wish to evaluate efficiency of use of Dnieper cascade
hydropower plants on the basis of common approaches to environmental
management. We evaluate the efficiency of use the flooded areas of the
hydropower station in agriculture. Assessment of the man-made risks includes
evaluation of static (regular maintenance of dams) and stochastic (probability of
artificial tsunami) components. According to the world statistics of disasters
caused by dam reservoirs, the probability of man-made tsunami is estimated
around 0.01%. Using this rate of probability we can state that expected losses van
be 5% of the confidence level. Dnieper reservoirs ranking on the degree of energy
risk (the possibility of man-made tsunami generation) was made.
Keyword. risk assessment, hydropower plan, electricity, agriculture,
environmental management.
Key Terms. MathematicalModel, Data, Environment, Infrastructure,
Development.
1 Introduction
Before the era of nuclear power, contribution of hydropower in the energy balance
of the former Soviet Union was considered indisputable. Thus the negative effects
associated with the creation of reservoirs on the plains were not taken into account e.g.
flooding of large areas, destruction of towns and historic monuments, increase of the
risk of man-made disasters. But time passed and in 1970s in Ukraine were built several
nuclear power plants and as a result appeared the need to develop solar, wind and
bioenergy and it led to decrease of the share of electricity generation by hydropower
plants to 5-7%. Over the past decade, the agricultural sector of the Ukrainian economy
has become one of the major players in the global food market and agricultural export
of the country has become one of the landmarks of the national economic development.
That is why there is an urgent need to use territory of the cascade of Dnieper
reservoirsfor agricultural purpose. However, beside inappropriate use of land resources
[16] and deterioration of the quality of water resources there is a high risk of man-made
disasters which can be caused by the functioning of the Dnieper cascade hydropower
plants.
205
A. Pigou [11], P.Samuelson [15], R. Coase [12] presented classical approaches to
exploration of the impact of externalities on economic performance (environmental
management). The main idea of this approach is that the price of products (in this
case electricity) does not respond the social price paid by people for violations of the
environment [13] and therefore assessment of economic growth should be calculated
taking into account the price of deterioration of the environment [1, 2] .
English researchers proposed classical approach to the exploration of the causes of
destruction of dams, they assert the classical definition of the threats which are
connected with creation of artificial reservoirs [16]. In Great Britain all the artificial
reservoirs (more than 25 000 cubic meters of the size 100m * 100m * 2.5m) were under
the control of local authorities and then the responsibility to control artificial reservoirs
was transferred to National Environment Agency.
For comparison, Kyiv reservoir has a volume of 3.73 billion cubic meters and it is
placed above the level of many districts of Kyiv [9]. Kurenevka tragedy which
happened in 1961 showed that even not significant in volume reservoirs (600 000 cubic
meters - 400m * 400m * 3,75m) can be extremely dangerous if they are placed above
the level of the nearby territories and can lead to generation of artificial tsunami [9].
During World War II in parts of the Dnieper River below the Dnieper dam the retreating
Soviet army tried to destroy the dam. The man-made disaster led to the flood victims
among whom were citizens of Zaporozhe and coastal villages and soldiers of the Soviet
Army (about 100 000 people ) [6].
Researchers emphasize the negative effects of the creation and functioning of the
Dniper reservoirs, besides flooding of large territories the negative effects concern a
change of hydrological, hydro chemical and hydro biological regimes and slowing of
water circulation [3, 6, 7]. In general, there is a great number of scientific papers on
significant negative effects connected with creation of the Dnieper reservoirs for the
environment of Dnieper, in particular, and for the economy of Ukraine in general. But
the issue of quantitative estimation of possible losses caused by artificial tsunami has
got little attention among researchers.
In this article we wish to explore a comprehensive risk assessment of further
functioning of Dnieper hydroelectric cascade considering alternative options of usage
of flooded areas and possible losses connected with future functioning of reservoirs and
to develop the methodology of losses assessment connected with destruction of dams
reservoirs.
2 Characteristics of Flooded Areas and Options of Alternative
Exploitation
As we already mentioned, in twenty-first century the hydroelectric power generation
ceased to be a decisive factor in the energy balance. The GDP growth in 2000-2007
was not connected with an increase in production of electricity. During this period was
an increase in production of cereals for which the usage of electricity was minimal. It
is difficult to estimate the total social costs of flooded areas, and overall benefits from
the functioning of large reservoirs of water. In addition, it is difficult to assess losses
206
connected with deterioration of water quality due to the lack of flow. There are a lot of
other aspects that do not prove the necessity and efficiency of the functioning of
reservoirs. However, we will focus on two main aspects: 1) alternative usage of
reservoir areas in agricultural production; 2) level of risk connected with further
exploitation of reservoirs (dams of the Dnieper reservoirs). Dnieper cascade
hydroelectric station was built during the period of planned economy, the first dam was
built on Dnieper in 1927 (Zaporozhe) and the last in 1976 (Kanev). General
characteristics of reservoirs and power plants are presented in Table 1. The total area
of Dnieper reservoirs is 6.9 thousand sq. km, 1.1% of the territory of Ukraine (Table
1). But if we take into account that the territory near rivers area was always the most
fertile for agricultural sector, it is necessary to assess the share of reservoirs in the
volume of agricultural land, which is 1,7%. Not all agricultural lands are fertile that is
why the factual area which is used in agricultural sectoris about 27 million hectares
(270 thousand sq. km) with a standard deviation 0.8 million hectares [4]. In this case,
the share of the Dnieper reservoirs increases up to 2.6% of the area used for agriculture.
Table 1.Structure of Land Resources of Ukraine
Total area
The main types of land and economic activity
Thousand sq.
% of total area
km
Agricultural land 415 68.8
Forests 106 17.6
Built-up areas 38 6.3
Territories covered by surface water (Dnieper 24(6.9) 4.0(1.1)
reservoirs)
Unsuitable land for agricultural production 21 3.3
Total (territory of Ukraine) 604 100.0
Source:[4]
Compare the coast of total volume of products available through agricultural
production from flooded areas after the creation reservoirs, and the cost of electricity
generated by hydroelectric Dnieper cascade. General characteristics of reservoirs and
their electricity generation capacity is presented in Table 2. From the total area of
reservoirs we extracted the natural are of water surface using natural characteristics of
the Dnieper and obtained the size of flooded areas which potentially could be used in
agricultural sector.
The area of flooded territory is 6 thousand. sq. km. Dnieper cascade which consists
of six hydroelectric power plant produce 10 billion kw * hr. per year, (40% are produced
by Dnieper, 15% by Kremenchuk and15% by Kakhovska, 13% by Dniprodzerzhynsk,
10% by Kaniv, 7% by Kyiv. Dnieper hydropower station (HPS) has the best ratio of
natural areas to the area of the reservoir - 38% and the worst ration has Kyiv HPS - 5%.
207
Table 2. Main Features of Reservoirs
man-made tsunami, J
The potential energy of
production, mln kW • h
Volume, million cubic
Flooded area, square
annual
The height of the dam,
area,
The average depth, m
Area, square km
Capacity, MW
natural
square km
Average
*1014
The
km
m
1 2 3 m 4 5 6 7 8 9
Kyiv 4.0 11.5 3730 3.4 922 44 878 408.5 683
Kaniv 4.3 10.5 2500 2.04 581 110.7 470.3 444 972
Kremenchuk 6.0 17 13520 19.8 2252 166.5 2085.5 632.9 1506
Dniprodzerginsk 4.3 12.6 2460 2.5 567 102.6 464.4 352 1328
Dnipro 8.1 35.4 3320 10.2 410 154.8 255.2 1569 4008
Kakhovske 8.4 16 18180 21.04 2155 276 1879 351 1489
6887 6032 9986
Source: [3;10]
We will explore the possibilities of obtaining agricultural production in flooded
areas, we will start from evaluation of the efficiency of agricultural areas during last
four years. Due to the high risk of the agricultural sector we use averaged indicator of
efficiency during four last the years (Table 3).We obtained the indicator of efficiency
of the usage of 1 thousand square kilometer of flooded areas which is equal o 0.89
billion UAH (prices of 2012), with a standard error of 0.03 billion. This means that we
can get agricultural products at total value of 5.4 billion UAH (with a standard error of
0.2 billion) from flooded territories which are under Dnieper cascade
Table 3. General characteristics of the agricultural sector for the period 2010-2013
2010 2011 2012 2013
x( ( x))
Volume of 194.9 233.7 223.2 252.9 226.2(10.3)
production (billion
UAH)*
Area (sq. km) 246.4 247.1 261.3 262.0 254.2(3.7)
Agriculture return 21.1 27.0 20.5 11.2 20.0(2.8)
(%)
* prices of 2012
Source: AgriculturalUkraine 2013 / Kyiv.-2014-p.187-200.
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The value of electricity produced during a year and financial value of potential
agricultural products are presented inTable 4.
We introduce the concept of efficiency of areas of separated reservoirs as the ratio
of the value of the annual volume of electricity produced to the potential value of
agricultural products that can be grown on flooded areas.
Table 4. The effeciency of the flooded areas in monetary terms
Output of
Price of
Flooded agricultural
electricity The efficiency of
area, products on
Name of reservoir produced, bln. the flooded areas,
square the flooded
USD. (VAT %
km. areas, bln.
included)
USD.
Kyiv 878 0.78 0.22 28.2
Kaniv 470.3 0.42 0.31 74.8
Kremenchuk 2085.5
1.86 0.49 26.1
Dniprodzerginsk 464.4
0.41 0.43 103.5
Dnipro 255.2 0.23 1.29 568.6
Kakhovske 1879 1.67 0.48 28.7
Total 6032 5.37 3.22 60
Source: own calculations
The total amount of the value of electricity produced is significantly less than the
potential value of agricultural products that can be grown on the flooded areas, the value
of electricity is only 60% of the potential value of grown agricultural products relative
to the average indicator of Ukraine agricultural productivity. Graphical representation
of efficiency for certain reservoirs is shown in Figure 1.
209
2,0
1,5
Output of agricultural
bln.UAH
products on the flooded
1,0 areas, bln. USD.
0,5
Price of electricity
produced, bln. USD. (VAT
0,0 included)
Fig.1.Comparison of possible income from agricultural production and power generation
Source: own calculations on base table 4
Data in Table 4 show that the efficiency of the flooded areas is significantly different
for different reservoirs. The most effective reservoir is Dnieper HPS, because it was
built in the place where the flow of Dnieper is rather fast (significant differences in
levels). Further construction of power hydro stations led to the flooding of large areas
that would have greater value if they were used in agricultural sector.
3 Risks Evaluation of Further Dnieper Cascade Functioning
All possible losses connected with functioning of reservoirs are not limited to the
wastage of flooded areas. The general scheme of the risks evaluation of further
functioning of reservoirs is presented in Figure 2. They can be divided into three
groups: economic, technological and environmental.
We made an attempt to assess the expected total annual losses L which consist of
economical - Lеk ; ecological - Lekol ; and technological - Lt :
L Lеk Lekol Lt (1)
In the first approximation economic losses are equal to the difference between the
price of potential agricultural products Vap and the value of producing electric energy
Ve :
Lek Vap Ve (2)
210
Risks
Eco o ic Ma - ade
E viro e tal
Thetotala ual expectedloss
Fig. 2.Model of possible risks of functioning of Dnieper reservoirs
Environmental risk in a first approximation must be evaluated on the basis of cost
of measures aimed to bring the mass of water in the reservoir (with absence of flow)
to state of the river water.
The most difficult to evaluate are technological (man-made) risks, which present
both static (regular repair of dams, measures aimed to support state reservoirs) and
stochastic components. The latter is relevant to the possibility of artificial tsunami due
to partial or complete destruction of the dam. Taking into account the global statistics
the probability of the destruction of the dam is evaluated around 0.01% [14]. At first
glance it is a small probability and it seems that is can be ignored, but the evaluation of
the probability of depressurization of the reactor of Chernobyl type was considered
lower for two orders of magnitude (0.0001%), which did not prevent this to happen.
We evaluate the risk of man-made reservoir functioning for each reservoir. The
potential energy that depends of the height of the dam and of the volume of reservoir
after the destruction of the dam creates an artificial tsunami (Table 2). We wish to
explore the least effective case (Table 4) and the most dangerous in terms of potential
losses– Kyiv reservoir.
The approximate evaluation of the power of the artificial tsunami in case of
destruction of the dam of Kyiv HPS can be calculated on the basis of the potential
energy of water masses and sludge. The volume of the Kyiv reservoir is 3730 million
ton. (Table 2) to which we add 90 million tons of radioactive sludge [8]. The average
depth of reservoir is 4m and the average height of dam is 11.5m, dam reservoir center
of gravity is situated at a height of 9.5 m according to the water level of the Dnieper
River after the dam. That is why the potential energy of artificial tsunami that threatens
Kyiv is:
211
Eц m h g 3730 10 9 9.81 11.5 4.2 1014 J
m (3.73 0.09) 1012 kg;
(3)
h 11.5 м 2 м 9.5m;
g 9.81m / s 2
According to the energetic characteristics the potential tsunami that threatens Kyiv
is equal to five nuclear charges dropped during the Second World War on Hiroshima
(15-20 kt. TNT) [15]. Of course, the shock effect of nuclear explosion and artificial
tsunamis is difficult to compare because the shock wave in the first case expands at
speed exceeding the speed of sound and artificial tsunami speed is determined by the
depth of the Dnieper, and taking into consideration the depth of Dniper the speed will
not exceed 30 km / h.).
The situation is complicated by the presence of 90 million tons of radioactive sludge
at the bottom of the reservoir, the presence of which can contribute significantly to
strengthening of the effects of artificial tsunami and the risk of radioactive
contamination of the Dnieper and coastal areas to Kanev reservoir. In the case of this
scenario, 10% of Kyiv may be contaminated [9].
Similar characteristics are calculated for each of the reservoirs (Table 2).
Kremenchuk and Kakhovka reservoirs have the highest level of risk connected with
emergance of artificial tsunami, it can be explained by volume of the accumulated
water.
Losses caused by artificial tsunami in certain time t due to the violation of the
integrity of the dam are proportional to the product of the tsunami energy ( E ts ) and
cost values (urban infrastructure) located in the area of artificial tsunami( S ots ):
Lt k Ets S ots (4)
where, k – coefficient of dimension J-1, which can be determined only empirically.
The expected losses:
L t p Lt (5)
Variance:
2 p L2t (1 p) p L2t Lt p (6)
Losses in confidence level α - L ( p( L L ) ) [13]:
L L t x Lt p Lt ( p x p ),
(7)
where x -quantile of the normal distribution.
212
We make an assessment of potential losses of Kyiv which can be caused by the
potential of artificial tsunami concentrated in the Kiev reservoir.
Up to 10% of the houses located in Kyiv according to the evaluation of hydrologists
are under the tsunami risk. The volume of living area in houses in Kyiv is 62.2 million
square meters [5]. The cost of 10% of Kiev buildings, at an average price of 0.5
thousand dollars per sq. m, is 3.1 billion USD. Hence, the expected losses for a given
probability of violating the integrity of the dam is 3·105 dollars. Losses in confidence
level α:
L L t x Lt p Lt ( p x p )
3.1 10 9 (10 4 1.65 10 4 ) (8)
3.1 10 0.0166 5.1 10
9 7
This means that the annual potential losses from the use of the Kiev reservoir taking
into account the risk of man-made tsunami are near 51 million USD.
After analyzing potential threats and possible damage, which can be caused by
artificial tsunami in Kyiv we cannot propose the immediate dismantling of all the dams
on the river Dnieper. The data in Table 2 on artificial potential energy of the tsunami
should be supplemented by information connected with potential losses according
expression (8). There must be made a forecast of losses caused by the destruction of
the reservoirs. After all the calculations, we can evaluate the hazard rank of every
reservoir and thus offer the procedure of their disassembling in order to restore the
natural state of the Dnieper.
4 Conclusions
New information technologies and development of the theory of environmental
management leads to a revision of the main concepts of the planned economy. Thus it
leads to the change of our view on necessity and efficiency of functioning of
hydropower stations. We analyzed the energetic efficiency of certain reservoirs on the
basis of an alternative use of the flooded territory in agriculture. Energy efficiency of
different reservoirs is rather different. A significant share of electricity is produced by
Dnieper hydropower station, thus there is an opportunity of gradual transition to use
of updating energy sources that do not threaten energy security. Therefore, the final
decision about dismantling of hydropower stations should be made on the basis of
comprehensive assessment of economic-ecological efficiency and evaluation of losses
which can be caused by man-made tsunami.
We propose a complex approach to risk assessment of use of the Dnieper cascade
hydropower station. We use a stochastic method of assessment of potential losses
connected with the use of Dnieper reservoirs in order to assess the losses, which can be
caused by violation of the integrity of the dam. We evaluated the potential losses of
man-made tsunami for Kyiv reservoir. In the research was made evaluation of the
potential hazards of each of the Dnieper reservoirs which can be caused by man-made
tsunami. On the basis of the achieved results we ranked the reservoirs according to the
degree of economic insecurity.
213
Transformation of the of the key symbol of the Ukrainian state of rapid flow into the
system of stagnated reservoirs has no economic reasons taking into account that
hydropower stations produce only 5% of the electricity of the total amount and the
flooded areas can be used more efficiently. are more effectively use the flooded areas.
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http://ohranatrud-ua.ru/stati-po-gz/927-gidrodinamichnoji-nebezpeki-v-ukrajini.html (in
Ukrainian)
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Progress, 1985. (in Russian)
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16.J Andrew Charles, Paul Tedd, Alan Warren Delivering benefits through evidence, 2011.
214
Behavioral Aspects of Financial Anomalies in
Ukraine
Tetiana Paientko
National University of State Tax Service of Ukraine
tpayentko@mail.ru
Abstract. This article is devoted to the problems of financial anomalies in
Ukraine. Groups of main financial anomalies, and the key reasons for the
development of such financial anomalies will be herein defined, and the
behavior of the economic agents which frame financial anomalies in Ukraine
will be explained. Possibilities for overcoming such financial anomalies will
also be examined.
Keywords. Financial anomalies, economic behavior, revenue loss, shadow
economy
Key terms. Model, Research
1. Introduction
The current state of the Ukrainian economy is most difficult. Government reforms
which were decelerated have had a decisive impact on the further development of
Ukraine as an independent nation. However, questions arise as to what the mechanism
for implementing such reforms should be, and to the usefulness of implementing
policies on the basis of foreign experience. The past few years show that most of the
changes in the economy of Ukraine were as a result of taking into account foreign
experience. However, applying such experience does not always result in the intended
manner. One reason is that foreign policy examples were implemented quite
imperfectly in the Ukrainian economy. Another reason is the underestimation of the
time needed to properly implement reforms. Thirdly, one of the most significant
reasons is the unexpected behavioral response of Ukrainian economic agents, which
was quite different to reactions in other countries.
2. Theoretical and Methodological Background
Groundbreaking research work on understanding the fundamentals of the behavior
of economic agents has been published by the leading scientists of institutional
theory. In particular, D. North was one of the first who proved the existence of
anomalies in an economy and finance that cannot be explained solely on the basis of
economic laws (D. North, 1990).
215
J. Buchanan was one of the first who explained the role of social choice in the
development of an economy and the reaction of economic agents on political
decisions (J. Buchanan and G. Tullock, 1962). J. Stiglitz deeply investigated the
causes of the global economic crisis of 2008, revealing the behavioral aspects and
further consequences for a society (J. Stiglitz, 2011).
Research by Ukrainian scientists on the behavioral aspects of financial anomalies
has been essentially unstructured. O. Pruts′ka explains how differences in the
development of various societies are marked by reactions by members of the society
to different types of externalities (O. Pruts’ka, 2003). A. Gritsenko has described
aspects of economic anomalies in the economy of Ukraine and developed a
classification of them (A. Gritsenko, 2003). V. Vishnevsky has researched the causes
of financial anomalies (V. Vishnevsky, 2006). R. Pustovìjt has investigated the nature
of transaction costs in the economy of Ukraine (R. Pustovìjt, 2004). Y. Ivanov and
O. Jeskov maintain that one of the reasons for the failures of many reforms are
attempts by the government to remedy the mistakes of the past without considering
possible reactions by economic agents in the present (Y. Ivanov and O. Jeskov, 2007).
The causes and nature of financial anomalies in the economy of Ukraine have been
studied using various methodological principles. Firstly, work was done on the basis
of theoretical judgments and generalizations (O. Pruts’ka, 2003, A. Gritsenko, 2003),
and secondly, using the tools of economics and mathematical modeling. Here arises
another problem, because not all tools can be applied. For example, the use of
correlation-regression analysis provides opportunity to describe the behavior of a
group of agents (rather than the reaction of one agent) in specific terms for a specified
period of time. This means that the use of predictive models based on data correlation
for past periods could be incorrect. This explains the miscalculations in the
development of state budgets, the failure of the planned indicators of budget, etc.
In this case, more accurate the results would be reached by fuzzy logic simulation
modeling (V. Vishnevsky, 2006; O. Rajevnieva, 2007). However, in my opinion, such
research should be complemented by the results of the application of game theory. It
is a toolkit game theory and can explain the reasons for the behavior of each
economic entity in a relevant situation.
3. Efficiency Estimation Procedure
The recent stage of development of the Ukrainian economy is characterized by a
number of financial anomalies, which have been described in the publications of
A. Grytsenko (2003), T. Paientko (2013), etc. Among the major financial anomalies
are the following:
1. Deformed structure of economy of Ukraine, in which the dynamic
development of the financial sector has not contributed to an increase in the
volume of funding to the non-financial corporation sector. This issue is explored in
detail in the article by T. Paientko and Y. Syrotiuk (2014).
The problem lies in the fact that the growth of the assets of financial institutions
does not ensure the necessary growth of investments in the non-financial corporation
sector of the economy. The crisis in Ukraine has further worsened the situation
216
regarding financing in that sector of the economy. First, bank lending has been
actually paralyzed. The increases of the NBU discount rate initially to 19.5%, and
then to 30%, have actually robbed banks of real opportunities to inject funds into the
economy.
Secondly, in 2014-2015, 39 banks declared insolvency, and most banks have
problems with liquidity and the ability to return deposits to customers. This was one
of the causes of the bank panic and the outflow of deposits. The situation involving
savers has worsened the steep inflation and devaluation.
Thirdly, problems with solvency have affected many insurance companies. This
happened because they were placing their reserves mainly as deposits in banks,
including those who have since become insolvent. Fourthly, mass poverty is
developing within Ukraine, and that part of the population which forms the bulk of
the depositors now appears on the brink of poverty.
Thus, the financial sector now finds itself on the brink of survival. The situation
exists where the greater part of the population believes there is nowhere to invest.
Furthermore, that part of the population that has savings in foreign currency will soon
not be willing to inject funds into the financial sector. The behavior of economic
agents in such situations can be described by using a toolkit of game theory. These are
the possible strategies of a depositor and a bank:
1. The depositor puts money into a deposit account and the interest rate exceeds the
rate of inflation (payout 1).
2. The depositor invests in a deposit account and the interest rate is lower than the
level of inflation (payout 0).
3. The depositor puts money on deposit and the interest rate is lower than the
inflation rate and the rate of devaluation (payout – 1).
4. The bank is ready to return the deposit by the end of the term together with
interest (payout 1).
5. Temporary administration will be introduced in the bank during the term of the
deposit. The depositor will receive compensation from the fund of guaranteeing
deposits of individuals (payout 0).
6. Temporary administration will be introduced in the Bank during the term of the
deposit. The depositor will not receive compensation (payout – 1).
Then the payout matrix will look this way (table 1):
Table 1. The matrix of payouts of the depositor and the bank
Bank (4) Bank (5) Bank (6)
Depositor (1) (1; 1) (1;0) (1; –1)
Depositor (2) (0;1) (0;0) (0; –1)
Depositor (3) (-1;1) (-1;0) (-1; –1)
N.B. – 1, 2, 3, 4, 5, 6 are strategies
As can be seen from the table, there is only one equilibrium strategy which
provides a payout for both sides – (1; 1), which is possible with a probability of 1/9.
Two strategies (0; 1) and (0; 0) do not provide payout for the depositor, with
probability 2/9. The other strategies are without payout for the depositor with the
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probability of 6/9. Potential depositors are unlikely to trust their savings to a bank
because of this combination of circumstances.
There is a dilemma in such situations: the non-financial corporation sector of the
economy requires an increase in funding, and the financial sector cannot provide it as
a result of the outflow of funds. To overcome the described abnormalities, the
government should take measures to stimulate the growth of personal savings.
Reducing real income leads to a lower limit in the propensity to save. The drop in the
propensity to save is now faster than the fall in real income.
2. Lack of correlation between the decrease in the tax burden and the dynamics
of foreign investment in Ukraine's economy. This situation is also a financial
anomaly caused by several institutional factors. Over the past twenty years, the
Ukrainian government instituted significant tax benefits and other preferences for
foreign investors. However, within the post-socialist space Ukraine remains an
outsider in the attraction of foreign investments per capita. In addition, most foreign
investment is coming into Ukraine from regions where there exists a more favorable
investment climate, offshore entities, and Russia (table 2).
Table 2. Foreign direct investment (equity) in Ukraine's economy,%
Indicators 2010 2011 2012 2013 2014
Total 100,0 100,0 100,0 100 100,0
Which includes
Cyprus 22,2 25,6 31,7 32,7 29,9
Germany 15,8 15,0 11,6 10,8 12,5
Netherlands 10,5 9,8 9,5 9,6 11,1
Russia 7,6 7,3 7,0 7,4 5,9
Austria 5,9 6,9 6,2 5,6 5,5
United Kingdom 5,3 5,1 4,7 4,7 4,7
Virginia Islands (Brit.) 5,1 4,5 3,5 4,3 4,4
France 3,9 3,5 3,2 3,1 3,5
Switzerland 3,3 3,3 2,9 2,3 3,0
Italy 2,7 2,1 2,0 2,2 2,2
USA 2,2 2,0 1,9 1,8 1,9
Poland 2,1 1,9 1,7 1,7 1,8
Belize 1,9 1,8 1,7 1,5 1,4
Other 11,5 11,2 12,4 12,3 12,2
As is evident from the data presented in table 2, the largest volume of foreign
investment in Ukraine’s economy is coming from Cyprus. In its essence it is not an
investment, but the return of capital removed previously from Ukraine. In most
developed economies, providing tax incentives to foreign investors provides an
increase in foreign investment. In Ukraine, this tool does not work. According to the
World Investment Report and Ranking, the reduction of business taxation is not a
determining factor when deciding on investing in Ukraine. Even before the beginning
218
of the armed conflict, key analysts and potential investors indicated greater concern
over the issues of the low level of protection of property rights and the high level of
corruption. Domestic investors are also not actively investing in the domestic
economy. On the contrary, much of the internal capital has been removed from
Ukraine. This is an extra negative indicator for foreign investors.
Investors (domestic or foreign) make investment decisions taking into account the
following probabilities:
1. The government will change the rules of the game and preferences for foreign
investors will be eliminated – p (А).
2. The prevalence of bribing – q (B).
3. The infringement of ownership rights of the investor – 1– (p+q) (C).
Probable scenarios of the government can be described as follows:
1. An investor makes a decision about investing in the Ukrainian economy in spite
of the existing risks. Investments are long-term. This is an absolute win for the
economy, which denotes 2 (if we assume that 0 is the loss to the state in the absence
of investment).
2. The investor does not assume all of the risk, but decides to invest in the
economy. However, such investment is generally directed into short term projects
intended for a fast return. Under such circumstances the economy would win, but it is
smaller than the previous version – 1 (B).
3. The investor takes no risks and decides not to invest in these conditions (C).
The described version is a game that will repeat. There is the possibility that a
future investor will change his course of action. However, the probability of investor
choices changing depends on how the government shapes the business environment.
The payoff matrix is presented in table 3.
Table 3. Game Matrix: Investor and the Government
The choice of the Government
The choice of
the investor
A B C
A (1;2) (1; 2) (–2; 2)
B (1; 1) (1;1) (0; –1)
C (0; 0) (0; –1) (0; –2)
Source: compiled by author
In this case the probability of investor payout can be described as:
The probability in a change of rules of the game initiated by the government:
p+q+0(1 –(p+q)= p+q
The probability of a bribe being requested:
p+2q –1 (1 – (p+q)) = 2p+3q–1
The probability of infringement on ownership rights:
2p – q + 0(1 –(p+q) = 2p –q
All three options can be equally acceptable for domestic investors. As in the case
of limited foreign investment the cost of domestic investment increases. However,
this must be true:
p+q = 2p+3q–1 = 2p –q
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Having solved the equation, we obtain: q = ¼, p = ½, (1 – p – q) = ¼
So, the most decisive factor for investors is a change of the rules of the game by
the government. They believe that this risk is the largest. However, you can see that
the risk of bribing or infringement of rights is smaller. The risks do not stand alone.
Their real impact is expressed only with the risk of changes to the rules of the game.
It means that q = (1 – p – q) =¾. Under such conditions the likelihood of foreign
investment is preserved. However, it would likely be short-term investments in
projects with a fast turn-around period. Therefore, an improvement in the investment
climate in Ukraine provides for a stabilization of the rules of the game for the
investor. The investor should be guaranteed that the rules of the game would not
change within a fixed period of time.
3. Lack of correlation between the size of the tax burden and the dynamics of the
informal sector of the economy. One of the greatest problems for the Ukrainian
economy is the degree of its shadow economy. According to various experts the
volume of the shadow economy in Ukraine constitutes 40% (according to the
Ministry of Economic Development and Trade of Ukraine) to 80% (estimated by the
Schneider Institute). There is a misconception that the shadow sector of the economy
in Ukraine was formed after the breakup of the Soviet Union. However, shadow
economic activity existed in the times of the USSR.
The policy of "war communism" (1918-1921), from the outset, carried within
elements of shady dealings. It meant that the government resorted to violent methods
and centralized administrative pressures to accomplish their own goals. In those times
speculation, gangsterism, and robbery developed rapidly (R. Viseberg, 1925, p. 43).
In the time of Stalin about 30% of production was embezzled from socialist
enterprises, and about a quarter of the resources redistributed centrally was not by
intention.
A sharp reduction in the non-government sector in the late 1950s – early 1960s,
contributed to the further development of the informal sector of the economy.
Commercial cooperatives were eliminated in that period, the final transition from
state farms to collective farms happened, prohibitions of individual trade restrictions
on keeping personal subsidiary plots were decelerated, as was the ban on the holding
of cattle, etc. A trend towards further consolidation of production, an increasing
phenomena of monopolies in economics, ideological mandates proclaiming a further
transition to communism - all these factors shaped an economy with dual sectors −
official and shadow, which interacted with one another. Thus began the emergence of
speculative markets, clandestine workshops, black marketeers and speculators in
foreign currency. According to modern estimates, the 1960s saw that unofficial
production supplied 20% of industrial products, 40% of food products, and about 35-
45% of all scarce consumer goods was made available through speculative markets.
During the era of Brezhnev, the shadow economy flourished and took almost an
official color. By the beginning of the 1980s, all regions of the country began to
encounter clandestine workshops, using the state's equipment, material, and energy
resources, and funds. Production surpassed mandated limits which were set by the
State Supply and State Planning Commission, and the income was widely distributed
(T. Koriagina, 1990).
220
This shadow economy, tolerated by Leonid Brezhnev, yielded by the most
generous estimates 10-15% of GDP, and then rose to 50% of GDP in the period
before “Perestroyka”. The level of corruption between 1980-1985 in the Soviet Union
put it in the middle of a ranking of 54 countries, having a larger bureaucracy than
Italy, Greece, Portugal, South Korea and virtually all developing countries.
In the USSR at the beginning of the 1990s, the volume of the shadow sector was
assessed to be in the amount of 100 billion rubles by average valuation, 20-25 billion
rubles from the most conservative, and some pegged it at 150 billion rubles. In
comparison with the beginning of the 1960s, the growth of the scale of the shadow
economy across the whole range of ratings was from 4 to 30 times (T. Koriagina,
1990).
With the collapse of the USSR the Soviet shadow economy ended. However,
shadow economies began to resurface in the individual independent republics, and the
specific conditions and trends within each new country determined the dynamics and
scope of illegal operations. According to various estimates the volume of the
Ukrainian shadow economy at the beginning of its existence as an independent state
(1991) was estimated at 18% of GDP. Thus, the Government had from the outset
made an error in believing the tax burden was the main factor in the development of
the shadow economy in Ukraine. It ignored other contributing factors for the
development of a reducing shadow economy. Therefore, the reaction of the economic
agents was not as expected by the government.
After the collapse of the USSR the shadow sector continued to grow. A decisive
role in this was played not only by irrational tax policy. The development of shadow
economic activity contributed to hyperinflation, an increase in bartering, and the
opportunistic behavior of civil servants, etc. The growth of the tax burden in the
period 1991-1996 also played a negative role. However, we are not merely noting the
direct interdependence between the sum of money required to pay for the benefit of
the government, and the amount of shadow activities. A principle motive of shadow
economic relations and tax evasion was that taxpayers did not trust the government to
responsibly use tax revenues to the benefit of the greater society. This type of
economic agent truly believed that they could better use the savings than had the
government had the funds.
For an explanation of the behavior of economic agents, it is advisable to use a
model of expected utility, which was developed by Von Neumann and Morgenstern
(Von Neumann and Morgenstern, 1970). According to the standard model of choice
in conditions of uncertainty for taxpayers, it is also a game. They estimate the
payment of taxes in accordance with the expected utility. In conditions of uncertainty,
such behavior is described by the prospects theory. In general this theory is as
follows: Assume, the taxpayer has to play a lottery (x, p, q; y). This means that the
lottery has a result x with probability p and the result y with a probability of q. The
taxpayer assesses this lottery this way (1):
π(p) v(x) + π (q) v (y) (1)
v(x) – function values that the individual gives the winning or losing and π(р) –
weight, which the individual provides objective probabilities when making decisions.
Hypothetical functions v and p are presented on fig. 1.
221
Value
Losses Payout (winning)
Fig. 1. Hypothetical function values
This theory has three important features. First, the value of winnings and losses are
defined separately. This is consistent with the analysis of games and the choice of
people in conditions of risk. Second, it is a form of function values. Function is
concave in the interval of winnings and convex in the range of losses. This means that
taxpayers are shunning risk in the winning area and attaching risk to the losses area.
The function values must be 0 at the point of starting. It means there is more extreme
sensitivity to losses than to gains. This trait is called avoidance of losses. The third
feature is the nonlinear transformation of probability π (p). Unlike probability p, π (p)
is a weight that provides an objective probability when making decisions. As a rule π
(p) = p, but π (р)<р for large p. Small probability receives a relatively large weight,
with π (р)˃р (A. Lukashov, 2004, pp. 40-41).
Function definition of weight is also characterized by subcertainty property: for all
0<р<1, π(р)+π(1-р)<1. The principle of incomplete probability describes the attitude
of people to probable events. The weight of the two probabilities of complementary
events is less than the weight of the one event that must occur with a probability of
100%.
Taxpayers are more sensitive to the difference in probability at its higher levels.
According to experimental data, taxpayers would surely want to hide 10,000 UAH in
taxes at 100% certainty than receive social benefits from the state totaling 12,000
UAH with a probability of 80% that they would appear, while taxpayers believe that it
is better to have 12,000 UAH with a 20% probability, than 10,000 UAH with a
probability of 25%. According to prospects theory:
(2)
So, a 20 point increase in the probability of 0.8 to 1.0 has a greater effect than an
increase from 0.2 to 0.25. Therefore, lowering the tax rate on corporate income in
2004 (from 30 to 25%) did not cause a reduction of the shadow economy since the
probability of the growth of volumes of goods from the government was less than the
amount of unpaid taxes. Lowering the tax rate on corporate income between 2010 to
2014 (from 25% to 18%) also did not contribute to a reduction of the shadow
economy. Since the weight of probability of winning from the non-payment of taxes
222
exceeds the probability of a return of government benefits. Based on the foregoing,
the key factor in the reduction of the informal sector of the economy is changing the
behavior of the government, not the reduction of the tax burden.
Taking into account the results of research of previous financial anomalies, one can
expect businesses to exit from the shadows if the following conditions can be
fulfilled:
1. A change in the behavior of the government. Taxpayers must trust how taxes are
being utilized.
2. Preservation of property rights should be guaranteed and not merely proclaimed.
The next financial anomaly is closely associated with the above-described
situation. It is possible to explain how to use game theory (a zero sum game) by using
the model of expected utility and prospects approach. However, the best model in this
case would be the principal-agent theory.
4. Lack of meaningful communication between established punitive sanctions
for violations of tax legislation and the level of taxes.
Low taxes are the problem, which every Government in Ukraine is trying to
overcome. To improve the level of payments of taxes administrative methods were
mainly applied. In particular, there was an increase in the number of grounds for
carrying out unscheduled inspections and increasing the size of penalties. However,
this failed to achieve the desired level of tax payments. Also, the activities of tax
officials is characterized by low efficiency (tabl. 4).
Table 4. The results of the activity of tax police in Ukraine for 2007-2013, million UAH
Indicators 2007 2008 2009 2010 2011 2012 2013
Extra revenue for
budget, discovered 259.94 382.1 502.68 4370.59 1052.2 2082.76 2014.5
by tax police
Charge involving
130.39 173.53 3461.81 451.67 568.67 978.6 1023.2
tax police
The amount
stipulated damages
2429.78 2662.84 2406.57 2008.86 2173.89 1997.6 2117.4
in criminal cases
of tax evasion
Refunded the sum
of damages in
878.30 1155.97 829.52 816.78 869.71 888.2 902.3
criminal cases of
tax evasion
As can be seen from table 4, even in those years when there was a growth in the
shadow economy (2012-2013), large increases of revenues to the budget from
punitive penalties did not occur. The tax police did not execute one of their main
functions – to provide reimbursement of losses by the government.
Throughout 1997-2015, the government tried to increase the size of penalties for
violations of tax legislation several times. However, the discipline of taxpayers has
not changed. The approach used by regulatory agencies prior to the imposition of
penalties has not changed. Each year, the regulatory agencies set a planned amount of
punitive penalties. This means that the same amount of fines would have to be
223
recovered from taxpayers by the regulators. If the amount was less, then the head of
the relevant local authority would have to explain why the targets had not been
reached. If the amount collected was greater, then the following year the planned
penalty targets would be increased.
Such an approach was borrowed from Soviet times. It is false from the very
beginning. It thwarted an opportunity to build partnerships between the government
and the taxpayer. It violates clause 4.1.4 Article 4 of the tax code of Ukraine about a
presumption of legality. Also, the actions of regulatory authorities often violate clause
4.1.2 c. 4 of the tax code of Ukraine on the equality of all taxpayers. In practice, it has
not been uncommon to have cases of selective application of penalties. Such cases
discredit the image of the government and are not conducive to an increase in the
level of trust.
The question arises as to why these facts have a place. Indeed, at first glance, this
behavior is aberrant. This anomaly can be explained in terms of the theory of agency
relations. In this situation, the government is the principle. It sets the rules of the
game, based on existing information. However, the information is incomplete.
Regulators and taxpayers are agents who in real life have more information on a
specific situation.
It is a situation where both agents, if they want to be profitable, must behave
opportunistically. The taxpayer knows that in any case he will have to pay a penalty
(a plan of fines). The tax inspector must collect a minimum amount of fines. They are
not interested in overfulfillment of the plan. It is easier for taxpayers and a tax
inspector to engage in conspiracy and agree on the amount of the penalty. As a result,
the taxpayer may violate tax law and not expect a higher responsibility than that
agreed. Instead, the inspector receives a bribe and there is a loss of appropriate fines
and charges. There is a fairly simple way out of this situation. The government should
cancel the plan for punitive sanctions and reduce the number of cases of direct
communication of the taxpayer and the controller.
4. Conclusions
The described financial anomalies have a serious negative impact on the potential
for economic development. In terms of the theory of behavioral finance, the situation
is described as abnormal. They are the behavior reactions of economic agents to the
challenges of the environment. The economic policy of the government should
consider not only the potential economic effects, but also the expected behavioral
response of economic agents. During the development of the economic policy of the
government must pay attention primarily to such behavioral aspects:
1. Economic agents make decisions based on available information. Therefore,
information about the real economic situation should be fully disclosed. This will
reduce the information asymmetry in the relationship of the government to the
economic agent.
2. Economic agents make decisions based on the maximization of value, utility,
and the expected probability of receiving benefits. Therefore, the government should
ensure the provision of quality public benefits on the basis of tax revenues.
224
3. Economic agents invest in the economy if there is a guarantee of preservation of
property rights. For the investor, the decisive factor is that the rules of the game
remain constant from the government during the term of the investment. Therefore,
the government must ensure the stability of conditions for investment over long-term
periods.
In essence, consider behavioral aspects when developing economic policies to
overcome existing financial anomalies and to avoid the emergence of new ones.
References
1. North D.: Institutions, Institutional Change and Economic Performance, Cambridge
University Press (1990).
2. Buchanan J.M., Tullock G..: The Calculus of Consent: Logical Fundations of Constitutional
Democracy. Ann Arbor: University of Michigan Press (1962).
3. Stiglits J.: America, Free Markets, and the Sinking of the World Economy. Moscow,
EKSMO (2011).
4. Prutska O.: Institutionalism and Problems of Economic Behavior in Transition Economy.
Kyiv, Logos (2003).
5. Grytsenko A.: Features of the Institutional Structure of Ukrainian Society in the 21st
Century. Ukraine's Economy: Strategy and Long-Term Development Policy. Kyiv, Institute of
Economics and Forecasting, Phoenix (2003).
6. Vyshnevsky V., Vetkin A., Vyshnevskaya E.: Taxation: Theories, Problems, Solutions.
Donetsk, Donetsk IEP (2006).
7. Pustoviyt R.: Transaction Costs: Theoretical Concepts and Empirical Analysis. Economist
10, 26–29 (2004).
8. Ivanov Yu., Yeskov O.: Modern Taxation: the Motivational Aspect. Kharkiv, INJEK (2007).
9. Raievneva O., Goliad N.: Simulation of Anti-Crisis Management of Region. Kharkiv, INJEK
(2007).
10. Paientko T.: Institutionalization of Fiscal Regulation of Financial Flows. Kyiv, DKS center
(2013).
11. Paientko T., Syrotiuk Yu.: Accumulating of Financial Resources by Financial
Intermediaries and its Influence on Economic Development. Business infom. 8, 237–243
(2014).
12. Vaisberg P.: Money and Prices (An Underground Market in the Period of "War
Communism"). Moscow, State plan publishing (1925).
13. Koriagina T.: The Shadow Economy in the USSR. Questions of economy 3, 29–41 (1990).
14. Von Neiman J., Morgershten O.: Theory of Games and Economic Behavior. Moscow,
Science, (1970).
15. Lukashov A.: Behavioral Corporate Finance and the Company's Dividend Policy.
Management of Corporate Finance 2, 35–47 (2004).
225
The Formation of the Deposit Portfolio in
Macroeconomic Instability
Andriy Skrypnyk1, Maryna Nehrey1
1
National University of Life and Environmental Sciences of Ukraine
avskripnik@ukr.net, Marina.Nehrey@gmail.com
Abstract. In 2014 the main tendency of Ukrainian economy was the losing of
great deposit value. In this article we wish to explore a deposit portfolio struc-
ture in macroeconomic instability. We applied two approaches to the standard
optimization portfolio: risk minimization for a given maximum return and re-
turn maximization for a given maximum risk. Of the two approaches to the
standard optimization problem of portfolio: risk minimization at a given mini-
mum return and return maximization for a given maximum risk the advantage
was given the latter. The exchange rate risks are the main factors that have a
significant impact on the end result. The optimum structures deposit portfolio
was calculated for six different situations in national and world financial mar-
kets. Comparison of the optimal portfolio structure with real historical data
showed that customers of the banking system over evaluate the reliability of the
financial system.
Keywords. deposit, devaluation, portfolio, optimization, return, revaluation,
risk.
Key Terms. Data, DecisionSupport, Development, FormalMethod, Manage-
ment, MathematicalModel.
1 Introduction
The unstable macroeconomic situation in Ukraine and the crisis of the banking sys-
tem caused distrust in the banking institutions. According to the opinion of experts,
the Ukrainian population kept at home cash equivalent to $10 billion USA. In recent
years was observed the following tendency: in 2014 banks lost deposits in the amount
of 126 billion UAH, and around 18 billion UAH during first two months of the cur-
rent year [3]. However, storage of money at home has several disadvantages: for ex-
ample lack of income from capital and high risks, which lead to additional costs for
the implementation of the safety of their own homes and significantly decrease the
level of living.
Banking experts usually advise to divide money into three equal parts, two of
which are nominated into euros and US dollars according to the current exchange
rate, and put on deposit accounts in different banks which can be considered reliable
226
(it is advisable to choose banks which are included in the deposit insurance program
NBU) and wait for interests during this period (simple diversification). Unfortunately,
this method is connected with difficulties. It is almost impossibile to convert legally
the accumulated funds into any reliable currency, besides it is rather difficult to find a
reliable bank. This study is limited to two currencies - US dollars and euros, however,
presented method can be used to form a deposit portfolio using other currencies.
There are two approaches to the portfolio optimization problem: risk minimization
at a given minimum return and return maximization for a given maximum risk. For
portfolio optimization you need to determine in which currency to evaluate the result.
We can ask a question: “Why do we save money?” The answer can be the following:
“In order to increase consumption during our life (real estate, household appliances,
automobiles, traveling)” [2]. The vast majority of consumed goods in Ukraine are
produced outside the country and therefore it is better to measure the cost by the most
stable currency, which is now can be considered the US dollar. Alan Greenspan
devoted attention to keeping a low dollar inflation level than in the past since such a
policy, combined with the larger predictability of monetary policy, contributed to
making dollar capital denomination most attractive [11].
2 Markowitz Problem under Devaluation Condition
The Markowitz’s portfolio optimization problem can be solved using the well-
known term of return and risk (variance of return) components portfolio. If return is
measured as the deposit interest, the rate of risk is measured by its dispersion [4].
Linear model was proposed for credit risks in order to maximize bank profit [6, 10].
However, there is a factor that has a significant impact on the end result - an exchange
rate risks, which is more important for unstable economics [3]. Of course interests on
deposit and credit accounts for exchange rate risks, as the interest on UAH deposit
twice as much than the dollar deposit [1, 12]. The importance of foreign exchange
component in the sustainability of the banking system was emphasized in a number of
research [5, 13]. In this study we wish to evaluate the optimal structure of the deposit
portfolio during economic turbulence and make a comparison between real and opti-
mal structure deposit portfolio.
Exchange rate risks can be taken into account, if a devaluation matrix is specified.
We will consider the case-study of placing deposits for one year. We assume that
three macroeconomic situations, which determine the devaluation processes in the
3
country 1 ; 2 ; 3 , which are defined probabilities p1 ; p2 ; p3 ( pi 1 ) . Each
i 1
situation corresponds to a certain devaluation factor relative to USD defined as the
ratio of the exchange rate in a current moment to exchange rate what will be in a year.
We will denote devaluation multiplier for each economic situations i ( i 1,2,3 ) . If
we know the value of a random variable and the corresponding probabilities, we can
estimate the expected value of depreciation factor and its variance:
227
3 3
pi i ; ф pi i2
2 2
(1)
i 1 i 1
Later we will consider the case of uniform distribution of devaluation multiplier.
If 1 then dominate devaluation expectations, if 1 then dominate revalua-
tion expectations. There were short periods of revaluation of UAH, but we observe
the tendency of devaluation according to results of any year.
It is supposed to use the share denominated in euro for deposit portfolio, which has
currency instability relative to leading world currencies and the objective function is
denominated in USD, we need to specify the expected devaluation and its variance in
EUR against the USD for the next year. We will denote these parameters: ; 2 .
In this formulation dollar deposits is completely risk-free, which is rather optimis-
tic assumption. During the year, the interest on dollar deposits was changeable, which
can be used as a risk assessment. We denote the variance of interests on USD deposits
$2 . We assume that the current interest on USD deposits is in the interval 9-11% [8]
and is characterized by a uniform distribution, the dispersion interest is approximately
equal $2 3,3 10 5 .
We consider the standard formulation of the Markowitz problem taking into ac-
count the expected devaluation (revaluation) processes.
We present the particles deposit portfolio in UAH, EUR and USD:
d1 ; d 2 ; d3 ( d1 d 2 d3 1 ) , percentage interests r1 ; r2 ; r3 ( r1 r2 r3 ) are ranged
under level of risk of deflationary expectations. If an initial investment is S t than in a
year the expected amount of the deposit portfolio and its dispersion will be:
St 1 d1St (1 r1 ) d 2 St (1 r2 ) d 3 St (1 r3 ),
(2)
2 d12 St2 2 d 22 St2 2 d32 St2 $2 .
There are no members in portfolio variance that appear as a result of presence of
the connection between return components of portfolio. The reason is that in this case
independent devaluation processes influence on the profitability: euro and US dollar
and the processes of devaluation of the national currency because of macroeconomic
instability in the country. Therefore, we can assert absence of connection between
return of the portfolio shares denominated in different currencies in the proposed
formulation.
If the level of devaluation is high, the depositor will have loses ( St 1 St ) , that is
why we will limit the possible risk-free profit according to the interest which is equal
to r3 (the return of dollar deposits):
d1St ( 1 r1 ) d 2 St ( 1 r2 ) d3 St ( 1 r3 ) St ( 1 r3 ) (3)
228
From the last expression we can get maximum portfolio share of deposits denomi-
nated in UAH 1 :
d 2 ( r2 r3 )
d1 (4)
1 r3 ( 1 r1 )
We estimate the maximum share of UAH deposits in terms of catastrophic deval-
uation in 2014. The difference in interests denominated in euros and dollars is less
than 2%, the maximum value of the numerator is less than 0.01.
Devaluation multiplier for the previous year is approximately equal to 0.4 (8 USD /
UAH 20 = 0.4). Interests on deposits are r1 25% ; r3 10% . Therefore, the share of
UAH deposits in terms of landslide devaluation should not exceed 2%.
3 Optimal Portfolio Structure
We estimate the portfolio structure with maximum profitability and limited risks
for different combinations of UAH/USD and EUR/USD devaluation multiplier fac-
tors. Evaluation of devaluation multiplier factors is based on monthly time series of
UAH/USD (03.1997 - 02.2015) and EUR/USD (02.2007 - 02.2015) exchange rates.
Fig. 1. Dynamics of devaluation multiplier UAH/USD
Devaluation multiplier measured with one year interval (deposit time in optimiza-
tion problem) and currency pairs we calculated every month from March 1997 to
February 2014 (210 observations UAH/USD) and form February 2007 to February
2014 (98 observations EUR/USD). (Fig. 1, 2).
229
Fig. 2. Dynamics of devaluation multiplier EUR/USD
The period (1997-2014 for UAH/USD) consists of periods of economic growth
with fixed course and periods crisis when monetary system tends to new equilibrium.
Devaluation multiplier factor UAH/USD 1 under 155 observations (minor
revaluation probability pr 0,736 ), 1 under 55 observations (devaluation proba-
bility pd 0,264 ). Devaluation multiplier factor EUR/USD 1 under 44 observa-
tions (revaluation probability pr 0,449 ), 1 under 54 observations (devaluation
probability pd 0,551 ).
Devaluation multiplier EUR/USD has more natural character, when the equilibri-
um is set under the influence of many non-interrelated reasons and a stable tendency
is missing. The stationary hypothesis of the exchange rate of EUR/USD can be
proved if we explored a long time period. The same hypothesis for exchange rate of
UAH/USD must be rejected because of a full asymmetry of devaluation multiplier
relatively to unity level.
We consider the optimal portfolio structure in three cases: landslide devaluation
from 43% to 150% - 1 ( 0,7 ); moderate devaluation of 11% to 43% - 2
( 0,7 0,9 ); and a devaluation less than 11% - 3 (0,9 1,0). We regard the
distribution of devaluation multiplier at each of the intervals being uniform.
We consider two possible states in the global financial market for devaluation mul-
tiplier for EUR/USD: 1С ( 0,8 1,0 ) and revaluation multiplier:
С2 ( 1,0 1,2 ) . We present six possible situations that correspond to two situa-
tions of the world finance market (the euro-dollar) and three situations of devaluation
in the domestic market (Table 1).
230
We have used interests of one-year deposits in banks of first group (the most relia-
ble) to build optimization models. Of course, other banks interests can be significantly
higher, but in this case it is necessary to increase the risk measures of bankruptcy
probability due to the growth (receiving contributions under the insurance program of
NBU connected with the loss of time and interest and primary contribution for more
than 200 thousands UAH). We use the current annual deposit interests February 2015:
r1 rU 23%; r2 rE 13%; r3 r$ 12%.
Table 1. Expected value devaluation factors for different classes of national and
world economies in 2015
1 ( 0,7 ); 2 ( 0,7 0,9 ); 3 (0,9 1,0)
1С 0,55; 2 7 ,5 10 3 0,8; 2 3,3 10 3 0,95; 2 0,8 10 3
( 0,8 1,0 )
0,9; 2 3,3 10 3 0,9; 2 3,3 10 3 0,9; 2 3,3 10 3
С2 0,55; 2 7 ,5 10 3 0,8; 2 3,3 10 3 0,95; 2 0,8 10 3
( 1,0 1,2 )
1,05; 2 0,8 10 3 1,05; 2 0,8 10 3 1,05; 2 0,8 10 3
We consider the problem of calculation of the share of certain currencies in deposit
portfolio that maximizes the return of the portfolio for a given maximum risk level,
which is equal to variance of interests on USD deposits:
(r$max r$min )
$2 . (5)
12
For r$max r$min 0,02 $2 3,3 10 5 .
We obtain the following problem to be resolved for finding d , d (d1; d 2 ; d3 ) :
St 1 d1St ( 1 r1 ) d 2 St ( 1 r2 ) d 3 St ( 1 r3 ) max
d12 St2 2 d 22 St2 2 d 32 St2 $2 $2 ,
d 2 ( r2 r3 )
d1 , (6)
1 r3 ( 1 r1 )
n
d j 1,
j 1
d j 0, j 1,3.
We analyze the results of the calculation of the structure of deposit portfolio with
maximum return, depending on the situation in the global and domestic foreign cur-
rency markets (Table 2).
231
There are six situations according to the number of components in Table 2: (1, 1) -
moderate devaluation of the euro and the significant UAH depreciation; (1, 2) - mod-
erate devaluation of the euro and the moderate devaluation of the UAH (1, 3) - mod-
erate devaluation of the euro and slight currency depreciation; (2, 1) - moderate ap-
preciation of the euro and the significant currency depreciation; (2, 2) - moderate
appreciation of the euro and moderate currency depreciation; (2, 3) - moderate appre-
ciation of the euro and the slight depreciation of the UAH.
Table 2. Optimization of deposit portfolio according to the criterion of profit maximi-
zation
1 ( 0,7 ); 2 ( 0,7 0,9 ); 3 (0,9 1,0)
1С ( 0,8 1,0 ) d ( 0;0;1 ) d ( 0;0;1 ) d ( 1;0;0 )
St 1 1,12 St 1 1,12 St 1 1,1685
С2 ( 1,0 1,2 ) d ( 0;0,73;0,27 ) d ( 0;0,73;0,27 ) d ( 0;1;0 )
St 1 1,1685 St 1 1,1685 St 1 1,1865
In cases (1, 1) and (1, 2) optimal portfolio contains only dollar deposits with cer-
tain return. In the case (1, 3) portfolio consists only of UAH deposits (the return is
corrected to the expected depreciation up to 11.1%).
In cases (2, 1) and (2, 2) the same return is defined by 73% share of deposits nomi-
nated in euros and 27% of deposits nominated in dollars. In the case (2, 3) the return
which is equal to 18.65% is defined by 100% share of euro deposit. However, it is
better to based the assumptions on mathematical forecast about the structure of port-
folio that depends on the probabilities of the external environment: pi the probabil-
ity of devaluation i state (i = 1,2, ..., k) cross currency exchange rate UAH/USD,
q j the probability of the depreciation of the j-th state (j = 1,2, ..., n) cross currency
exchange rate EUR/USD, pij pi q j the probability of simultaneous occurrence
of the i and j devaluation states, d ij the optimal portfolio structure according to i
devaluation state of the UAH/USD and j state pair EUR/USD. Expected portfolio
structure is defined as:
k n
d pij d ij . (7)
i 1 j 1
We calculate the expected portfolio structure, assuming that the devaluation and
revaluation expectations of the euro-dollar are equal.
( p1 p2 0,5 ), the first basic variant is calculated according to the assumption
that all three devaluation states have the same devaluation probability (it is a situation
232
of absolute uncertainty). That is why pij 1 / 6 . This is basic structure of the portfolio
and its expected return:
d Б (0,167;0,41;0,423)....r Б 15,53%; Б2 7,4 10 4 .
We consider pessimistic option in which the probability of a significant devalua-
tion is twice higher than the probability of low, moderate devaluation and probabili-
ties moderate devaluation is equal to the sum of probabilities of large and small de-
valuation:
2 / 12....3 / 12....1 / 12
p ij (8)
2 / 12....3 / 12....1 / 12
In this case we obtain the following structure and return of the portfolio:
d (0,083;0,388;0,529)....r 14,98%; 2 6,4 10 4. .
We consider optimistic option in which the probability of a significant devaluation
is twice lower than the probability of moderate devaluation but the probability of
moderate devaluation is equal to the sum of probabilities of significant and moderate
devaluation:
1 / 12....3 / 12....2 / 12
pij (9)
1 / 12....3 / 12....2 / 12
In this case we obtain the following structure and return of the portfolio:
d (0,167;0,41;0,423)....r 15,53%; 2 7,4 10 4.
The last option is not different from the basic one. In macroeconomic environment
and exchange rate instability, the banking system and its clients replace the unstable
assets with stable, and this leads to an increase in dollarization of economy in general
and the banking system in particular (this quantitative criteria is measured as the share
of dollar deposits to the total amount of deposits [5]).
4 Historical Data Model Verification
Model verification can be made on the base of currency exchange rate (UAH/USD)
measured for a long period of time and tendencies of the exchange rate of two main
world currencies (EUR/USD). For model verification we use period of stable growth
of Ukrainian economy from 2002 to 2007 year, which coincides with period exchange
rate stability. We calculate the optimal portfolio structure for two periods: after-shock
period 2002-2005 and pre-shock period 2006-2007 on the base of NBU data. Average
233
annual deposit interests for this period is 10%; 5%; 6% and 14%; 9%; 9% (UAH,
EUR, USD).
Maximum dispersion magnitude has increased in four times in comparison with
previous calculations because of possibility of substantial changes in deposit interests
for long period. Optimal portfolio structure has not UAH component in all six possi-
ble situation (table 3) for 2002-2005.
Table 3. Optimization of deposit portfolio according to the criterion of profit maximi-
zation for 2002-2005 deposit interests: rU 10%; rЄ 5%; r$ 6%
1 ( 0,7 ); 2 ( 0,7 0,9 ); 3 (0,9 1,0)
1С ( 0,8 1,0 ) d ( 0;0;1 ) d ( 0;0;1 ) d ( 0;0;1 )
St 1 1,06 St 1 1,06 St 1 1,06
С2 ( 1,0 1,2 ) d ( 0;0,2;0,8 ) d ( 0;0,2;0,8 ) d ( 0;0,2;0,8 )
St 1 1,0685 St 1 1,0685 St 1 1,0685
Devaluation multiplier UAH/USD probabilities for Tabl.3 ranges calculated from
data analisis: p(1 ) 0,077; p( 2 ) 0,187; p(3 ) 0,736 . For EUR/USD devaluation
multiplier probabilities: p( 1с ) 0,449; p( 2с ) 0,551 . Next step probability evalua-
tion of simultaneous occurrence of all 6 possible devaluation states on long time in-
terval:
0,035....0,084....0,33
p ij p i q j (10)
0,042....0,103....0,406
The expected portfolio structure, for this probability matrix and optimal structure
portfolio for each of six situation:
d 2004 (0;0,11;0,89)....r 2004 6,47%, 2004
2
2,5 10 5.
This result differs from previously obtained for period of crisis. First of all, it con-
cerns the full absence of UAH component, and secondly, much smaller proportion of
the contributions in EUR. Both features are explained by ratio of key interests. Differ-
ence in interests in UAH was not enough to compensate devaluation risk of national
currency, additional interests on USD deposits for EUR provided a small share of
EUR deposits.
Optimal portfolio structure for pre-crisis period 2006-2007 differs in increasing
share of EUR contribution because interests on USD EUR deposits were equal, UAH
share is still equal to zero (Table 4).
The expected portfolio structure for 2006-2007 years:
234
d 2006 (0;0,449;0,551)....r 2006 11,4%, 2006
2
5,2 10 4
Table 4. Optimization of deposit portfolio according to the criterion of profit maximi-
zation for 2006-2007 deposit interests: rU 14%; rЄ 9%; r$ 9%
1 ( 0,7 ); 2 ( 0,7 0,9 ); 3 (0,9 1,0)
1С ( 0,8 1,0 ) d ( 0;0;1 ) d ( 0;0;1 ) d ( 0;0;1 )
S t 1 1,09 S t 1 1,09 S t 1 1,09
С2 ( 1,0 1,2 ) d ( 0;0,8;0,2 ) d ( 0;0,8;0,2 ) d ( 0;0,8;0,2 )
S t 1 1,1336 S t 1 1,1336 S t 1 1,1336
But real structure of bank deposits at that period did not correspond to optimal de-
cision, population prefered UAH deposits because of fixed interests and higher return.
It was thought that the strategy of the fixed exchange rate provided a decrease in
the level of dollarization of economy, which is defined as a ratio of foreign currency
deposits to all deposits. At this entire interval optimal strategy without risk accounting
consists of two key points: borrowing in foreign currency and placing of savings in
the national currency. At that time, nobody knew when the period macroeconomic
stability would be over, but now it has become clear that the financial crisis was only
a trigger for the system that was ready to collapse. UAH savers and currency borrow-
ers who were unable to complete their operations before 2008 crisis had losses. Bank-
ing customer behavior on the interval of economic growth can be considered on the
basis of the theory of “focusing illusion” [9] when banker clients exaggerate the im-
portance of one factor (fixed course), neglecting the influence of other factors, the
effect of which may lead to opposite results.
5 Conclusion
In this research we calculated maximum profitability three components UAH,
EUR, USD deposit portfolio structure (targeted function is denominated in US dol-
lars) with risk degree limitations in the economic growth period and periods of mac-
roeconomic instability. The exchange rate instability is regarded as main cause of
deposit risks and formalized by the relationship of current currency price to currency
price which will be in a year (devaluation multiplier).
Long time devaluation multiplier factor analysis gave possibility to evaluate prob-
abilities of six possible different devaluation (revaluation) situation for pairs
UAH/USD and EUR/USD. The optimal solutions were obtained for each of the six
possible different situations and for three interest options (two options during eco-
nomic growth and one during the period of economic turbulence). Expected deposit
portfolio was determined in conditions of macroeconomic instability for three possi-
ble choices: basic (probabilities of all states are equal), pessimistic (probability of a
235
significant UAH devaluation is twice higher than the probability of minor devalua-
tion) and optimistic (probability of a significant devaluation is twice less than the
probability minor devaluation). For optimistic option the part of UAH deposit must be
not more than 17%, in other situation expected UAH part must be not more than 8%.
Optimal portfolio structure in a period of economic grows has not UAH component
because of a small difference in the interests of UAH deposits and EUR, USD depos-
its. But this difference was enough to provide preferred growth UAH denominated
deposits. The reasons of this phenomenon is overconfidence of the clients of banking
system in UAH stability caused by fixed exchange rate according to NBU strategy.
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236
Dynamic Model of Double Electronic Vickrey
Auction
Vitaliy Kobets1, Valeria Yatsenko2 and Maksim Poltoratskiy1
1
Kherson State University, 27, 40 rokiv Zhovtnya st., Kherson, 73000 Ukraine
vkobets@kse.org.ua, max1993poltorackii@gmail.com
2
Taras Shevchenko National University of Kyiv, 90-A, Vasulkivska st., Kiev, 03022 Ukraine
ValeriaYatsenko@rambler.ru
Abstract. The paper deals with different approaches to the definition of e-
commerce, including special mechanisms for the distribution of goods and
payments, such as auction model. Different formats of auctions that change
welfare of their participants are investigated. Software modules were developed
for researching the effectivenes of double electronic Vickrey auction. It is
defined that in double Vickrey auction incentives for most buyers and sellers
are created to reveal their true types. The developed software module of double
Vickrey auction showed the highest efficiency in the terms of social welfare
among alternative formats and disproved the ability of Vickrey auction to
achieve results like market mechanism of perfect competition.
Keywords. e-commerce, online auction, e-auction, Vickrey auction, social
welfare.
Кey Terms. ElectronicAuction, Software, DoubleAuction, SocialWelfare.
1. Introduction
The current phase of civilization development is characterized by drastic
transformations in all spheres of life: from culture and sport to politics and
economics. Taking advantage of new methods, changing subject matter of
investigations, using neologisms such as digital economy, information economy, info-
networks economy, knowledge-based economy, Internet economy, "new" economy,
virtual economy, service economy. The variety of modern categories is typical for the
modern stage of evolutionary development of international economy, placing special
emphasis on the leading role of the triad of determinants of economic growth and
development of today, which includes intellectual capital, creative and innovative
factor as the basis for developing of knowledge-based economy.
Another feature of the modern epoch of human development is asymmetry of
socio-economic development of the international economic system, which is
deepening due to globalization. Most scientists think that essential determinants of
escalation of global asymmetries lie in ICT-sphere: This leads to more considerable
237
disproportion in international economy and increases social polarization [1]. ‘TСe
Golden BТllТon’ are enjoying their successful development due to unequal
relatТonsСТps wТtС perТpСerТes, as tСe number of “profТtable nТcСes” Тn global space Тs
СТgСly lТmТted; tСerefore tСe way to tСe cТvТlТzed “floor” can be easТly made due to
innovation-information achievements by means of integration the market mechanism
into the networked information economy [2].
The technological component of modern economic processes contributes to the
development of the networked economy as the synthesis of information and global
economies [3].
Works of W. Vickrey, E. Daniel, Gr. Dunkan ,G. Karypis, J. Konstan, P. Cotler, B.
Mahadevan, J. Riedl, A. Summer and B Sarwar are devoted to the problems of
establishment and development of global and local e-commerce markets in terms of
globalization processes. National scientists, namely A. Bereza, A. Berko, V.
Vysotska, I. Kozak, F. Levchenko, Y. Lyenshyna, V. Pasichnyk, L. Patramanska, E.
Strelchuk, T. Tardaskina do not stand apart of such scientific research. Theoretical
and statistical investigations of this category are being conducted by some
international organizations such as OECD, UNKTAD, UNISTRAL, WTO аnd ITU,
development projects and strategic programs in regard to e-commerce are being
elaborated by World Bank and EBRD.
The paper goal is to ground the impact of e-commerce on tСe partТcТpants’ welfare
through empirical experiment for electronic auctions, implemented by the means of
the relevant transactions via designed software that is economically desirable
distribution of goods and payments irrespective of strategic behavior of participants.
The paper has the following structure: the second part is devoted to literature
review; the third one determines auction formats; the fourth part constructs the
general model of double electronic Vickrey auction for true type and hidden type
agents; the fifth part concludes.
2. Related Works
Development of information economy has caused formation of e-society with its
integral parts: e-government in politics, e-business in economy, e-education, e-
ecology, e-medicine and others (Table 1). E-trading is deemed to be a part of e-
commerce which in its turn together with document control and business management
makes e-business [4].
In its narrow sense e-commerce is close to e-trading because its main function is
online purchase and sale transactions; in the wide sense the definition of e-commerce
covers any transaction effected using computer networks [5, 6, 7].
So e-commerce is a complex of business operations carried out using computer
networks (Internet, Intranet, Extranet), which are connected with the change of
material rights and all processes that support this process including Electronic Data
Interchange (EDI), Electronic Funds Transfer (EDF), e-trade, e-cash, e-marketing, e-
banking, e-Insurance, e-logistics.
238
Table 1. DТfferent ways of ТnterpretatТon tСe category “e-commerce”
Meaning Original Definition
OECD
(Ogranization
commerce=e-trade)
An e-commerce transaction is the sale or purchase of goods or
for Economic
services over computer mediated networks (broad definition) or
«narrow» (e-
Cooperation
via the Internet (narrow definition) 1.
and
Development)
R. Doernberg, L E-commerce means the ability to perform transactions involving the
Hinnekens, exchange of goods or services between two or more parties using
W. Hellerstein, electronic tools and techniques.
J. Li
E-commerce means any form of business process in which the
A. Sammer,
interaction between the actors happens by using the Internet –
Gr. Dunkan
(е-comerce = totality of business
technology
E-commerce includes searching for information, contracting,
supply of products, goods or services, making payments, sale or
purchase of goods or services, whether between businesses,
processes)
UN Experts households, individuals, Governments and other public or private
«wТde»
organizations, conducted over the Internet. The goods and services
are ordered over the Internet, but the payment and the ultimate
delivery of the good or service may be conducted on- or offline.
E-commerce is a wide array of commercial activities carried out
through the use of computers, including on-line trading of goods and
WTO
services, electronic funds transfers, on-line trading of financial
Specialists
instruments, electronic data exchanges between companies and
electronic data exchanges within a company 2.
Aspects of e-commerce are considered in Table 2 based on [8].
Table 2. Aspects of e-commerce
№ Aspect Essence
It is a method of delivery via telephone lines, computer networks,
1. Connections
electronic means
2. Process It is a technology to automate business operations.
It is a tool to reduce costs, improve quality of goods and services and
3. Services
accelerate delivery.
4. Time E-commerce allows to carry out operation online (24 hr. per day).
5. Space Open Internet infrastructure makes it a global environment.
According to most experts B2B is the largest segment of e-commerce (Table 3).
For example, according to UNCTAD data, B2B is a dominant segment in the
American market with twice higher volume of sales compared to those of B2C (559
billion dollars against 252 billion dollars).
1
Ecommerce Sales Topped $1 Trillion for First Time in 2012. Available
www.emarketer.com
2
E-commerce and Development Key Trends and Issues Available
www.wto.org/english/tratop_e/devel_e/wkshop_apr13_e/fredriksson_ecommerce_e.pdf
239
Table 3. Forms of interaction in e-commerce
Abbreviation Denomination Definition
Business-to- businesses make online transactions with other
B2B
Business businesses
Business-to- online transactions are made between businesses and
B2C
Customer individual consumers (social commerce)
Business-to-
B2А administrative document control
Administration
Business-to-
B2G operations between companies and public institutions
Government
e-commerce model in which a government entity buys
electronic
e-government or provides goods, services, or information to
government
businesses or individual citizens.
It is also confirmed by the structure of the e-commerce market in South Korea
based on open sources3. (Fig. 1).
Fig. 1. The structure of e-commerce in South Korea in 2013, %
Internet-shops make an essential part of e-commerce in Ukraine - sector B2C, but
B2B segment has great opportunities. For example, International center for electronic
trading B2B-center has been successfully functioning for three years in Ukraine, and
according to newsb2b.blogspot.com has made it possible to reduce procurement
prices for Ukrainian enterprises by 20% on the average as well as procurement labor
costs by 70%. The system allows to hold 43 kinds of tender, including more than 172
thousand companies from 110 countries of the world, among them 3500 companies
from Ukraine: Group of companies Privat, Ukreksimbank, PUMB, AZOT, Antonov,
Ergopak, Rubizhne cardboard mill, Volnogorsk glass, Kolos, Ukrrosmetal, Ukrolia,
and international group of companies – JTI, SoftServe, М , AllТanz. The number of
tenders held by Ukrainian segment of the B2B-center system annually increases by
60%. As of today there are two B2B trading sites functioning in Ukraine - b2b-
center.ua and b2b-center.uspp.ua, the latter was created by mutual efforts of B2B-
center and the Ukrainian Union of Industrialists and Entrepreneurs (UUIE), which
allowed it to make online purchases.
The main determinants of insufficient development of e-business and e-commerce
are undeveloped technical and technological base. Asymmetric levels of ICT-
infrastructure development cause disproportional global development of e-commerce
with its traditional key centers in Old and New World – Western Europe and North
America, and Asia-Pacific Region (Table 4).
At the same time the growth rates of B2C sales in the developing countries are
essentially falling. The highest level is traditionally demonstrated by China (63.8%)4.
(Fig. 2).
3
The Statistics Portal. Available www.statista.com
240
Table 4. Comparative analysis of the development of B2C e-commerce segment all over the
world in 2013 4
Sales, Growth Level of Share of sales,
Regions bln. dol. rates, % coverage, % %
Deviation %
North America 419,53 12,5 72 28,3 31,2 2
Asia Pacific 388,75 23,1 44,6 2,1 2,3 2,9
Western Europe 291,47 14 72,3 26,4 25,4 1
Central and Eastern
48,56 20,9 41,6 4,1 4 0,1
Europe
Latin America 45,98 22,1 33 34,9 32,9 0,1
Middle East and Africa 27 31 31,3 4,2 4,3 0,2
Total 1,22129 17,1 40,4 - - - -
Fig. 2. Growth rates of B2C sales from 2012 to 2014, %
High growth rate at the level of 20.9% is demonstrated by Central and Eastern
Europe, but it is lower than in Asia and North America (Fig. 3).
Analysis of commodity composition of e-commerce markets in Ukraine, Russia,
Switzerland and the U.S. in 2013 showed disproportional distribution of sales
according to segments: e-commerce market in the U.S. is well-balanced and offers a
wider range of products than Ukrainian market (Fig. 4). The range of goods in Swiss
e-commerce market is not wide but it is well-balanced in contrast to Ukrainian market
where 90% of all orders are distributed between two main sectors.
Despite the development of e-commerce business in Ukraine, online-orders do not
gain a great popularity with the population, the anticipated level in 2014 was about
3% comparing to 90% in the leading country – the U.S. What makes Ukrainian
4
Internet business in Ukraine. Available http://ain.ua
241
market special is that people here mostly use the Internet to learn about the goods, to
know about tecСnТcal specТfТcatТons of tСe products, to read otСer customers’
feedbacks, to compare prices and so on, and only a limited number of users place
orders, that is why the level of online-shopping and the number of online buyers
remain low.
Fig. 3. Dynamics of growth rate of B2C e-commerce sales in regions from 2012 to 2014, % 3
Fig. 4. The commodity structure of sales in B2C e-commerce segment in selected countries 5.
The results of the research showed the tendency typical for the national markets of
all countries – one leading company being in dominant position well ahead of its
nearest competitors. Ukrainian e-commerce market is entering the phase of growth
because of relatively low volumes of sales of Ukrainian companies (Fig. 5).
In spite of rapid development of e-commerce and e-business in Ukraine there are
still some certain difficulties and obstacles that reduce the growth rates of online
business as a whole (Table 5).
Fig. 5. Comparative analysis of the B2C e-commerce sales volumes in different countries
according to investigation in 2013, mln. dollars
242
Table 5 Problems and prospects of e-business in Ukraine 5
Factor Essence
insufficient development of IT;
Factors limited using of IT;
impeding the conservatism and distrust of innovations;
development of low purchasing power of the population;
e-business in lack of specialists;
Ukraine contractor’s mТstrust of tСe bankТng system;
lack of legal regulation
Prospects for e- creating jobs for skilled workers;
business in access to Western capital investment;
Ukraine increasing in tax revenues from the use of electronic payments
Factors development of electronic payment systems on the Internet;
accelerating legislative regulation of the e-commerce, the legal recognition of
development of electronic records and electronic signatures;
e-business in protecting commercial information during network transmission
Ukraine
One of the main impacts of e-commerce activity is the formation of certain triad of
consequences: product price cutting; speeding up the time and transformation of space
(elimination of borders); creation of horizontal links between players and direct
contact [4] (Fig. 6).
price
а
time direct contact
Fig. 6. The triad of e-commerce components
3. Auctions Formats
In most real markets sellers have no perfect information about the market demand,
and know only about its statistical distribution. Only buyers know exactly how much
product they want to buy at a definite price. Self-regulating market mechanism is not
always able to dТsclose all ТnformatТon about tСe buyers’ solvency and sellers’ costs.
The research of decentralized market mechanisms allows us to determine how and
why real markets collect and transmit information. Then special mechanisms for the
distribution of goods are created, such as auction models.
Auctions can implement the mechanisms of transformation of private information
about the value of goods for buyers into common knowledge. In turn, the rules of the
auction can stimulate sellers to disclose private information about their cost of goods.
Maximum purchasing capacities of the buyer and seller costs are called agents types.
5
Ukraine overview. Available www.ebrd.com/where-we-are/ukraine/overview.html
243
Designing economic mechanisms for auctions allows building a model of relevant
institutions that determine the conditions and means of achieving the goal of the
designer [Kobets, 2014]. This model is effective if it allows the planner to create
incentives for the disclosure of information held by others to achieve private or public
purpose.
To solve these problems auctions mechanisms are designed which motivate the
agents to truthfully reveal their private information. Auctions are important for goods
that have no natural market, such as bankrupt firms, mobile and radio frequencies.
Here accurate information about the number of regular buyers is missing, variance of
buyers’ values can be very large, and pre-sale valuation and transaction costs are
significant.
Operating of Internet-auction is a necessary condition for the development of e-
commerce segment and its further growth grounded on [4, 12] (Fig.7).
Effective use of electronic auctions has been confirmed empirically by the most
famous giants of global e-commerce such as eBay.com, Sothbys.Amazon.com
Yahoo!Auctions and DigiBid.com, which actively use a similar mechanism to
promote and sell products and services. Westernbid.com, lotok.com.ua, eTorg.com
auctions are gaining their popularity in Ukraine. There are several types of auctions
with specific methods of pricing (Table 6):
If a product is sold to the individual who values it most, the auction is efficient.
Auction yielding maximum revenue to the seller is optimal [13-14].
Vickrey auction
Agents convey their true type only if it gives them maximum (expected) payoff.
RevealТng tСe type means tСe seller’s payoff maxТmТzatТon and effТcТent allocation of
resources (the buyer who values the product most receives it). Vickrey auction (sealed
bid second price auction) best of existing auctions formats reveals the types of
participants. True strategy is a dominant for Vickrey auction format (as opposed to
the first price auction) [15]. The winner receives a payoff as the difference between
his own purchase capacity and second price. So when one of the agents has a greater
solvency than others, he gets a discount equal to the difference between the first and
second largest bids. If Vickrey auction has several winners, then it will select one of
them with equal probability.
Then there were 2 extensions of this approach: the revelation principle, which
showed that direct mechanisms are similar to indirect ones and implementation theory
that helps to built mechanism so that all its equilibria were optimal ones [16].
Double auction
Theory shows that double auctions, where traders (buyers and sellers) charge their
prices can be effective trade institutions, where each agent has private information
about his own values of goods.
With the increasing number of traders, the double auction will more effectively
generalize personal information so that eventually all information is reflected in
equilibrium prices (as argued WТlson). TСese results are consТstent wТtС F.Hayek’s
argument that markets efficiently summarize relevant private information.
Vickrey auction theory gained wide support from the economists; some elements
of the theory have been used in the US in B2G(A) type of e-commerce in organizing
the trade licenses to use national radio frequencies. The US State Treasury asked FTC
to use this type of auction for revenues maximization.
244
Internet- auction
Requirements: Characteristics of Rules of
simple client
software; the goods in the functioning
obligatory
Goods
ensuring an auction:
appropriate level of New high-tech registration of
confidentiality by using products; participants;
the protocol that quickly collectible product must
eliminates customer products, rarities, always be paid for;
information; artifacts; offer to sell can
the complexity of the not be removed
communication protocol before deadline;
depends on the volume Income goods for sale
and number of messages; commission on the
flexibility of rules -
transaction Characteristics:
the possibility of
Results: a significant
costs are directed for concentration of
resource supporting; supply and demand;
receiving first hand Web- site
interaction of
information about the Internet- shop parties 24 hours a
demand for goods and day:
services; Internet-
auction
Fig. 7. The mechanisms of pricing in Internet- auctions
Table 6. DТversТty of Іnternet - auctions
Type Subspecies Essence
Descending Next bid is lower than the previous.
Order
Growing Next bid must be higher than the previous.
sealed bid first- TСТs auctТon does not dТsclose tСe partТcТpants’ offers. TСe
According to the degree of openness
price auction buyer who offers and pays the maximum price will win.
Closed
sealed bid Vickrey auction means the partТcТpants don’t dТsclose tСeТr
second price proposals. The winner, who has offered the maximum price,
auction pays the second after it.
The main characteristic of the auction is that buyers know
English auction about competТtor’s offers. TСe prТce starts from a certaТn
minimum level mark. The winner pays the highest price.
The main characteristic of the auction is that buyers disclose
Open
Dutch auction their bids. The maximum price is fixed and reduced until a
buyer agrees to accept it.
The main characteristic of the auction is that buyers and sellers
disclose their bids and asks respectively. The seller and the
Double auction
buyer interact the same time - as a result, the equilibrium
market price is fixed.
The challenges of the market mechanism require creating rules of interaction for
bidders, realized by means of transactions on computer platforms with appropriately
developed software and leading to economically desirable distribution of goods and
payments deprived of collusion or dishonest behavior of participants.
245
4. Double Electronic Vickrey Auction Model
To construct the auction model, we introduce the following assumptions. Seller
offers one indivisible good to N buyers, who are risk neutral. Buyer i has purchase
capacity vi , i 1,..., N . Evaluation of solvency of buyer i is obtained from the
interval [1;100] in accordance with the distribution function Fi (vi ) and distribution
density fi (vi ) . Buyers’ values of good are mutually Тndependent. Every buyer knows
his/her own value and does not know the values of other buyers. However, density
distribution functions f1 ,…, f N are common knowledge and are known to both
buyers and the seller. Although the seller is uninformed about the exact solvency
value of the buyer, he knows the distribution from which each value is received. If the
solvency of the buyer who wins the product is vi , and he pays the price p , his
consumer surplus equals CSi vi pi . TСe seller’s sСort-run profit will change when
the auction format changes.
Sealed bid first-price auction
Buyers make sealed bids bi that depend on their ability to pay vi . Buyers’ bТds are
considered as a strategy in the form of functions mapping their solvency in non-
negative bid: bi R . Expected payoff of buyer i will be:
CS (r; v) F N 1 (r ) (v b (r )) , (1)
N 1
where r - buyer bid, v - buyer reservation price, F (r ) - the probability that the
buyer bid on the goods is the highest among all applicants. After first order condition
for function maximization (1) and for conditions F (v) v and f (v) 1 we get size
of equilibrium bid for sealed bid first-price auction:
v
b (v ) v . (2)
N
So in this auction format, each buyer conceals his true solvency, relying on a lower
bid level than its reservation price.
Double electronic Vickrey auction for true type’s agents
Buyers will behave differently in sealed bid first price auction and Vickrey auction.
First price auction offers 2 motives for buyer: (i) an incentive to rise his stake to
increase his chance of winning; (ii) an incentive to reduce his bid to reduce the price
he pays when winning. For Vickrey auction the second motive is not valid, because
the winner pays the price which does not depend on his bid. This allows to expect
aggressive competition for the good at Vickrey auction. Let B be the second largest
bid at the auction, then a winner disclosing his reservation price will win payoff
CS (v) v B .
Suppose that M risk neutral sellers operate in the market. The cost distributions for
sellers are obtained from the interval [1;100] in accordance with the known
distribution functions. Sellers make sealed asks ai that depend on their costs ci . If
tСe seller’s cost Тs ci , and he gets the price p , his producer surplus (profit) is
PSi pi ci .
246
Consider our software module for electronic Vickrey auction in Fig. 8.
Fig. 8. Double electronТc VТckrey auctТon for true type’s agents
In general the number of buyers and sellers may differ N M . TСe buyers’ abТlТty
to pay is ordered from maximum to minimum and for sellers it is from minimum to
maximum.
The agreement between agents (deal = 1) occurs when a price offered by buyer is
not below the price set by the seller ( b(vi ) a(ci ) ), otherwise the agents refuse the
transaction (deal = 0). The price for each transaction for each pair of buyer and seller
is set at the average level:
v c
Pi i 1 i 1 , (3)
2
The auction continues until the highest price offered by a buyer will be lower than
the minimum price charged by the seller: b(vi ) a(ci ) (Fig. 9). After each transaction
the benefits of buyers are defined in the form of consumer surplus CS and sellers
gains – as producer surplus PS . The sum of consumer and producer surplus forms
social welfare SW as efficiency indicator of Vickrey auction format (Fig. 10).
Fig. 9. BТds and asks dТstrТbutТon at double electronТc VТckrey auctТon for true type’s agents
247
Fig. 10. Dynamics of consumer and producer surplus, social welfare at double electronic
VТckrey auctТon for true type’s agents
Fig. 10 shows that functions CS , PS and SW are decreasing in the number of
transactions, because during each round of the auction buyers with the highest ability
to pay and sellers with lowest cost will benefit. In each round of double Vickrey
auction the price of good at first increases and then remains constant, then begins to
decrease until it reaches zero (Fig. 11).
Fig. 11. PrТce dynamТcs Тn double electronТc VТckrey auctТon for true type’s agents
VТckrey auctТon agents’ underestТmatТng tСeТr abТlТty to pay or overestТmatТng tСeТr
costs will result in reducing consumer surplus, producer surplus and social welfare.
As soon as agents with larger ability to pay and lower cost can not deal in auction,
they will discover during few periods that revealing their true type will allow them to
maximize their own surplus.
Proposed model of double electronТc VТckrey auctТon for true type’s agents Тs
described by the following algorithm by the means of C#:
publicvoid Deal(Auction auction)
{intcount_take = 0;
intcount_not_take = 0;
stringpattern_one="The transaction took place (1)";
stringpatter_second="The transaction did not take place
(0)";
for(inti=0;i=
auction.Seller_auction[i].Ask)
248
{count_take += 1;
richTextBox5.Text +=+i+1+pattern_one + "\n";}
else
{count_not_take += 1;
richTextBox5.Text +=+i+1+patter_second + "\n";}}}
publicList Price(Auction auction)
{intprice_did_not = 0;
float average = 0f;
for(inti=0;i=
auction.Seller_auction[i].Ask)
{average = (float)(auction.Customer_auction[i+1].Bit +
auction.Seller_auction[i+1].Ask) / 2;
averageList.Add(average);
this.richTextBox3.Text += average.ToString()+"\n";}
else if (auction.Customer_auction[i].Bit <=
auction.Seller_auction[i].Ask)
this.richTextBox3.Text += price_did_not.ToString()+"\n";
if (i + 1 == auction.Customer_auction.Count)
break;}
returnaverageList;}
Double electronic Vickrey auction for hidden type’s agents
During the sale of goods through the auction mechanism a buyer tends to
undercharge his own ability, while the sellers tend to overvalue their own costs. So
electronТc VТckrey auctТon for true type’s agents Тs less lТkely tСan e-auction for
СТdden type’s agents. In tСeory double VТckrey auction motivates participants to fully
disclose their types, because they pay the second largest cost. However, the proposed
here new model of double VТckrey auctТon for СТdden type’s agents demonstrated tСat
some of agents can hide their true type, despite the existing incentives for disclosure.
According to traditional models of double Vickrey auction agent type is disclosed
completely.
ConsТder software module ‘VТckrey auctТon’ for double electronТc VТckrey auctТon
for СТdden type’s agents (FТg. 12).
249
Fig. 12. Double electronic Vickrey auction for СТdden type’s agents
In this module first we enter Numbers of buyers and Numbers of sellers. Consider
equal numbers of buyers (15) and sellers (15). After entering the data into the
approprТate fТeld (FТg. 12), we obtaТn buyers’ real abТlТty to pay real bid (as a random
number between 1 and 100) and deviation bias for bid (as a random number in the
interval (0, 1)), which reduces percent of real solvency and gives us actual ability to
pay actual bid. Therefore the relationship between indicators for buyers looks like:
actual bid = real bid * (1- bias for bid). Similarly, we obtain the real costs of seller
real ask and deviation bias for ask, percent of which overstates the actual costs, and
reported expenses actual ask are received. Thus, the relationship between indicators
for sellers is as follows: actual ask = real ask*(1+bias for ask).
After that reported solvency actual bid is arranged in descending order, and
reported costs actual ask is arranged in ascending order. Then pair-wise comparison
takes place between the buyer with the highest ability to pay and seller with lowest
cost. If bi ai then there is an agreement (deal=1) between buyer i and seller i at
the price of Pi (bi 1 ai 1 ) / 2 . For deal i consumer surplus of buyer is
CSi bi Pi , producer surplus is PSi Pi ai , social welfare is SWi CSi PSi .
Otherwise, the agreement between the buyer and the seller does not take place
(deal=0). Buyers and sellers who do not deal have the incentive to reveal their true
types (solvencies or costs).
Proposed model of double electronТc VТckrey auctТon for СТdden type’s agents Тs
described by the following algorithm by the means of C#:
publicList Deal(Auctionauct, ListDealList)
{intcountdeal = 0;
intcountnodeal = 0;
for (inti = 0; i=auct.Seller_auction[
i].ActualSell)
250
{DealList.Add(true);
countdeal++;}
else
{DealList.Add(false);
countnodeal++;}}
returnDealList;}
publicList PS(Auctionauc, ListListPs,
ListListPrice)
{float temp;
floatps;
for (inti = 0; i0 &&
auc.Customer_auction[i].ACtualBid>auc.Seller_auction[i].A
ctualSell)
{ps = ListPrice[i] - auc.Seller_auction[i].Ask;
ListPs.Add(ps);}
else
{ps = 0;
ListPs.Add(ps);}}
returnListPs;}
But the agreement between buyers and sellers is not completed. Those buyers and
sellers who have no deals may revise their bids, that is to reveal their real types. They
Сave an ТncentТve to do so because tСey Сaven’t got tСe desТred unТt of good. After
revealing their true type their deviation will be zero: bias for ask = 0, bias for bid = 0.
Further agreements will be revised to reflect the new bids. Then those agents who in
the first round were able to buy (sell) goods at their bid and concealed their true type
in the second round may lose this opportunity. Then they will get an incentive to
disclose their true types. This procedure continues until the final round yields no
changes in the redistribution of goods compared to the previous round. It means that
the double Vickrey auction for СТdden type’s agents Тs completed.
Fig. 12 demonstrates that the buyers’ solvency of 2, 6 and 14 remains hidden while
the remaining buyers fully reveal their types. Similarly, sellers 1, 4, 8 and 12 did not
disclose their true costs, while the rest of the sellers do it. Thus our Vickrey auction
model compared with other auctions formats reveals some true types of agents, but
this auction format does not motivate all to do as stated in classical Vickrey auction
model. In proposed auction model low cost sellers and high solvency buyers can
conceal their true types.
For our example 80% of buyers and 73% of sellers reveal their types (i.e. 76% of
all traders). 20% of buyers and 27% of sellers conceal their types (i.e. 24% of all
traders).
5. Conclusions
To improve e-commerce efficiency there are special mechanisms for distribution of
goods and payments such as auctions models that are designed to convert private
information about the value of goods for buyers and sellers into common knowledge.
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Vickrey auction (sealed bid second price auction) best of the existing auction
formats reveals the types of participants. Software modules for dynamic double
electronic Vickrey auction were first developed to generalize this auction format. It is
determined that in double electronic Vickrey auction incentives are created for most
buyers and sellers to reveal their true solvencies and costs. But for some buyers and
sellers these incentives are not enough to disclose their types, which reduces the
efficiency of the auction format. The designed program of dynamic double electronic
Vickrey auction is closest to perfect competition market and in terms of social welfare
ahead of alternative auction formats such as first price auction, English and Dutch
auctions, in which the vast majority of agents are hiding and not revealing their types.
References
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252
Which Data Can Be Useful to Make Decisions on Foreign
Exchange Markets?
Karine Mesropyan
Chekhova 41 Rostov-on-Don, Russia 344006
carine@list.ru
Abstract. A communication, settlement of deals, and other services for
participants of foreign exchange markets are mostly served by electronic
infrastructures. Knowledge of the volume change of aggregated data of deals is
useful for all evolved businesses to support their decisions in practice. This
paper investigates whether market data of infrastructures, namely CLS, SWIFT,
and ETFs, can be used as the volume indicators of some FX segments.
Keywords. Foreign Exchange, Data, Time Series, Review, Flow
Key Terms. DecisionMaking, Management
1 Introduction
The largest and the most influential market for the global and national economies,
the foreign exchange market (FX) is opened 24 hours worldwide. According to a
regular semi-annual market research an amount of monetary flows traded on the FX
in all national currencies (global FX volume) is estimated at 5 trillion US dollar
average per day (Bench & Sobrun, 2013). The survey of the Bank for International
Settlement (BIS survey) is an important source of the FX knowledge as it aggregates
semi-annual surveys from FX committees and provides aggregated statistics of the FX
market segments (Fratianni & Pattison, 2001). The monetary amount of trades in
every currency is considered in this research as a segment volume indicator of the FX
market.
The volume dynamics demonstrates variable numbers which affect exchange rates
for national currencies and present volatile level of risk for traders and investors. That
is why a kind of the FX volume indicator is a part of system of key performance
indicators for assets management among FX market participants. This system helps
them in planning and decision making processes such as investment, currency
diversification in saving, and development of transnational networks. Market volume
is also necessary to be evaluated by national market regulators and central banks in
order to have current information on global tendency of their currencies volumes and
exchange rates as a consequence.
The concept of volatility is used on financial markets to measure fluctuations of
exchange rates by their standard deviation during a taken time interval (Schwartz,
253
Byrne & Colaninno, 2011; Bubak, Kocenda & Zilkes, 2011). As the volatility of the
FX volume is a recognized quantity indicator of the exchange rates dynamics,
financial organizations use it in order to estimate their risks on the FX. They usually
predict in which extent the exchange rates fluctuate between current level and
expiration date.
In order to construct volatility-based market volume indicator, researcher is aimed
to investigate area of electronic statistics which is relevant to the FX volume. Several
types of time interval can be taken to construct the indicator, namely day, month, and
year. The importance of choosing of the time interval for data was emphasized in
previous research (Gill, Perera & Sunner, 2012, p.1): “Over recent years technological
developments and the digitisation of information and activity have generated a vast
array of electronic data, which can potentially be analysed on a daily basis, or even in
real time. Some of these data cover very large numbers of individuals and businesses
– far more than many traditional surveys used by statistical agencies – and have the
potential to be useful for monitoring and measuring aggregate economic conditions.”
The BIS survey cannot provide frequent FX statistics, meanwhile market
participants become also more interested in monthly volume indicators (Cerutti,
Claessens & McGvair, 2012).
Alternative sources of information are investigated in this paper. The FX electronic
communication and settlement infrastructures also aggregate statistics on their
transactions. Continuously Linked Settlement Bank (CLS) and Society for Worldwide
Inter-bank Financial Telecommunication (S.W.I.F.T. or SWIFT) serve financial
organizations by secure settlement of their interests on the FX. Exchange traded funds
(ETFs) also widely play on the FX market as investment companies which provide
efficient and attractive sets of financial instruments in a variety of currencies.
With this research we intend to get a better idea of how the FX market can be
measured by using globally aggregated electronic statistics of CLS, SWIFT, and
ETFs.
In the first paragraph we state the problem. In the second paragraph we study
distinctions and commonality of CLS, SWIFT, and ETFs data regarding to the
segments of the FX market. In the third paragraph we investigate relationships
between some FX segments volume indicators, namely ETFs in developed currencies
and CLS. In the fourth paragraph we discuss methods and our results and in the fifth
paragraph we discuss findings and make conclusions.
2 Foreign Exchange Markets in the Last Decades
Developed in 2000s investment opportunities provide a ground for constant
enlargement of trades in developing currencies (Bryan, 2008). The latter are
reasonably called exotic currencies among the FX practitioners (Tsuyuguchi &
Wooldridge, 2008) because they did not find suitable conditions for stable growth
worldwide. Thus, from beginning of the post Bretton Woods system in condition of
US dollar domination less than 5 % of global trading was made in other local
currencies (Pojarliev, 2005). “The relative insignificance of these currencies in
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international markets reminds us of the growing disjuncture between countries and
“their” currencies. Most Indian- and Chinese-related trade and investment is
undertaken in US dollars, with that currency often being used directly without any
formal currency conversation (for example, for the purchase of US bonds).
Alternatively, for those outside India and China looking for a share of their growth
economies, it is possible, using derivatives, to take on exposure to their growth
without the need for actual investment in these countries nor for foreign exchange
conversion to local currencies.” (Bryan, 2008, p. 503).
One could see different environments struggling with implementation of
diversification strategies of exchange, saving, and investment in “3 big currencies”
and domestic currency. Term of “3 big currencies”, namely US dollar, euro, and yen,
has become recognized due to trinity’s domination in the FX structure (Pojarliev,
2005).
Next, after a crisis of 2008 the global FX market has created a fertile ground for
diversification. The post-crisis market conditions have immediately influenced the
exchange in a variety of currency pairs, especially in the currencies of developing
countries (Bryan, 2008): “…with a declining role for the “big 3” currencies in
aggregate, perhaps even the status of any leading national currency being treated as a
proxy global anchor is being challenged. Consistent with this trend, it is apparent that
foreign exchange is itself being treated increasingly as an asset class (a store of value)
as well as a means of exchange, so that investors see intrinsic benefit in holding a
wider range of currencies in a diversified asset portfolio.”
Nowadays the first candidates to leaders on the FX are Chinese renminbi (yuan)
and the Indian rupee which present economies of two members of BRICS (Brasil,
Russia, India, China, and South Africa). By World Bank estimation, BRICS
contributes a quarter to global domestic product that is more than any other group of
developing countries. Although “evolution of the Chinese currency on the FX market
remains slow and runs the risk of failing” (Batten & Szilagyi, 2012, p.2), there is an
expectation of long-term shift in currency markets. As an evidence of this tendency,
New Development Bank (BRICS Development Bank) has been established in 2013
by 5 developing countries as an alternative to International Monetary Fund and World
Bank.
Along with currencies diversification a way of presence at the FX is also important
for market players. As BIS survey reported, some participants of the FX communicate
for trading by using services of brokers but major players replace such supervision by
making over-to-counter operations (OTC) themselves. Such market participants are
usually members of CLS or SWIFT.
CLS bank serves other banks and financial institutions by mitigating a settlement
risk that appears when one party of exchange pays the currency it sold but does not
receive the currency it bought (Fisher & Ranaldo, 2011). This kind of risk is called a
settlement risk. CLS executes exchange operations (CLS instructions) through
provision of its unique payment operation versus payment settlement service. Owing
to its service value the CLS is highly appreciated by international financial
community (Fisher & Ranaldo, 2011). According to CLS strategy, its large
255
contribution to the developed markets accompanies by absence on the developing
ones.
To serve secure FX transactions, SWIFT plays another role in the industry (Scott &
Zachariadis, 2010).
It communicates financial institutions, corporations and their counterparties by
SWIFT messages. Their customers are financial institutions, fund managers and
brokers, fund managers, settlement members and central settlement systems including
CLS members. SWIFT message (MT300) consists of all information about
transaction on the foreign exchange such as currency pair, monetary amount, type of
trading, and others (SWIFT, 2015).
Nowadays SWIFT possesses a worthy demand in the industry because of its
capacity to operate with high value delivered and relatively lower costs in comparison
with rivals on both types of markets (developed and developing). This stable trend
implies its importance in the industry which provides the SWIFT data potential
contribution to the FX volume measurement. Besides, SWIFT does not limit its
custodians by a kind of currency to trade. CLS, on the contrary, executes operations in
17 currencies which are mostly developed.
Current tendency on the market is an extremely high growth of ETF segment in
both developed and developing economies. Nowadays such indices are traded in a
number of currencies on the FX due to its attractiveness for investors.
3 Use of Global Data of CLS, SWIFT and ETFs
CLS data was usually an adequate way of the FX volume estimation. Its monthly
market review indicates dynamics of trades on the developed part of the FX. For
instance, recently BIS have leveraged CLS information and own data (Bench &
Sobrun, 2013). Owing to a mixed approach in monthly numbers measurement,
estimated this way FX dynamics was able to explain sources of odd jumps and drops
of the market by concrete instruments, which have been described in the BIS survey
in a detailed way. Fig. 1 illustrates this first attempt to measure aggregated FX
volume for all currencies, including the developed and developing ones owing to the
local FX committees’ contribution. It makes clear the necessity of the different
sources of data combination.
Meanwhile, being outside of mutual work of CLS and BIS, SWIFT could pretend
to be considered as a source of data for the FX volume estimation. Its statistics is
usually published only in its annual market review where the FX trends are shortly
described and illustrated by SWIFT service activity during the year.
Resent research (Cook & Soramaki, 2014) shows that SWIFT data (MT300
message type) is correlated with the FX volume for currency pairs of US dollar and
Chinese renminbi (yuan). Authors have found linear relationship between these values
(Fig. 2). Absence of similar research of US dollar and yuan from other data sources
(CLS, for example) makes impossible to conclude which data is more useful for
market analysts by comparing with results of (Cook & Soramaki, 2014) with others.
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Fig. 1. Monthly CLS data in estimation of global FX volumes in all type of currencies (Bench
& Sobrun, 2013)
Alternative source of information comes from investment funds or exchange traded
funds which publish their indices volatility. The concept of volatility is used to
indicate uncertainty regarding degree of ETFs’ volume changes (Schwartz, Byrne &
Colaninno, 2011). Although it has been traditionally used for analysis of exchange
rates volatility dynamics (Britten-Jones & Neuberger, 2000), we have found examples
of its application to measure the range of probable change of traded volume by its
dispersion analysis (Melvin & Peiers Melvin, 2003).
Fig. 2. Monthly relationship between SWIFT data and developed currencies FX segment
volume (Cook and Soramaki, 2014, p.27)
As it was reported above nowadays constant growth of the ETF worldwide
accompanies by increasing ETF contribution to the financial markets of developing
economies. The evolution of financial instruments led to use of ETFs which had
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provided implementation of extremely successful trading strategies after the global
financial crisis in 2008 (Bryan, 2008, p. 502). As a result, in developed countries, for
instance, in the United States ETFs have contributed 40 % of the financial market
volume (Guedj & Huang, 2009). As for developing countries, ETFs in currencies
have contributed 23 % of the FX market (Fig. 3).
Fig. 3. Yearly ETFs contribution to FX developing currencies segment volume
We have found several studies which are focused on relation between volatility of
volume of one of the FX ETF (FXE) and volume of other market segments (Daigler,
Hibbert & Pavlova, 2014). Other researchers studied the ETF segment statistics much
more widely (Li, Klein, & Zhao, 2012). The common way to construct time series is
ARIMA method but the specific for volatility variables is ARCH method (Le &
Zurbruegg, 2010). Data about ETFs flows is available on website of Currencyshares’
and Powershares’ on-line databases which present three largest global currency ETFs
indices (US dollar, euro, and yen).
4 Methods and Findings
We have analysed the FX structure by using information from the BIS Survey
(2013). According to the survey, traditionally the largest volumes of trading take
place in Europe, USA and Japan. Respectively, this trend is presented by the biggest
volumes of the FX trading in the main currency pairs, namely Euro versus US dollar
(EUR-USD), US dollar versus Yen (USD-JPY), Euro versus Yen (EUR-JPY).
Data have been taken from the website of CLS bank, Currencyshares’ and
Powershares’ on-line databases which present three largest global currency ETFs
indices, namely ETF FXE (euro), ETF FXY (yen), and ETF UUP (US dollar).
Data of this research consist of five elements for every month during period from
January 2008 till March 2014, namely:
average number of CLS operations (instructions);
volatility of volume of exchange-traded fund FXE;
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volatility of volume of exchange-traded fund FXY;
volatility of volume of exchange-traded fund UUP.
We have studied autocorrelations of these volumes. Table 1 shows that all levels
of tested variable of t-statistics are not statistically significant for CLS. According to
these results, there are significant autocorrelations between the nearest levels of lags
(from month to month) for each time series of ETFs except the time series of CLS.
Table 1. t-statistics of autocorrelation (ACF) and partial autocorrelation functions (PACF)
Lag ACF PACF
ETF ETF ETF ETF ETF ETF
№ CLS CLS
FXE FXY UUP FXE FXY UUP
1 6,59* 4,64* 5,74* 1,73 6,48* 4,56* 5,64* 1,62
2 5,37* 4,30* 4,93* 0,29 0,48 2,42* 1,82 -0,31
3 4,34* 3,14* 4,24* 0,95 -0,03 0,13 0,63 0,97
4 3,15* 2,90* 3,10* 0,69 -0,90 0,56 -0,80 0,01
5 2,19* 2,66* 3,16* -1,13 -0,25 0,61 1,17 -1,32
6 1,28 1,99 3,06* -1,79 -0,52 -0,35 0,74 -1,03
7 0,29 2,87 2,01* 0,31 -0,82 1,63 -1,33 1,13
8 -0,12 1,68 2,16* -0,15 0,47 -0,85 0,64 -0,32
9 -0,62 0,86 1,97 -1,05 -0,45 -1,49 0,47 -0,11
10 -1,17 1,02 1,03 -0,59 -0,58 0,76 -1,21 -0,39
11 -1,05 0,92 1,32 -0,09 0,83 0,33 0,43 -0,6
12 -0,69 0,64 1,39 -1,59 0,75 -0,63 0,91 -1,19
Significant levels are signed by (*) on the base of t-statistics critical values at the
confidence level of 97,5%
Next step should consist of regression models constructing on the base of the time
series by using the results of significant lags’ autocorrelation. As we have not found
out existence of linear relationship between CLS operations from month to month, we
could not estimate regression of the CLS and ETFs volumes.
5 Conclusion
A lack of frequently available data can negatively affect strategic decisions of
businesses. This research has been motivated by industry’s willingness to explain
sources of the FX market volume dynamics in developed and developing currencies.
In this field we found out several results. Owing to international finance
259
transformations, nowadays currencies of developing countries become more often
used among deals on the FX market than several years ago. This trend had been
appeared in the post-crisis period after 2008. The financial organizations had to
struggle between two options by making choice on the FX markets. They could adapt
to decreasing trends of US dollar domination or they could seize opportunities
relating to currencies of developing economies. In 2013 the BIS survey has concluded
that unpredictable trends on emerging currencies markets attract more attention of
participants to this FX segment volume measurement.
We have also studied what kind of time interval should be taken for the FX volume
indicator. We have found that market participants are interested in the FX volume
indicators to fill absence of monthly data (Cerutti, Claessens & McGvair, 2012, p.2).
Our findings are confirmed by existing statistics source, namely the Triennial Central
Bank Survey of Foreign Exchange and Derivatives Market Activity. It collects only
long-term overall statistics of volume so the survey cannot respond to need of
frequent availability of the FX data without additional market information. That
confirms the opinion that “while official statisticians are increasingly using electronic
data in the production of economic indicators, this is still very much in its infancy.”
(Gill, Perera & Sunner, 2012, p.1).
In our review we have concluded that month could be taken as a time interval to
make decisions on the FX market by constructing volatility-based volume indicator.
Meanwhile, our experimental findings did not provide enough evidence for that.
Next, we have studied the FX data regarding developed and developing currencies.
The FX has a number of participants and nowadays only three infrastructures’
performances can indicate its overall activity’s performance from month to month.
Thus, CLS, SWIFT and ETFs data’ features analysis has helped to shed a light to data
search for the FX volume estimation.
On the one hand, as class of major developed currencies has mostly become an
area of CLS business. CLS data can help to measure a volume of trading in currencies
of developed countries. CLS does not include trades in currencies of the BRICS
countries. South Africa is only one exemption in this group of 5 countries as its
currency is considered as a major one and it can be traded by CLS members.
On the other hand, today SWIFT is known as a provider of efficient supply chain
for financial organizations in majority of countries including developing ones. SWIFT
services are available for all exotic currency pairs on both developed and developing
markets. That is why SWIFT membership has become more popular, especially for
banks which were not members of CLS.
Potential role of SWIFT information for the FX volume measurement has not been
acknowledged yet. Meanwhile, SWIFT has already presented its contribution to
economy forecast which was presented by dynamic models for developed (Gill,
Perera & Sunner, 2012), developing, and global economies (Bauwens, Gillain &
Rombouts, 2011). Thus, SWIFT analytics are more concentrated on current trends of
some developing currencies’ internationalization such as Chinese Yuan, RMB (Batten
& Szilagyi, 2012).
Finally, in our research we have stated a question: ‘To which extent does volume
of CLS activities indicate the standard deviation of volume during a month for three
260
major ETF FX segments in developed currencies?’ We have calculated the ETF
standard deviation on the base of daily volumes in order to aggregate data on the
volatility of ETF volume for each month. We have obtained results which have not
approved a hypothesis that relation between CLS volumes and ETFs volatility-based
estimation of volumes does exist. We were focused on the ETF segment and its three
major representatives. These imperfections have affected our research by its inability
to extrapolate directly our results for the whole ETF segment of the FX. Next stage of
this research could be conducted with more types of ETFs statistics and SWIFT data.
As CLS bank and SWIFT are rapidly evolving competitors in the industry, they
consider promotion of the own business intelligence to the FX volume estimation. It
makes possible to start research projects in this field. In future research a question can
be stated as following: ‘To which extent do SWIFT and CLS activities indicate the
volume of the major FX segments?’ The research objective can be FX volume
indicator constructing. Sources of information for the FX size measurement can come
from the website of CLS bank, SWIFT, and ETFs (Currencyshares, Powershares, and
others) on-line databases.
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Econometric Analysis of Educational Process on the
Web-Site
Alexander Weissblut
Kherson State University, Kherson, Ukraine
veits@ksu.ks.ua
Abstract. The paper describes the site “Lesson pulse”. It is the tool allowing a
teacher to obtain the objective information on the results of a lesson in real-time
mode. However, adequate interpretation for the results of such interrogations is
impossible while we do not separate true students from the others. Besides,
interpretation of the results of interrogations and decision-making grounded on
them demand to realize what exactly this specific group means by clearness of
explanation, objectivity of marks, etc. For anonymous interrogations it means
the necessity of the correlation and regression analysis of the results and an
estimation of their statistical significance. So these factors require the use of
econometric analysis.
Keywords. Factor, statistical, econometric, analysis, correlation, decision-
making.
Key Terms. Research, Management, Model, Knowledge, Management
Process, Knowledge Management Methodology, Mathematical Modeling.
1 Introduction
The site “Lesson pulse” is considered in this article. It is the tool allowing a teacher
to obtain the objective information on the results of a lesson in real-time mode.
However, adequate interpretation for the results of such interrogations is impossible
while we do not separate true students, for which educational process is a
considerable part of their life, from those who would prefer to keep far away from it
[1]. Besides, interpretation of the results of interrogations and grounded on them
decision-making demand to realize what exactly this specific group means by
clearness of explanation, lesson atmosphere, objectivity of the marks, etc. [2]. For
anonymous interrogations it means the necessity of correlation and regression
analysis for the results and an estimation of their statistical significance. So these
factors require the use of econometric analysis [3].
The site “Lesson pulse” allows a student or a pupil to react to a lesson course at
any moment, having answered one or several questions, for example:
1. Is lesson interesting to you?
2. Is the explanation clear to you?
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3. Are you tired? Are you satisfied with the rate of the lesson?
4. Do you have some questions to the teacher?
5. Are marks objective?
(Formulations of questions are defined by the teacher) (Fig. 1).
Fig. 1. Lesson pulse
The site displays average marks on responses on the screen. It is the "pulse" of the
lesson in real-time mode. At any moment a teacher can ask to answer such or more
profound groups of questions (their examples are given below). So, he (she) can
measure the “lesson pulse” just at certain moment. Such interrogations do not demand
computer auditorium: they can be carried out on a tablet or on a mobile gadget, and
then results can be transferred to a site.
1) All groups of questions considered further have been chosen in result of
“brainstorming”, where students of fourth year study of the Faculty of physics,
mathematics and informatics at the Kherson State University acted as experts. This
expert interrogation has been constructed by a technique of “six hats of thinking” by
E. Bono [4], which provides the maximal openness and relaxedness of participants.
All experts have solidly agreed that this set of questions is full and fair.
2) Then students of speciailties “Physics”, “Mathematics”, “Informatics” and
“Software Engineering” of Kherson State University have been interviewed under
selected questions. The respondents estimated each question from 0 (at firm “no”) up
to 10 (at firm “yes”). He arbitrarily set a name of the folder containing his
interrogation (i.e. his key). The volunteer – a participant of interrogation – collects all
folders in one main folder and sorts them here (i.e. shuffles). Only after that the main
folder is transferred to the teacher: this simple and open procedure guarantee to
participants anonymity of interrogation. Alternative and technically simpler variants
are answers that are seen on the web-site or could be chosen on a tablet: the variant of
choice is defined by the kind of interrogation and the level of trust of an audience to
the interviewing teacher.
264
3) Results of interrogation then are transferred to the site “Lesson pulse”, which is
realized in PHP language and uses MySQL database (see [5]). The queries, realizing
now on the site, give out results of the econometric analysis of interrogation. They
include the plural correlation analysis of factors, the regression analysis and an
estimation of the statistical importance of the received results with the use of Student
and Fisher criteria ([6]).
The site interface is oriented to the user, generally speaking, knowing nothing
about the econometric analysis (Fig. 2)..
Fig. 2. Site interface
2 The Analysis of Interrogations on the Results of a Lesson and
Feedback Interrogations
Results of interrogation on a lesson and Feedback interrogation are, of course,
absolutely various [7] depending on a lesson, a teacher, an audience, etc (Fig.3).
265
Fig. 3. Results
However, the correlation analysis of factors led to similar outcomes (at 20 % of
significance level by criterion of Student). Everywhere below we use the
interrogations of the group having typical results on a specialty “Mathematics”
(Fig.4).
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5 6 7 8 9 10 11 12 13
-0,2
-0,4
-0,6
Fig. 4. Questions Distribution
Here is the histogram for distribution of correlation coefficients between answers
to a question “Do you like the lesson?” and following factors:
1. Is the explanation clear?
2. Is the rate of an explanation good enough for you?
3. Are you tired at a lesson?
4. Is lesson atmosphere comfortable?
5. Is the statement filled enough with examples?
266
6. Objectiveness of marks given at the lesson.
7. Do you have some questions to the teacher?
8. Do you want one more lesson on this topic?
9. Have you prepared for this lesson?
10. Are you intending to continue studying at home?
11. Congruity of a lesson to home assignment.
12. Were you interested in the lesson?
13. Have you taken out something useful or do you regret about spent time?
The most significant factors had appeared (in decreasing order) 1 (0,91), 4 (0,87),
12 (0,83), 13 (0,75) 5 (0,63), 9 and 11 (0,59). Objectivity of marks is only further
(0,51) and inverse correlation – 0,39 for 7 specifies that a good lesson for the
majority is the one after which there are no questions remained to the teacher.
The real importance of examined factors for the lesson estimation is finally
established by the regression analysis. At first, we use the most essential factors
mentioned above. Then we obtain such linear model:
Y = 0,845454 x1 + 0,556967 x2 + 0,32442 x3 + 0,19571 x4 + 0,269908 x5 +
0,24677 x6 + 0,19877 x7 , where the variable хi corresponds to the factor i (1 ≤ I ≤ 7).
The determination factor for such model is equal to 0, 84572. Using all the factors
except insignificant factors 2 and 3, we obtain the following model:
Y = 0,657012x1 + 0,282476x4 + 0,1349x5 + 0,01807x6 - 0,1097x7 - 0,063159x8 +
0,00809x9 + 0,033186x10 + 0,126973x11 + 0,192209x12 + 0,1266x13
with the determination factor 0,93647 (Fig.5).
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-0,2
-0,4
Fig. 5. Questions Distribution
Here is the histogram for distribution of coefficients’ correlation between answers
to a Feedback question “Do you like your teacher?” and following factors:
1. Do you like the lesson?
2. Student’s estimation of the knowledge received at the lesson.
3. Is an explanation clear?
267
4. Were students’ answers clear and adequate?
5. Weather the explanations are filled enough by examples.
6. Using of various approaches during studying.
7. Does the teacher aspire to interest and motivate students?
8. Lessons atmosphere: is it comfortable, is it pleasant to you at the lesson?
9. Availability of the teacher, his inclination to listen the students, to lead a
discussion with them.
10. Teacher’s competence.
11. Insistence (regular and frequent control of knowledge).
12. Punctuality (comes in time at lessons).
13. Possession of an audience (students are interested in subject and do not
make too much noise at the lessons).
14. Objectivity in the teacher’s estimation of the student. Are the criteria of
estimation in all subgroups identical?
15. Correspondence of the lesson’s material to control tasks.
The most significant factors appear (in decreasing order):
8 (0,92), 7 (0,85), 6 (0,775), 4 (0,75), 9 (0,72), 3 (0,675), 13 (0,58).
Only further with factor of correlation 0,51 follows 1 - Do you like the lesson?
Corresponding linear regression model is:
Y = 0,048604x1 + 0,17976x3 + 0,22221x4 + 0,076545x6 + 0,35703x8 + 0,800305x9
+ 0,280308x10 + 0,23398x14 + 0,150449x15 ,
where the variable хi corresponds to the factor i (1 ≤ i ≤ 15). The determination factor
for such model is equal to 0,8463.
And major factors of estimations of the teacher and lesson are considerably
differing. Further the histogram of differences between factors of correlation for
questions “Do you like your teacher? and “Do you like the lesson?” is resulted
(Fig. 6):
0,6
0,4
0,2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
-0,2
-0,4
-0,6
Fig. 6. Questions Distribution
268
The factors much more essential at an estimation of a teacher, than a lesson are 6
(using of various approaches at training) and 7 (teacher’s aspiration to interest and
motivate students). On the contrary, at an estimation of a lesson it is much more
essential factors 14 (accordance of a lesson’s material to control tasks) and 10 –
insistence (regular and frequent control of knowledge): probably, according to
students, insistence is good at the lesson and it is not so good for the teacher.
Certainly, the correlation matrix contains decomposition on factors also for each of
15 questions. So it is found out that 5 (explanation filled enough by examples) is most
closely connected with 15 (accordance of a lesson’s material to control tasks); 3 (are
you tired at a lesson) with 7 (questions to the teacher); 13 (possession of an audience)
with 14 (objectivity in estimation of the student).
It is interesting to compare 12 (is it interesting to you at a lesson) with 13 (have
you taken out something useful at a lesson) from interrogation about results of the
lesson (Fig. 7).
1
0,8
0,6
0,4
Interesting
0,2 Useful
0
1 2 3 4 5 6 7 8 9 10 11 12
-0,2
-0,4
Fig.7. Comparative results
As we see, from the student’s point of view, what is interesting and what is useful
is not the same. So 4 (lesson atmosphere) correlates with the factor ‘interesting’,
while factor 5 (is the statement filled enough by examples) – with 11 (accordance of a
lesson’s material to home assignment).
3 The Analysis of Interrogations on the Factors Influencing the
Lesson
Unlike interrogations about results of lesson and Feedback results of interrogations
about the factors influencing the lesson course [8] are close enough in different
269
groups. The histogram for distribution of interrogation requisites on the relation to
lesson is below (Fig. 8, Fig. 9).
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Fig. 8. Questions Distribution
Here:
1. Do you like the lessons? Is the study interesting to you?
2. Do you believe that education is “the road to the future”?
3. Is your speciality interesting to you?
4. Does the training program for your speciality satisfy you?
5. Are you satisfied with your teaching level?
6. Have you chosen university and a speciality on your own?
7. Would you like to change your speciality or enter another university?
8. Do you attend lessons regularly?
9. Are you often prepared with your homework?
10. Did you have any conflicts with teachers?
11. Were you afraid of an elimination from the university?
12. Are you willing to take part in scientific work, in Olympiads on your
speciality?
13. How often do your classmates address to you for the help?
14. Do you wish to enter postgraduate study after you studying ends?
15. How much time do you spend for preparation for lessons (hours per day)?
Similar results of interrogation on external factors are the further:
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10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Fig. 9. Questions Distribution
Here:
1. Close interaction with teachers.
2. Accessibility of the Internet at university.
3. Preparedness of an auditorium for a lesson (working projectors, computers,
the software; comfort of an auditorium).
4. Presence of enough points for the centralized feeding.
5. Accessibility of contacts with the future employers.
6. Accessibility of summer recreation.
7. Participation in scientific work.
8. Teaching level at the university.
In a correlation matrix under all these factors there are only few factors which
correlations are close to 1. These are factors:
1. Do you attend lessons regularly? with factors
1) are you often prepared with your homework (0,87)
2) teaching level at the university (0,84)
3) participation in scientific work (0,63)
4) have you prepared for this lesson (0,59)
5) accessibility of summer recreation (– 0,5).
2 Are you often prepared with your homework with factors
1) do you attend lessons regularly (0,87)
2) teaching level at the university (0,815)
3) have you prepared for this lesson (0,66)
4) participation in scientific work (0,56)
5) accessibility of summer recreation (– 0,52).
3 Teaching level at the university with factors
1) do you attend lessons regularly (0,843)
2) do you regularly prepare homework (0,815)
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3) have you chosen university and a speciality on your own (0,65)
4) have you prepared for this lesson (0,59)
5) participation in scientific work (0,56)
6) accessibility of summer recreation (– 0,55).
Besides them correlation factors above 0,7 appear still only twice: between factors
Did you have any conflicts with teachers and Were you afraid of an elimination from
the university (0,85); and between factors participation in scientific work and Are
you satisfied with your teaching level (0,74). Occurrence in such line the factor
teaching level at the university is, probably, the best compliment for Faculty of
Physics, Mathematics and Informatics of the Kherson State University for all its
history. Our main task is to use the mental orientation, fixed thus in the correlation
analysis of factors, for separating true students, for which educational process is a
considerable part of their life, from those, who would prefer to keep far away from it.
Using already cited data and the following table 1:
Table 1 Data
Factor Average Root-mean-square
value deviations
Teaching level at the university 7,2 2,17
Regularly attendance of lessons 8,85 2,3
Regularly prepare homework 8,4 2,6
we choose as a differentiating sign between groups the factor regularly of homework
preparedness. In this case mutual correlations of defining sign are closer to 1; and the
dispersion is more, that testifies about more variability of respondents under this
factor. Besides, among others selected it corresponds more to such sign in common
sense.
4 Results of Interrogations about Lesson and Feedback on
Subgroups
To the selected differentiating sign among 20 respondents of group the 12
participants is allocated, who for a question Are you often prepared with your
homework have answered with 10 or 9 points. The additional subgroup consists of 8
respondents. Do such subgroups correspond to required division into true students and
the others? Below there is the histogram for average results of interrogation on the
lesson on the allocated subgroups (Fig. 10, Fig. 11).
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12
10
8
Prepare
6
Don't prepare
4
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Fig.10. Comparative results
So, the factors considerably different in subgroups (in decreasing order of modules
of differences between average values in subgroups) are:
2 Is an explanation clear? (7,92 – 4,25 = 3,67)
1 Do you like the lesson? (7,1 – 4,38 = 2,72)
12 Accordance of a lesson to home assignment. (9,91 – 7,5 = 2,41)
6 Is the statement filled enough by examples? (9,41 – 7 = 2,41)
10 Have you prepared for this lesson? (8,75 – 6,5 = 2,25)
13 Is it interesting to you at a lesson? (7,92 – 5,87 = 2,05)
14 Have you taken out something useful at a lesson? (9,1 – 7,4 = 1,7)
5 Lesson atmosphere (7,66 – 1,25 = 1,41)
9 Do you want one more lesson on this topic? (3,66 – 2,65 = 1,01)
The averages of additional group are more only twice, there are:
4 Are you tired at a lesson? (6,5 – 7,62 = – 1,12)
3 Is the rate of an explanation good enough to you? (5,5 – 6,37 = – 0,87)
Last result seems strange at first sight, but it is steady for all groups and it is easy
to explain this phenomenon psychologically: the less the student is adjusted for the
study, the more he would like to speed up lesson’s time.
Further there are similar results for Feedback interrogation.
273
12
10
8
Prepare
6
Don't prepare
4
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Fig.11. Comparative results
Here are the factors considerably different in subgroups:
5 The explanation is filled enough by examples (9,17 – 6,37 = 2,8)
6 Using of various approaches at studying (6,36 – 4 = 2,36)
16 Accordance of a lesson to control tasks (8,9 – 6,87 = 2,03)
4 Are the answers clear enough? (7 – 5,25 = 1,75)
9 Lesson atmosphere (6,36 – 4,85 = 1,51)
The obtained data corresponds to a hypothesis about required division into groups,
anyway they don’t contradict it.
5 The Latent Division in Group
The site “Lesson pulse” offers also group division into classes with a given value
of mutual correlation: between two respondents from one class it is possible to find a
chain of respondents of this class in such a way, that the correlations of answers
between consecutive respondents of this chain is not less than the given value. Such
division into subgroups allows finding out distinctions in the group, which are not
appreciable directly.
At mental interrogation about factors of influence on lesson and the set minimum
level of mutual correlation 0,6 in test group 421 splitting into 3 classes has turned out:
from 4, from 5 and from basic subgroup of 11 respondents. Let's compare averages of
the basic class to averages of the first and the second subgroups under those factors in
which appreciable differences have come to light (Fig. 12).
1) Is the program of training for your speciality satisfying you?
2) Would you like to change the speciality or enter another university?
274
3) Are you willing to take part in scientific work, in Olympiads on your
speciality?
4) Do you wish to enter postgraduate study after training end?
5) Participation in scientific work.
6) Preparedness of an auditorium for a lesson.
7) Accessibility of summer improvement.
8) Accessibility of contacts with the future employers.
12
10
8
Class 1
6 Class 2
Main class
4
2
0
1 2 3 4 5 6 7 8
Fig.12. Comparative results
Respondents from classes 1 and 2 much less than the basic group are satisfied by
the program of training of the speciality (point 1). They would like to change the
speciality or to receive additional higher education much more than the basic group
(point 2). Their difference clearly comes to light in point 3: unlike the basic group
they do not wish to take part in scientific work or in the Olympiads on the speciality
at all. So, apparently, the speciality has lost now its appeal for them. Respondents
from class 2 are not interested in the postgraduate study (point 4), however, they are
not against taking part in scientific work (point 5). The main thing, they have the most
interest in contacts to employers (point 8). Apparently, it is search for their
employment out of the speciality. Respondents from class 1 are focused differently:
they have a little interest in scientific work and employers (points 5 and 8), but they
wish to enter postgraduate study (point 4).
References
1. Research Spotlight on Academic Ability Grouping (NEA Reviews),
http://www.nea.org/tools
2. Jennifer J. Kaplan, John G. Gabrosek, Phyllis Curtiss, and Chris Malone Investigating
Student Understanding of Histograms, Journal of Statistics Education 22(2) (2014)
275
3. Greene, William H. Econometric Analysis, Prentice Hall. (2012)
4. De Bono E. Six Thinking Hats. Penguins Books. (1997)
5. PHP Book, http: // www.phpreferencebook.com/
6. Hansen B. E. Econometrics (2012), http: //www.ssc.wisc.edu
7. Pam Boger Building the Numeracy Skills of Undergraduate and Elementary School
Students, Journal of Statistics Education 13(3) (2005)
8. Factors Affecting Learning, http://www.gdrc.org/info-design
276
The Multidimensional Data Model of Integrated
Accounting Needed for Compiling Management Reports
Based on Calculation EBITDA Indicator
Yatsenko Viktoria
Kherson National Technical University, 24, Beruslavske st., Kherson, 73008 Ukraine
Viktorijajacenko@rambler.ru
Abstract. Organization and method of assembly management report using a
definition of EBITDA indicator (Earnings before interest and tax, amortization
and depreciation) are considered on the practical example of Kherson river
port’s activity. The process of constructing a multidimensional model, that is
necessary for determining EBITDA of integrated accounting using the program
"1C: Accounting for Ukraine", and implementation of the model using
PivotTable in MS Excel are represented. The range of possibilities to
implement the process named “Data Mining” of the models is demonstrated.
The management report, formed on the basis of multidimensional data model is
used to determine the profitability of the business units, business processes and
enterprises considering the organizational architecture of the entity.
Keywords: Multidimensional data model, EBITDA, Рivot table, Management
Reporting.
Кey Terms: KnowledgeManagementMethodology, Management, Model,
ModelBasedSoftwareDevelopmentMethodology.
1 Introduction
The process of the evolutionary development of accounting and reporting in
Ukraine has a long history of changes and qualitative transformations, first of all,
resulting from the wish to timely provide the various groups of interested users with
the reliable data. The accounting and financial reporting is considered by lots of
people as a formally obligatory phenomenon approved and regulated by the state
legislation. Actually, it is a fundamental basis of the de facto existing accounting and
analytical system able to perform the primary functions of a business management.
The current realia of a business management require expending the boundaries of
the existing accounting and reporting systems be means of including the tasks of
planning, control and performance measurement regarding the activities, business
processes, business units, the company as a whole, and elaborating the strategy of
operation and development. Additional "non-standard" for the accounting requests
277
from the information users and different vision of the functional tasks’ development
essentially enforces the formation of various types of accounting (financial, fiscal,
management, strategic, etc.) and the methods of data interpretation in order to define
the financial indicators such as (EBIT, EBITDA, ROA, TIER etc). One of the priority
trends of the accounting development is creating the accounting and analytical system
of a company that can provide all the necessary information to every level of
management on a real-time basis. In this paper we present a variant of an integrated
accounting data model on a company incomes and expenditures allowing you to
create the management report items based on the indicator computation EBITDA, and
which is in practice used at Kherson river port.
2 The System of Integrated Accounting
New approaches to shaping the views of the category "accounting" are based on
the theory of the system: any system can be represented as a set of the inter-related
and linked elements forming a certain unity and value. In addition, it is necessary to
emphasize the impact of the system theory on understanding the accounting system as
a multidimensional and complex informational space. Determination of the core
system features is an important factor allowing seeing the accounting elements in a
single accounting system. These features include: the ability to assess data to solve
problems in the same monetary units; matching the economic resource cycle model,
their origin, and business processes represented in the general Chart of accounts;
actuality and retrospectiveness of the data obtained within the framework of
accounting; legal (documentary) proofs of business transactions. The system approach
to formation of the indicators to draw the various forms of reporting (financial,
statistical, fiscal, management) makes it possible to assert of the establishment and
operation of an integrated accounting system.
In recent years, the problem of integration of the accounting information has
become particularly relevant for the scientists. A lot of them raise the issue of the
necessity to get the information that allows separating the costs not only for the
reproducing process as a whole, but also for all types of the core and service
processes which is important to identify the most costly processes, develop measures
to reduce the costs for their implementation [1].
The integrated accounting is the main element of the accounting and analytical
business management and the basis for the accounting system functioning that allows
you to transform information in order to draw various forms of reporting and
identifying the indicators characterizing the degree of the approved plans
implementation.
Analysis of the possibilities of the special-purpose programs of various decision
support systems (DSS) available on the Ukrainian market confirms that the software
products meet the requirements put forward by the modern company executives and
enable to simulate any business processes with due consideration of the external and
internal factors, and can automatically calculate the economically sound company’s
performance indicators. The main criteria for choosing the software for the Ukrainian
companies is the minimum price, usability, compatibility with accounting programs
usually on the 1C platform, and preferably not involving any IT experts.
278
3 The Multidimensional Data Model
Let us give consideration to the real-life experience of the Kherson river port on
solving the tasks mentioned.
Evaluation of the performance of the Kherson river port is based on the EBITDA
indicator, which, according to the foreign authors, is the key to determine the
profitability, and is used all around the world [2].
The indicator EBITDA (Earnings before interest and tax, amortization and
depreciation) means Earnings before interest, taxes, depreciation and amortization [3].
There are several algorithms for calculating EBITDA. The company in question uses
the following order to calculate the analytic indicator, as adapted to the realities of its
economic activity:
EBITDA = NР + ITE – SIT + IE – EI +АA – DA, (1)
where NР - net profit, ITE - income tax expense, SIT - satisfied income tax, IE -
interest expenses, EI - earned interest, АA - amortization of assets, DA - depreciation
of assets.
Kherson river port maintains the financial accounting and prepares financial
statements pursuant to the national Regulations (standards) of accounting (NP(S)A)
and the International Financial Reporting Standards (IFRS) in parallel, which meets
the requirements of the Law of Ukraine on Accounting and Financial Reporting [4]. It
is clear that the definition of EBITDA is not possible on the basis of the financial
accounting data without further transformation.
The process of accounting and financial reporting at the company in question is
automated using "1C: Accounting for Ukraine". Necessary details of the accounting
data in "1C Accounting for Ukraine" as the raw data to determine the resulting
indicator EBITDA is achieved by constructing a hierarchy of the analytical
accounting levels through the structured directories for storing objects that can be
hierarchically classified according to selected features. Important for the
determination of EBITDA and preparation of management reports is the
organizational structure, under which one should understand a complex of the typical
elements of accounting in general and some of its parts in particular. Given the
category features and integrated accounting, to build a multidimensional data model
of EBITDA determination, a basic scheme of the integrated accounting of income and
expenses is used at the company in question on the "asterisk" principle (table 1).
Construction of the model takes into account the complex organizational
architecture of the company as well as the details of its activity. The point at issue is
that the business units of the company are strongly interrelated and also perform the
maintenance functions of the company in general, therefore, it is important to separate
the data relating to the internal business volume to prevent any result
misrepresentation.
279
Table 1. The multidimensional organization model of the integrated accounting of the Kherson
river port.
Characteristic
Dimension
Period Subject Object Area
characteristics
Dimension of
Impact
Data unit
on the Type
Business Unit
Month result of of
(BU activity)
activity activity
(+/-)
loading and
January unloading
І quarter
operations
February
Elevator
І half-year
March Income
Port
Meaning of characteristics
Complex fleet
April
service
Result of dimension
ІІ quarter
Internal turnover
May Mechanization
Operating
Financial
Another
Cargo and
Year
June passenger
services
July
Another
ІІІ quarter
August
ІІ half-year
Sand
September Costs
October
ІV quarter
November Non-core assets
December
4 Implementation of the Model in Рivot Table MS Excel
The process of drawing a management report based on EBITDA for the Kherson
river port is realized in the pivot Excel tables, "... one of the most convenient means
applying the OLAP technology, the main purpose of which is to process information
for analyzing and decision making. The advantage of OLAP is to create queries using
flexible ad hoc approaches without involvement of the IT experts. The pivot tables
280
provide using of the multidimensional classifications, detail and integration of the
data, identifying trends, patterns, forecasting, analysis, thus representing a weighty
tool for operation of the accounting and analytical system of a multi-segment
company in the real-time mode" [5].
Formation of items of the management statements based on the multidimensional
data model of the integrated accounting and the algorithm for determining the
EBITDA indicator in the pivot Excel tables are shown in Table 2,3.
Table 2. The management report items in the Pivot Tables in MS Excel of the Kherson river
port.
Status The management report items Abbreviation
(=) Total revenue TR
(-) Logistics costs LC
(-) Special engineering SE
(=) Present revenue PR
(=) Variable costs VC
(=) Marginal revenue МR
(=) Marginal revenue, % МR, %
(-) Material costs MC
(-) Energy E
(-) Insurance I
(=) Services of external organizations SEO
(-) Staff costs SC
(-) Depreciation D
Change of residues unfinished goods and
(-) CBR
finished goods, corrections of balance residues
(-) Operating taxes OT
(=) Fixed costs FC
(=) Total profit TP
(+) Other income OІ
(-) Other costs OC
(=) Profit before taxes 1 TP1
(+) Financial income FI
(-) Financial costs FC
(=) Profit before taxes 2 TP2
(-) Income tax IT
(=) Net profit NP
(=) Net profit, % NP,%
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Table 3. The calculating algorithm of performance indicators of the management report in the
Pivot Tables in MS Excel of the Kherson river port.
Indicators Abbreviation Algorithm for calculating
SUM (TR_ cargo fleet: TR_
transportation fleet ports; TR_ cargo
handling; TR_ comprehensive fleet
Total revenue TR
maintenance; TR_ rental income; TR_
industrial activities; TR_ non-core
activity; TR_ other income)
Present revenue PR SUM (TR; LC; SE)
SUM (v_ fuel; v_ material costs; v_
Variable costs VC
port charges; v_ energy; v_ taxes)
Marginal revenue МR SUM (PR; VC)
Marginal revenue, % МR, % IF (TR=0;0;МR/PR)
Services of external SUM (f_ assignment; f_ repair; f_ rent;
SEO
organizations f_ connection; f_ other costs)
SUM (f_ material costs; f_ energy, f_
insurance; f_ services of external
Fixed costs FC organizations; f_ staff costs; f_
depreciation; f_ corrections of balance
residues; f_ operating taxes)
Total profit TP SUM (МR; FC)
Profit before taxes 1 TP1 SUM (TP;OІ;OC)
Profit before taxes 2 TP2 SUM (TP1;FI;FC)
Net profit NP SUM (TP2; IT)
Net profit, % NP,% IF (PR =0;0; NP / PR)
EBITDA SUM (NP; IT; FC; FI ; D)
5 Capabilities of the Model
A management report implemented in the pivot tables represents the data as to
several informational slices - forming a subset of a multidimensional amount of data
corresponding to one or more elements of measurement. For example, selecting a
subset of values of the company’s fixed costs over certain time, as a structural unit in
general, and those of a business unit in particular, highlighting the internal business
volume (fig. 1).
282
Fig. 1. Detailed fixed costs of the Kherson river port.
The model can not only be used for determining EBITDA and making a
management reporting form, but can be a basis for implementation of the process of "
Data Mining". Therewith, the spectrum of the problem solving by methods of Data
Mining can be broad enough, from the sales revenue classification by types and
business units to feasibility of a business unit in view of the internal business volume
(fig. 2).
Fig. 2. Detailed total revenue by origin and business-units including internal turnover.
283
6 Conclusion
Analysis of practical experience in the construction and operation of management
accounting at the company in question, the reporting procedure for management and
the algorithm for determining EBITDA are indicative of using the accounting system
for the absorption - costing system which is focused on the owners (investors)
requests regarding the effectiveness of the funds invested.
Organization of accounting using “1C Accounting for Ukraine" allows
representing accounting as an information system in the form of a multidimensional
data model to achieve a number of results, namely the creation of a single integrated
accounting system, which meets both, "standard and non-standard" user requests;
bridges the gap between the formation of actual financial and management accounting
data; summarizes data for the preparation of management reporting forms with a
given level of detail.
Use of the Pivot Tables in MS Excel provide for the appearance of new aspects of
actual data usage, introduction of new connections between the data of financial and
management accounting, which in turn does not lead to reconstruction of the whole
accounting model and accounting database in general. In the pivot tables there are
tools of data analysis allowing for the intellectual assessment, that is to summarize,
group, delete unnecessary data, or increase the reliability by establishing links and
accuracy of calculations. Good design of the tables can significantly facilitate the
laborious process of making the management reporting forms and analyzing the
company’s activities.
References
1. Kolesov, A. V.: Conceptual model of the analysis of expenses when using process
approach. Vopr. economy and rights 12, 257--264 (2011)
2. Khalfallah, M., Moschetto, B. L., Teulon, F.: Evaluation of the profitability of companies
financed by venture capital (CVC) listed on the French Market. Journal of Applied
Business Research (JABR) 2, 313--328 (2014)
3. Strnadova, M., Karas M.: The Effect of Ownership Structure on the Performance of
Manufacturing Companies. European Financial Systems, 588--595 (2014)
4. Law of Ukraine "On Accounting and Financial Reporting in Ukraine" № 996 XIV
16.07.1999 http://zakon2.rada.gov.ua/laws/show/996-14
5. Yatsenko, V.: Accounting and analytical system of multisegment enterprise: theoretical
basis and practical implementation. Accounting and Auditing 11, 25--37(2014)
284
Statistical Analysis of Indexes of Capitalization of the
Ukrainian Firms: an Empirical Research
Anastasiia Kolesnyk1 and Ihor Lukianov2
1
Kherson State University, 27, 40-Rokiv Zhovtnya Str., Kherson 73000, Ukraine
anastacia_kolesnik95@mail.ru
2
Taras Shevchenko National University of Kyiv, 60, Volodymyrska Str., Kyiv 01601, Ukraine
lukia2007@ukr.net
Abstract. The document considers the performance and effectiveness of
Ukrainian companies on the Warsaw Stock Exchange. With this end in view,
the document examines the following issues: raising capital for investment,
eliminating barriers for the Polish investors, capitalizing product reputation on
the market, increasing investor recognition of companies, enhancing the corpo-
rate image. The document also analyses aspects of familiarity with local finan-
cial community, commitment to corporate governance standards, and the possi-
bility of M&A. These figures are to indicate the status of Ukrainian companies
on the Warsaw Stock Exchange.
Keywords. IPO, Warsaw Stock Exchange, Wig-Ukraine.
Key Terms. Industry, Management, Market, MathematicalModel, Research.
1. Introduction
Warsaw Stock Exchange is the largest national financial instruments exchange in
the region of Central and Eastern Europe and one of the fastest-growing exchanges in
Europe. The Group offers a wide range of products and services within its trading
markets of equity, derivative, debt and structured products, electricity, natural gas,
property rights, as well as clearing of transactions, operation of the Register of Certif-
icates of Origin of electricity and sale of market data.
WSE started operation in 1991 as a company held 100% by the State Treasury. In
2010, the State Treasury arranged a public offering of WSE shares; as a result, shares
of the Exchange were newly listed on the WSE Main Market on 9 November 2010.
For instance, there are 471 companies represented at the WSE, including 51 foreign
companies. Total market value of all companies is about 290 bl. Euro.
Poland's stock exchange market is growing stronger and becomes more interna-
tional day by day. Its evolution is supported by the active marketing policy of the
Warsaw Stock Exchange working to promote the entire infrastructure of Poland's cap-
ital market. These efforts have produced tangible results.
285
The Warsaw Stock Exchange conducts trading in financial instruments on three
markets:
The Main List has been in operation since 16 April 1991. This market is supervised
by the Polish Financial Supervision Authority and notified to the European Commis-
sion as a regulated market. The following securities and financial instruments are
traded here: equities, bonds, pre-emptive rights, rights to shares, investment certifi-
cates, structured instruments, ETF and derivatives, i.e. futures contracts, options and
index participation units.
NewConnect is a market organised and maintained by the WSE as an alternative
trading system. It was designed for startups and developing companies,
especially from the sector of new technologies. NewConnect was launched on
30 August 2007. Instruments which may be traded under this alternative trading
system include equities, rights to shares, pre-emptive rights, depository receipts,
as well as other equity based instruments.
Catalyst is a debt instruments market for municipal, corporate and mortgage
bonds Founded on 30 September 2009, it consists of two trading platforms
organised by the WSE as a regulated market and as an alternative trading system
(ATS) for retail customers, and two analogous markets operated by BondSpot
and designed for wholesale clients.
2. Problem Statements
If a company wants to be listed on the stock exchange, it should complete Initial
public offering (IPO).1
Initial public offering (IPO) or stock market launch is a type of public offering in
which shares of stock in a company usually are sold to institutional investors (that
price the company receives from the institutional investors is the IPO price) that in
turn sell to the general public, on a securities exchange, for the first time.
IPO benefits:
Access to capital to fund growth
Public placement of shares on a stock exchange allows the company to attract
capital to fund both organic growth (modernization and upgrade of production
facilities, implementation of capital-intensive projects) and acquisitive expansion. If
retained earnings and debt funding are insufficient, IPO becomes one of the most
realistic and convenient ways to secure the continuing growth of the business. It
provides access to a massive, timeless pool of capital and boosts the investment
credibility of the business.
Creation of liquidity and potential exit for the current owners
Formation of a public market for the company’s shares at fair price creates
liquidity and provides an opportunity to sell the shares promptly with minimal
transactional costs. The private owners of the company can dispose of their stakes in
the business both during an IPO (this route is often taken by the minority financial
1
IPO calendar, http://www.fixygen.ua/calendar/ipo/
286
investors such as venture or private capital funds) and at a later stage (this is often
preferred by the majority shareholders).
Maximum value of the company
Normally, an IPO is an offer to a large number of institutional and retail investors
to become shareholders of the company. The very multitude of large investors and
their confidence in the liquidity of their investment in a public entity assure the
current owners of a private company about achieving the maximum possible valuation
of the business at the time of an IPO or afterwards.
Enhancement of the company’s public profile
Listing on a recognized stock exchange means that the business will receive wide
media coverage, usually a very favorable one, thus increasing the company’s visibility
and recognition of its products and services. The company’s activities will also be
reflected in the reports by professional financial analysts. Such public profile supports
liquidity of the shares and contributes to the expansion of the business contacts. It also
helps to increase confidence among the company’s business partners.
Improvement in debt finance terms
For domestic (Ukrainian or other CIS country-based) financial institutions – used
to working with the low-transparency businesses and often inadequate financial
reporting – a company listed on a recognized stock exchange becomes a desirable and
reliable partner. Banks are often ready to extend loans to public companies in larger
amounts, under smaller collateral, for longer maturities and with lower interest rates.
Even the largest and most prestigious banking institutions are keen to work with
public companies – whose transparency and corporate governance serve as additional
factors of confidence for banks and other suppliers of credit.
Extra assurances for partners, suppliers and clients
Partners and contractors of a public company feel more confident about its
financial state and organizational capabilities as compared to those of a non-
transparent private business. Partners take additional comfort in the fact that the
public company has gone through rigorous legal, financial and corporate due
diligences – all of which are required for a successful completion of an IPO.
Confidence among partners and contractors is a sound foundation for stable and
predictable business relations with the public company, and allows the latter to obtain
additional leverage in negotiating better terms for doing business.
Enhanced loyalty of key personnel
Publicly available information about the share price of a public company allows
development of employee motivation schemes based on partial remuneration of staff
in the form of participation in the equity capital (for example, share options). Equity-
based incentive schemes stimulate the key personnel to become more efficient in their
work in order to support the company’s growth rates and profitable development –
which in turn increase the operational and financial efficiency of the company and its
market value.
Superior efficiency of the business
Conduct of various due diligences during the IPO process requires a thorough and
comprehensive analysis of the company’s business model. During the IPO
implementation process, certain internal changes take place, including modification of
287
the organizational structure; selection of the key personnel and delegation of
responsibilities; improvement of internal reporting and controls; as well as critical
evaluation of the efficiency of the entire business. Normally, such extensive internal
efforts result in significant improvements of the communication system, management
and controls; they also help eliminate any previously hidden shortcomings in the
internal functioning of the business.
The IPO process can be very complicated. There are certain steps you must take
along the way. These steps will help insure that your IPO is successful.
Planning for the IPO Process
You need to determine at the beginning whether it's a good time for an IPO.
Choosing the ideal time to go public is very important. Plan in great detail what you
hope to accomplish. Examine your financial needs and wants.
It's helpful for a business to act like a public company even before it goes public.
This can be done a couple of years in advance of the IPO. Develop a business plan
and prepare financial statements.
Choosing Underwriters
Most companies use underwriters to help them with IPOs. Choosing the right
underwriters is key to having a successful offering. They're usually the ones
responsible for buying and selling the securities to the public. They're also responsible
for investigating your business to verify the financial information given to the
investors. You should select the underwriters at least a few months before the IPO
date.
Filing a Prospectus
Your business must file a registration statement with the US Securities and
Exchange Commission (SEC). This statement contains detailed information about the
offering. It also includes information about the business, its financial history and its
future plans.
The registration statement becomes the preliminary prospectus once it's filed with
the SEC. A prospectus is a legal document explaining the securities offered to the
public. The preliminary prospectus is also called the red herring. It's called this
because red ink is used on the front page to indicate certain information may change.
The SEC will examine the registration statement during a "cooling off" period. It
informs the business of any necessary changes. The statement becomes the official
prospectus once any necessary amendments are made. The prospectus can be used by
the public to help them determine whether they want to purchase the securities for
sale.
IPO Promotion
A business going public has to market the IPO. Representatives from the company
and underwriters go on a "road show" around the country. They make numerous
presentations to potential investors. Typical stops include New York, Chicago,
Boston, Los Angeles and San Francisco. Even international trips may be set up for
overseas investors.
Final Offering Price and Amount
Choosing the final offering price and the amount of securities to be sold are very
important decisions. Market conditions and the expected demand for the securities
288
need to be examined closely. These final decisions are usually made right before the
offering.
Selling on the Stock Market
The IPO is normally declared effective a few days after the final prospectus is
received by the potential investors. This declaration is usually done after the stock
market has closed. The securities will then be available for trade the next day. The
IPO will hopefully be successful and provide new capital for the business for their
present and future plans.
Taking into consideration the benefits of being involved in the Warsaw Stock
Exchange activities, many Ukrainian companies want to be listed. However, in order
to be listed at the WSE, a company is obliged to meet special requirements as follows:
1. Only a joint stock company may be an issuer of shares listed on the WSE. This
does not bar entities operating under any other legal form from listing, but their
owners need to transform them into joint stock companies or establish joint stock
companies and transfer the entities assets thereto.
2. As a next step, the General Shareholders Meeting should adopt a resolution
approving a public offer of shares and an application for admission of the shares to
trading on the regulated market.
3. The decision to apply for admission to trading in the regulated market may
require the preparation of a relevant information document (issue prospectus or
information memorandum) so the company will need to work with:
an auditor who will audit the company's financial statements and convert them
into a format comparable year to year;
a brokerage house which will offer the company's shares in a public offer.
Depending on the issuer's individual needs, the company may need to hire legal
and financial advisors. The contents of the issue prospectus are laid down in the
Commission Regulation (EC) No. 809/2004 of 29 April 2004 as regards information
contained in prospectuses.
4. Next, the company will need to submit the working draft of the issue prospectus
to the Polish Financial Supervision Authority (KNF). KNF may communicate its
comments, and once the company has accommodated those in the final draft of the
issue prospectus, KNF will decide whether to approve the prospectus.
5. Before opening the public offer, the issuer will need to execute an agreement
with the National Depository for Securities (KDPW) whereby the securities subject to
the public offer will be registered by the Depository.
6. The public offer may now proceed. Before allocated shares of a new issue are
registered, rights to shares may be traded on the WSE.2
7. Once the offer is closed, the company will submit an application for the
admission of shares (and possibly also rights to shares) to stock exchange trading on
the main or the parallel market. The WSE Management Board will examine the
application. The application must include, among others, the final draft of the issue
prospectus accommodating all recommendations made by the KNF.
2
WSE, http://www.ipowse.com.ua/about/
289
8. Once all shares introduced to trading are deposited with KDPW, the public offer
is closed, and the shares of the new issue registered by the court, the company will
file with the WSE Management Board an application for the introduction of shares to
trading on the main or the parallel market. The WSE Management Board will indicate
the trading system and the date of the first trading session.
Some Ukrainian companies have already been listed at the regular market of the
WSE. There are some descriptions of such companies:
Kernel is a leading diversified agribusiness company in the Black Sea region listed
on the Warsaw Stock Exchange. Handling about 6 million tons of agricultural
commodities per year, Kernel supplies international markets with grain and sunflower
oil produced in Ukraine and Russia. The production assets extend from black soil
farmland to oilseed crushing plants supported with essential agricultural infrastructure
including silos and deep-water export terminals. 2007 marked also a new stage in the
development as Kernel became a publicly listed company: listed Kernel on the
Warsaw Stock Exchange in November 2007 and new shareholders entered the capital
of the Company to participate in the growth story. 3
Founded in 1993, “Astarta–Kyiv” is a vertically integrated agro-industrial holding
specializing in sugar and agricultural production. It has proven to be a growing,
transparent company, as well as a reliable partner and supplier. Implementing a
strategy of vertical integration, ASTARTA created a fully integrated production cycle
of sugar from growing the beet to sugar production and sales. Growing sugar beets
lowers dependence on the external supply of sugar beets, lowers the cost of produced
sugar, and guarantees constant manufacturing and the highest possible yield and
quality. In August 2006, ASTARTA’s shares are listed on the Warsaw Stock
Exchange.
Group of Companies «Ovostar Union» is one of Ukrainian leading agro-industrial
companies, entering TOP 3 Ukrainian egg producers. The history maintains 14 years
of experience, leadership and innovations. The main advantage is vertically integrated
business organization structure, providing accurate product quality control at any
production stage. Each enterprise of GC «Ovostar Union» is an integral part of whole
business, important and high-grade link, performing its obligations effectively, and in
this way ensuring the common great result. It’s the conformity of all Company
activity vectors determining products guaranteed quality and in general high business
profits. In 2011 GC «Ovostar Union» has debuted on the Warsaw Stock Exchange
and attracted 93 million zlotys in an initial public offering (IPO). It has been using to
carry out the group’s investment program. 1.5 million shares were placed (25% of the
capital) at a price of 62 zlotys per share. The price is equal to the maximum price. 4
Industrial Milk Company (IMC) is an integrated agricultural business operating in
Ukraine. In May 2011 IMC conducted IPO on Warsaw Stock Exchange.
The main areas of IMC’s activities are:
cultivation of grain & oilseeds crops, potato production
storage and processing of grain & oilseeds crops
3
Kernel, http://www.kernel.ua/en/
4
Ovostar, http://www.ovostar.ua/ru/
290
dairy farming
IMC is among Ukraine’s top-10 agricultural companies (source of ratings:
AgriSurvey, “The largest agro holdings in Ukraine”, 2014, based on results of year
2013). In May, 2011 the company completed IPO on Warsaw Stock Excange, IMC
raised US$ 24,4 mln to finance the development of the company. 5
Milkiland is an international diversified dairy producer with the core operations in
the CIS and EU. The Group’s total annual milk processing capacity exceeds 1 million
tons. The company is proud to produce natural dairy from the best milk: a wide range
of fresh dairy, different types of cheese, and butter to satisfy the consumers in their
everyday needs for healthy and tasty foods. Milkiland’s dry dairy products are
exported to over 30 countries. The international Dobryana brand is popular among
cheese and dairy consumers in Ukraine, Russia and other CIS countries.
Ostankinskoye is a traditional brand for whole-milk products produced by Ostankino
Diary Combine, well known by Moscow consumers. Fresh dairy under Ostrowia
brand is also well known in Poland. 21.48% of the shares of Milkiland N.V. are in the
free float at the Warsaw Stock Exchange.6
KDM Shipping is one of the leaders of the Ukrainian shipping industry, primarily
involved in the niche segment of dry bulk river-sea freight in the Black, Azov and
Mediterranean Sea regions. The Group’s cargo fleet consists of 10 river-sea, dry
cargo vessels of total 29,673 DWT, which due to their shallow draft can access major
river and sea ports in Black and Azov Sea regions. The Group also provides passenger
river transport services in the Kiev and other regions of Ukraine (operating the fleet of
8 passenger river vessels), as well as ship repair services at its own shipyard located
in the city of Kherson. According to International Economic Rating “League of the
Bests” in 2012, the Group is ranked as # 1 in river activity and 3rd in maritime
activity in Ukraine.7 The Group has developed a vertically integrated business model.
The Group’s main activity of dry-bulk shipping is supported by its own ship repair
yard, its own ship agency in selected ports as well as its own crewing department.
Such business model allows the Group to benefit from certain cost efficiencies and
sustain competitive advantages.
Coal Energy S.A. was incorporated in the Grand Duchy of Luxembourg and has
been listed on the Warsaw Stock Exchange in Poland since 08 August 2011. Coal
Energy S.A. is a holding company for a group of 12 companies operating in the coal
industry in Ukraine which rank the Company as the 3rd largest in terms of coal
deposits and the 4th largest in terms of extraction volumes private coal mining
enterprise in the country based on the calendar year 2011 data (hereinafter – “the
Group” and/or “Coal Energy”).
Principal business activities of Coal Energy are mining, beneficiation and sales of
thermal and coking coals as well as dual purposes coal. Companies of the Group are
directly cooperating with all the largest heat and power generation plants and
metallurgic plants in Ukraine. Due to its favorable geographical location and wide
5
Industrial Milk Company, http://www.imcagro.com.ua/ru/
6
Milkiland, http://www.milkiland.nl/ru
7
KDM Shipping, http://kdmshipping.com/
291
products’ palette Coal Energy is able to export produced thermal coal to power
producing stations in Turkey, Moldova, Bulgaria, Slovakia and other countries where
the Group has established contacts with the largest power generations.
KSG Agro is one of the most dynamically developing agricultural groups in
Ukraine. We take innovative approach for our key business philosophy. The search of
non-standard approaches and creative decisions requires professional experience and
passion for a native land. Our main values are people and land. Everything we
produce is made by people and for people. That is why we highly appreciate your
trust and consider it a key factor of the Group’s success. Trust is impossible without
responsibility. Providing an example of long-term and prosperous cooperation among
the state, society, and agricultural business, we create the foundation for leadership.
Nowadays the Group gained a lot to be proud of; however we still strive for more.
Highly-profitable agricultural industry with a high level of diversification and vertical
integration gives growth prospects and sense of security. We have got the main factor
for this purpose which is our team of like-minded professionals. The core business of
the Group is cultivation of land and production of agricultural crops. Complex
approaches to farming and focus on intensive development of business ensure high
profitability and also create the conditions facilitating high yields.
The Group focuses on the following business directions:
Crop production
Vegetables production
Fruits production
Food processing business
Supplies of food to retail networks
3. Results
The full list of Ukrainian companies listed at the Warsaw Stock Exchange:
Table 1. Ukrainian companies at the WSE
Name of the com- Date of IPO The percentage of Sum of the capitali-
pany capitalization zation
Astarta Kiev August 2006 20% of shares 23,7 bl. Euro
Kernel Holding November 2007 37,98% of shares 136,5 bl. Euro
Agroton public November 2010 26,2% of shares 38,25 bl. Euro
limited
Milikiland December 2010 22,4% of shares 60 bl. Euro
Sadovaya Group December 2010 25% of shares 23,15 bl. Euro
Industrial Milk May 2011 23,9% of shares 20,7 bl. Euro
Copmany
KSG Agro May 2011 33% of shares 27 bl. Euro
Westa June 2011 25% of shares 32 bl. Euro
Ovostar Union June 2011 25% of shares 22,2 bl. Euro
N.V
292
Coal Energy August 2011 25% of shares 56 bl. Euro
KDM Shipping August 2012 11 % of shares 6,3 bl. Euro
WIG-Ukraine is the second national index calculated by WSE. Its portfolio in-
cludes companies listed on the Warsaw Stock Exchange, where a company or head
office is located in Ukraine, or whose business is conducted to the greatest extent in
this country. It has been calculated since May 4, 2011. The historical values were re-
calculated since December 31, 2010 (the base date). The initial value of the index was
1000 points. WIG-Ukraine is a total return index and thus when it is calculated it ac-
counts for both prices of underlying shares and dividend and subscription rights in-
come. 8
Composition of WIG-Ukraine
(as for 24 February 2015)
Table 2. The composition of WIG-Ukraine
Instrument ISIN Share Market value Quota
of shares (PLN) (%)
KERNEL LU03273 9,509,000 286,601,260 37.877
57389
ASTARTA NL00006 9,253,000 227,346,210 30.046
86509
OVOSTAR NL00098 1,725,000 122,233,500 16.154
05613
IMCOMPANY LU06072 9,809,000 63,169,960 8.348
03980
MILKILAND NL00095 8,276,000 26,152,160 3.456
08712
KDMSHIPNG CY01024 3,329,000 18,775,560 2.481
92119
COALENERG LU06461 11,252,000 6,638,680 0.877
12838
KSGAGRO LU06112 5,093,000 5,755,090 0.761
62873
(1)
M(t)-capitalisation of index portfolio at session "t"
M(0)-capitalisation of index portfolio at base date
K(t)-adjustment coefficient for session "t"
Now, using application package of MS Excel, we shall determine the effect of
Ukrainian companies to index. The following table draws up the results:
8
Wig-Ukraine, http://www.gpw.pl/opis_indeksu_WIG-Ukraine_ru
293
Table 3. The effect of Ukrainian companies to index
b8 b7 b6 b5 b4 b3 b2 b1 b0
1.47 -1.70 0.889 2.69 1.38 0.385 2.69 4.96 6.08
0.15 0.996 0.042 0.22 0.159 0.052 0.028 0.039 3.42
t(b8) t(b7) t(b6) t(b5) t(b4) t(b3) t(b2) t(b1) t(b0)
9.99 1.71 21.01 12.26 8.69 7.33 94.799 126.43 1.78
Signi- Insigni- Signi- Signi- Signi- Signi- Signi- Signi- Insigni-
ficant ficant ficant ficant ficant ficant ficant ficant ficant
tkr 1.97
Obtained results in the table are equal to the following equation multiple linear re-
gressions:
y=6.079+4.956*X1+2.686*X2+0.385*X3+1.379*X4+2.693*X5+0.889*X6-
1.705*X7+1.473*X8 (2)
We shall interpret it as following:
6.079 – performs, that after zero changes of prices of shares of all companies
і к з the index shall be increased by 6%
4.956– performs, that after 1 % increase of prices of shares of Kernel Hold-
ing the index shall be increased by 5%
2.686– performs, that after 1 % increase of prices of shares of Astarta Kiev
the index shall be increased by 2,7%
0.385– performs, that after 1 % increase of prices of shares of Ovostar Union
the index shall be increased by 0,38%
1.379– performs, that after 1 % increase of prices of shares of Industrial Milk
Co. the index shall be increased by 1,34%
2.693– performs, that after 1 % increase of prices of shares of Milkiland the
index shall be increased by 2,7%
0.889– performs, that after 1 % increase of prices of shares of KDM Ship-
ping Public Ltd the index shall be increased by 0,9%
1.705– performs, that after 1 % increase of prices of shares of Coal Energy
the index shall be increased by 1,7%
1.473– performs, that after 1 % increase of prices of shares of KSG Agro the
index shall be increased by 1,5%
Application of Student's t-Tests shows, that almost all companies have an effect on
the index. Though, we can point out two of them, namely Kernel Holding, Astarta Ki-
ev, having the most considerable effect on the index. Their shares account for the
most considerable percentage, in particular for 67% of Wig-Ukraine index. More im-
portantly, Kernel Holding and Astarta Kiev are the first companies to be listed at the
regular market. They have already adapted to the market, having a great superiority as
compared to other Ukrainian companies. Moreover, Kernel Holding is also included
in composition of WIG30 index which is based on the value of portfolio of 30 major
and most liquid companies on the WSE Main List. Both companies are engaged in ag-
294
ricultural business, which is the most distinctive feature of the Ukrainian companies,
involved in international business activity.
4. Conclusion
The following results were obtained in the course of this research:
The primary reason (motive) for the Ukrainian companies to be listed at WSE is
the possibility of acquiring access to the capital;
The reputation and credibility of the stock company (market) provides the
Ukrainian companies with the possibility of finding new investors or potential
financial partners;
As of today, there are 11 Ukrainian companies at WSE and 2 companies at the
NewConnect market;
More than two billions Euros were attracted by the Ukrainian companies;
In fact, Warsaw Stock Exchange is the most effective way of entry into the
international market for the Ukrainian companies, which, in the meantime,
enables the companies to strengthen their positions on the market, raise capital
and gain investments in the future.
References
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The Hybrid Service Model of Electronic Resources
Access in the Cloud-Based Learning Environment
Mariya Shyshkina
Institute of Information Technologies and Learning Tools of the National Academy of
Pedagogical Sciences of Ukraine, Berlinskii Str., 9, Kyiv, Ukraine
marple@ukr.net
Abstract. Nowadays, the search for innovative technological solutions to the
organization of access to electronic learning resources in the university and
their configuration within the environment to fit the needs of users and to
improve learning outcomes has become key issues. These solutions are based
on the emerging tools among which cloud computing and ICT outsourcing have
become very promising and important trends in research. The problems of
providing access to electronic learning resources on the basis of cloud
computing are the focus of the article. The article outlines the conceptual
framework of the study by reviewing existing approaches and models for the
cloud-based learning environment’s architecture and design, including its
advantages and disadvantages, and the features of its pedagogical application
and the experience of it. The hybrid service model of access to learning
resources within the university environment is described and proved. An
empirical estimation of the proposed approach and current developments in its
implementation are provided.
Keywords: hybrid model, learning environment, cloud computing, university.
Key Terms: ICTInfrastructure, Model, TeachingProcess
1 Introduction
Progress in the area of ICT and network technology has provided new insights into
the problems of the formation and development of the educational environment of the
university, showing a need for advanced ICT access, especially with regard to the use
of the cloud-based tools and resources. There is a need for modernization of learning
technologies, supported by emerging ICT, on the basis of advanced network
infrastructures.
Cloud computing technology (CC) enhances multiple access and joint use of
educational resources at different levels and domains. On the basis of this technology,
it is possible to combine the corporate resources of the university within a united
framework. To achieve this aim, a set of cloud-based learning models should be
created for the elaboration and design of learning resources and the learning
environment architecture to deliver access to learning resources.
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The purpose of the article is analyse the current trends in the university cloud-
based learning environment formation from the perspective of different service
models used, and to substantiate and validate the hybrid service model of access to the
learning resources.
The research method involved analysing the current research (including the
domestic and foreign experience of the application of cloud-based learning services to
reveal the concept of the investigation), examining existing models and approaches,
estimating the current state of research development, considering existing
technological solutions and psychological and pedagogical assumptions about better
ways of introducing innovative technology, and conducting pedagogical experiments,
surveys and expert evaluations.
2 Problem Statement
The progress of ICT has a significant impact on the formation of the educational
environment of the university bringing with it new models of the organization of
learning activity which arise on the basis of decisions about innovative technology. In
this regard, the phenomenon of the cloud-based learning environment has come to the
forefront as it has many progressive features including better adaptability and
mobility, as well as full-scale interactivity, free network access, a unified
infrastructure among others [4, 19, 20].
The challenges of making the information technology infrastructure of the
university setting fit the needs of its users, taking maximum advantage of modern
network technologies, and ensuring the best pedagogical outcomes to increase the
learning results, has led to the search for the most reasonable ways of organizing tools
and services within the framework of this environment. For this purpose, the
modelling and analysis of its structure and functions, and determining the possible
types and forms of learning activity in the organization have come to the fore. Among
the priority issues for ICT infrastructure design is the access to software and
electronic educational resources provision [4]. To choose the best solution there is a
need to consider existing approaches and models to reveal possible ways of service
deployment, and to analyse the existing experience of its use.
3 State of the Art
According to the recent research [4, 9, 13, 18, 19], the problems of implementing
cloud technologies in educational institutions so as to provide software access,
support collaborative learning, implement scientific and educational activities,
support research and project development, exchange experience and are especially
challenging. The formation of the cloud-based learning environment is recognized as
a priority by the international educational community [16], and is now being
intensively developed in different areas of education, including mathematics and
engineering [2, 8, 11, 25, 27].
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The transformation of the modern educational environment of the university by the
use of the cloud-based services and cloud computing (CC) delivery platforms is an
important trend in research. The topics of software virtualization and the forming of a
unified ICT infrastructure on the basis of CC have become increasingly popular lines
of research [8, 18, 23]. The problems with the use of private and public cloud
services, their advantages and disadvantages, perspectives on their application, and
targets and implementation strategies are within the spectrum of this research [7, 8,
25].
There is a gradual shift towards the outsourcing of ICT services that is likely to
provide more flexible, powerful and high-quality educational services and resources
[4]. There is a tendency towards the increasing use of the software-as-a-service (SaaS)
tool. Along with SaaS the network design and operation, security operations, desktop
computing support, datacentre provision and other services are increasingly being
outsourced as well. Indeed, the use of the outsourcing mechanism for a non-core
activity of any organization, as the recent surveys have observed happening in
business, is now being extended into the education sector [9]. So, the study of the best
practices in the use of cloud services in an educational environment, the analysis and
evaluation of possible ways of development, and service quality estimation in this
context have to be considered.
The valuable experience of the Massachusetts institute of technology (MIT) should
be noted in concern to the cloud based learning environment formation in particular as
for access to mathematical software. The Math software is available in the corporate
cloud of the University for the most popular packages such as Mathematica,
Mathlab, Maple, R, Maxima [27]. This software is delivered in the distributed mode
on-line through the corporate access point. This is to save on license pay and also on
computing facilities. The mathematics applications require powerful processing so it
is advisable to use it in the cloud. On the other case the market need in such tools
inspires its supply by the SaaS model. This is evidenced by the emergence of the
cloud versions for such products as Sage MathCloud, Maple Net, MATLAB web-
server, WebMathematica, Calculation Laboratory and others [2, 8]. Really there is a
shift toward the cloud-based models as from the side of educational and scientific
community, and also from the side of product suppliers. The learning software
actually becomes a service in any case, let it be a public or a corporate cloud.
There are many disciplines where it is necessary to outsource the processing
capacity: for example, the computer design for handling vast amounts of data for
graphics or video applications. This is also a useful tool used to support the
collaborative work of developers, as the modern graphical applications appear to be
super-powerful and require joint efforts [7]. There is a research trend connected to the
virtual computing laboratories (VCL) [14, 26] delivered in the cloud-based paradigm.
This trend is inherent in the field of informatics, and learning resources for processing
and sharing are needed.
Nowadays there are various universal cloud consumer applications, in particular
MicrosoftOffice 365, Google Docs and others which gain an appropriate use in
educational process [9, 23]. There is also a wide range of cloud services such as
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online photo and video editors, web pages processors, services for translation, check
spelling, anti plagiarism and many others which are now available [23].
There is a principal transformation of approaches in concern to services supply
within the cloud based infrastructure. It is considered to be a new stage of the service
oriented models development [10, 24]. There is a branch of research devoted to the
service oriented infrastructure in this actual perspective. The issues of service oriented
architecture development and are described in [10]. The problem of turning software
into a service is also posed [24]. For example, more powerful approaches for services
integration appear while services compositions are used as building blocks in a
process of elaboration of programming code [14]. The CC development brought the
term the service orchestration into scientific discussion while number of web services
can be combined to perform the higher level business process to manage and
coordinate execution of the component processes [12]. In this regard the notion of the
global software development (GSD) is considered as novel trends overcome
geographical limits [12]. There is a significant revise of approaches to ICT services
elaboration and this is concerned to its integration and composition.
An essential feature of the cloud computing conception is dynamical supply of
computing resources, software and hardware its flexible configuration according to
user needs. Due to this approach, access to educational software set on a cloud server
or in a public cloud is organized. So comparison of different approaches and cloud
models of software access is the current subject matter of educational research [7, 8,
23, 25]. Also the problems of quality criteria for software choice in the learning
complexes to be implemented in a cloud arise. Despite of the fact that the sphere of
CC is rather emerging there is a need of some comparison of the achieved experience
to consider future prospects [23].
Another set of problems is concerned with the hybrid service models and
infrastructure solutions combining different public and corporate services on the
united platform. This trend is now especially promising for the sphere of education [8,
17]. The challenge regarding novel technological solutions and their impact guide the
search for the most reasonable method of implementation.
Thus, in view of the current tendencies, the research questions are: how can we
take maximum advantage of modern network technologies and compose the tools and
services of the learning environment to achieve better results? What are the best ways
to access electronic resources if the environment is designed mainly and essentially
on the basis of CC? This brings the problem of cloud-based services modelling,
integration and design to the forefront.
4 Pedagogical Aspects of Electronic Resources Delivery and
Indicators of Research
Cloud computing technology is now one of the leading trends in the formation of
the information society. It constitutes an innovative learning concept and its
implementation significantly affects the content and form of different types of
activities in the sphere of education [4, 13, 18].
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Along with the emergence of cloud computing, the number of objects,
developments and domain applications are continually growing, which indicates the
rapid spread of the innovation [20]. The concept of the cloud-based learning
environment is now in line with the wider trend; that is to say, the ICT environment of
the university, where some didactic functions as well as some fundamentally
important functions of scientific research are supported by the appropriately
coordinated and integrated use of cloud services [20]. The aim of the cloud-based
learning environment formation is to meet the users’ educational needs. To do this,
the introduction of cloud technology in the learning process should to be holistic and
carried out according to the principles of open education, including meeting the
following needs: the mobility of students and teachers, equal access to educational
systems, providing qualitative education, and forming and structuring of educational
services [3, 20].
The main elements of the cloud computing conception, including the types,
application service models, essential features, ICT architecture and others, are
reflected in the structure of the modern educational organizational systems [5].
Therefore, a number of concepts and principles that characterize the development and
application of CC-based services are significant in the consideration of the
educational environment design.
The concept of electronic educational (learning) resources (EER) appears to be
the centre of attention. In particular, at the Institute of Information Technologies and
Learning Tools of the National Academy of Pedagogical Sciences of Ukraine the
conception that provided the definition of electronic educational resources (EER) its
classification, and the ways it can be applied has been developed and proposed [5].
According to the definition given in [5, p.3], "The electronic educational resources
are a kind of educational tool (for training, etc.) that are electronically placed and
served in educational system data storage devices which are a set of electronic
information objects (documents, documented information and instructions,
information materials, procedural models, etc.)”.
The elaboration of the electronic learning resources should be considered as a
specific activity, which is linked to the mandatory need to take into consideration the
psychological and pedagogical aspects of building an educational system
methodology, the design of an open computer-based learning environment, and the
involvement of the scientific and pedagogical staff, including the best teachers and
educators [4].
Cloud Service – is a service that makes software applications, data storage or
computing capacity available to users over the Internet [16]. These services are used
to supply the electronic educational resources that make up the substance of a cloud-
based environment, and to provide the processes of elaboration and use of the
educational services.
Electronic resources appear to be both the objects and the tools of activity for a
learner; therefore, these resources are used to maintain certain functions that are
realized in the learning process. By the educational service we mean a service
provided at the request (in response to an inquiry etc.) of a user that meets some
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service function carried out by the organization or institution (service provider,
outsourcer) [4].
Nowadays, the various types of electronic educational resources that may be
delivered by the cloud in the learning environment of the university constitute
libraries and depositories of EER or those retrieved when open analytical information
systems are used. The EER supports different types of learning and research
activities, such as theoretical material studies, the search for useful information,
translation and grammar checking, task solutions, testing, training, simulation,
making experiments and others.
Along with the development of information and communication technologies for
education, the ways and tools of access to electronic resources have changed in an
evolutionarily way and its custom properties have improved. There are new types of
EER supplied by means of cloud technologies. The EER of the public cloud can
occupy the role of software for general purposes such as office applications, systems
support processes for communication and data exchange and others, and also the
special software designed for educational use [13, 23]. The number of EERs is
increasing and this trend is likely to intensify. By means of CC-based tools, a
significant lifting of restrictions on the implementation of access to qualitative leaning
resources may be achieved. Now, these questions are not a matter of future
perspective, they need practical implementation. For this purpose, the problem of the
design and delivery of electronic educational resources in the cloud-based
environment is a complex one and not only should technological needs be considered,
but also the pedagogical aspects.
With the advance of ICT, CC technologies appear to be a factor in the change in
the content, methods and organizational forms of learning and development of the
open education models. Now, cloud computing technology is used to improve the
educational process through the presentation of a modern learning content adequate to
the goals set, the quality monitoring and evaluation of learning results at the various
stages, the creation of new organizational forms of learning, the creation of innovative
educational and scientific resources and electronic systems and their implementation
in the process of students’ self-study and classroom study, advances in computer-
aided and mixed models of training and so on [20].
As noted in [5], the necessary measures for the development of the human
resources’ component of the software industry created in Ukraine that concern the
organization of EER access in the educational institutions are as follows:
improvement to EER quality, scientific-methodological research on the
implementation of innovative technologies and prospective models and methods in
education, the development of the normative regulatory framework, strengthening the
firms and companies in the IT industry and their participation in providing
educational hardware and software and so on.
Due to the significant educational potential and novel approaches to environmental
design, its formation and development, these questions remain the matter of
theoretical and experimental studies, the refinement of approaches, and the search for
models, methods and techniques, as well as possible ways of implementation [4].
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To carry out research and experimental activities and the implementation and
dissemination of the results, the Joint research laboratory of the Institute of
Information Technologies and Learning Tools of the NAPS of Ukraine and the
Kherson State University was created in 2011 with the focus on issues of educational
quality management using ICT [29].
As part of the programme of joint research work, the Kherson State University was
approved as an experimental base for research on the definition and experimental
verification of the didactic requirements and methods of evaluating the quality of
electronic learning resources in the educational processes of the pilot schools [29].
The purpose of the experiment carried out was to identify and experimentally verify
the requirements and methods of evaluating the quality of the electronic learning
resources used in the educational process in secondary schools [29].
The quality evaluation of EER in the cloud-based learning environment is a
separate line of work in the Laboratory’s research. In this case, there are different
approaches and indicators. The access organization has been changed so the models
of learning activity have been changed also. There are the following questions: What
features and properties have to be checked so as to measure the pedagogical effect of
the cloud-based approach? With regard to the pedagogical innovation, what are the
factors influencing pedagogical systems, their structure and organization? Is the
improvement in learning results achieved due to the cloud-based models? In this
context, the quality of EER is a criterion for estimating the level of organization and
functioning of the cloud-based learning environment.
With regard to this, the following hypothesis is to be posed: the design of the
learning environment on the basis of cloud models of access to learning resources
contributes to the improvement of the quality of these resources and the improvement
of the processes in this environment and their organization and functioning, resulting
in an improvement in learning results.
In the cloud-based learning environment, new ways of EER quality control arise.
There are specific forms of the organization of learning activity related to quality
estimation. For example there are e-learning systems based on the modelling and
tracking of individual trajectories of each student’s progress, knowledge level and
further development [28]. This presupposes the adjustment, coordination of training,
consideration of pace of training, diagnosis of achieved level of mastery of the
material, consideration of a broad range of various facilities for learning to ensure
suitability for a larger contingent of users. The vast data collections about the
students’ rates of learning are situated and processed in the cloud [28]. There are also
collaborative forms of learning where the students and teachers take part in the
process of resource elaboration and assessment; this is possible in particular by means
of the SageMathCloud platform [2].
The prospective way of the estimation of the quality of learning resources is by
means of the cloud-based environment. As the resources are collectively accessed,
there is a way to allow experts into the learning process so they may observe and
research their functioning. This is a way to make the process of quality estimation
easier, more flexible and quicker. The process of estimation becomes anticipatory and
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timely. The estimation may be obtained just once along with the process of EER
elaboration, and it is very important to facilitate the process.
This method of estimation was developed and used in the Joint laboratory of EER
quality control [29]. In this case, the different quality parameters will be detailed and
selected. It is important that the psychological and pedagogical parameters are
estimated in the experimental learning process, while the other types of parameter
such as technological or ergonomic may be estimated out of this process.
The indicator of accessibility is also included in the focus of this investigation [15].
This property is essential because it is prior to other features such as scientific
correctness, clarity, consistency and others, which may be researched only if this
resource is available and feasible. The accessibility is characterized in turn by such
features as convenience of the access organization, ease of use, interface consistency,
advisability and others.
5 The Types of Service Models for Learning Resources Access
According to recent research, a unified storage architecture is an advantage of
cloud based settings allowing application virtualization [18, 19]. This architecture is
designed for the large complex data sets retrieving and management and it has the
following features:
different storage protocols are maintained in the same system (FC, NFS,
FcoE, CIFS, iSCSI);
various storage functions are implemented within the same device (storage,
security, backup, recovery);
storage space is scaled and modified without interruption of usual operations;
data are integrated in a standard pool, which can be controlled over a
network and managed via standard software package;
data are used for different range of applications while storage area is not
necessarily separated to enable saving computing capacity through virtualization.
Application virtualization is a technology for software access and development
without installing it on a personal computer of a user. Data processing and storage is
fulfilled in a data centre, and working with applications is not different for a customer
from the working with applications installed on his (her) own desktop.
There are three main types of service models [16] that correspond to different ways
the ICT outsourcing used to provide software and computing resources access [4]. In
particular, SaaS (Software-as a Service) is to deliver software applications of a
provider via the Internet; PaaS (Platform as a Service) is to develop and implement
software applications created by a user via the Internet; IaaS (Infrastructure as a
Service) is to provide on-line infrastructure where a customer may develop whatever
software applications [19].
P.Mell and T.Grance define various service models of the cloud-based architecture
(Fig.1) [16]. These models may be purposefully used for providing software access in
educational institutions.
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SERVICE MODEL ARCHITECTURES
Cloud Cloud Cloud
Infrastructure Infrastructure Infrastructure
SaaS
architectures
IaaS
PaaS PaaS
SaaS
SaaS SaaS
Cloud PaaS
Cloud Infrastructure
Infrastructure architectures
IaaS
PaaS PaaS
Cloud IaaS
Infrastructure
architetures
IaaS
Fig. 1. Service model architectures (After P.Mell, T.Grance [16]).
There are also four service deployment models for cloud computing application
that reflect the mode of the cloud infrastructure set up in a particular organization: the
corporate cloud is owned or leased by the organization; the cloud community is a
shared infrastructure used by a community; the public cloud is a mega-scale
infrastructure that may be used by any person under some payment terms; the hybrid
cloud is a composition of one or more models [4, 16].
In view of the different models for cloud service architecture, when choosing the
most appropriate solution that is suitable for a particular organisation, both collective
and individual users should be considered. Selecting the SaaS model in this respect
can be justified by the fact that these services are the most accessible, although a
thorough market analysis and educationally prudent choice of the necessary
application that could fit learning or scientific purposes is to be made. This kind of
service may be purposefully used by an individual and also a collective user.
At the same time, for the settlement of the ICT infrastructure of the institution by
the PaaS or IaaS model, the selection and approval of the relevant cloud platform is
necessary. This solution is concerned with a number of organisational issues, such as
the formation of a special unit of ICT personnel skilled in setting up and deploying
this infrastructure, configuring the hardware and software complexes, planning and
working out the environmental design tasks, testing and approving its modules and
components, filling it with the necessary resources, monitoring its implementation,
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maintaining quality control, training the teaching staff, etc. [4]. In this case, given the
results of recent research and the current trends in IT sector development, the use of
hybrid service models appears to be a promising and prospective solution. The hybrid
solutions are reported to be well-embedded into existing settlements provided by
leading cloud suppliers, and this tendency is growing [9]. The hybrid cloud
incorporates public and corporate cloud tools that do not necessarily exclude the
involvement of software-as-a-service applications [19].
As shown in Fig.1, there are three approaches to implementation of learning
software access in the SaaS architecture. In the first case (directly SaaS) the cloud
platform deployment is not necessary in the educational institution this work is
undertaken by a service provider. In both other cases the corporate or hybrid cloud
deployment is needed. In this case the appropriate cloud platform (eg, Amazon Web
Services, Microsoft Azure, Eucaliptus, Xen, WMWare etc.) is used to deploy the
certain service model. In the process of cloud infrastructure configuration the
guidelines are usually supplied by the vendor [1]. These guidelines contain a number
of basic deployment scenarios that can be implemented. It is possible to build the
cloud by means of different software and services but the basic notions are to be
considered. One of the basic concepts of the cloud based learning environment
configuration is the concept of a corporate cloud or a virtual private cloud (VPC).
Sometimes the term is used not very clearly so as to describe the corporate cloud that
may include a public and also a private part so being the hybrid one. Depending on
the scenario chosen the certain model of software access is considered.
As a rule the cloud provider may propose services of several types. For example, it
is possible to rent additional disk space (S3); the virtual machine (EC2), with certain
parameters of the processor, memory, and disk capacity, it may be with some installed
operational system and software; remote database (SimpleBD, RDS) and others [1].
Depending on the chosen scenario these resources are configured within the cloud
infrastructure.
There are four types of scenario for the cloud infrastructure configuration that are
mostly proposed by the provider [1]:
Scenario 1: VPC with only public subnet. The configuration of the virtual cloud
under this scenario contains a single public subnet and Internet gateway so as to
enable communication over the Internet. This configuration is recommended if it is
necessary to run the single level, public web applications such as blogs, web sites [1].
Scenario 2: VPC with public and corporate subnets. The configuration for this
scenario includes a public and corporate (private) subnet. This configuration is
recommended if it is necessary to run a public web application, while internal servers
are not publicly available. An example is a multi-website with the web servers
situated in a public subnet, and the database servers to be in a corporate subnet. It is
possible to configure the security services and routing so that the web servers could
interact with the database servers [1].
Scenario 3: VPC with the public and corporate subnet components and virtual
private network (VPN) access. The configuration for this scenario includes the virtual
hybrid cloud with the public and corporate subnets and the virtual corporate gateway
namely the VPN connections. In an educational institution may be own subnet, which
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should be expanded by augmented cloud services, such as additional disk space,
databases, virtual machines, network gateways, additional "desktops" and so on.
VPN-connection is used to enable communication with this subnet. You can also
create the virtual cloud subsystem (subnet virtual machine) with access to the
corporate subnet via the Internet [1]. For this scenario, the multi-level applications
with scalable web services may be run, some parts of these applications are in the
public subnet, and another parts are in the corporate subnet, which is connected to
own subnet through the VPN channel [1]. This allows you to keep some data in the
limited access.
Scenario 4: VPC subnet with the corporate VPN access components. The
configuration for this scenario includes the virtual corporate subnet and the virtual
gateway to allow communication with own subnet through the VPN channel. This
scenario is recommended if there is a need to expand own subnet into the cloud, as
well as to provide direct access to the Internet from this subnet without making it
"visible" from the Internet [1].
On the stage of environment design all the possible configurations were considered
and the model of the Scenario 3 was chosen so as to provide the hybrid infrastructure
were the corporate and public components were used (Fig. 2).
Internet IC2
VPC
Public Subnet
VPN Privat Subnet
server
Fig. 2. The Hybrid Cloud configuration.
6 The Hybrid Service Model of Learning Software Access
To research the hybrid service model of learning software access, a joint
investigation was undertaken in 2013–2014 at the Institute of Information
Technologies and Learning Tools of the NAPS of Ukraine and Drohobych State
Pedagogical University named after I.Franko. At the pedagogical university, the
experimental base was established where the cloud version of the Maxima system
(which is mathematical software), installed on a virtual server running Ubuntu 10.04
(Lucid Lynks), was implemented. In the repository of this operational system is a
version of Maxima based on the editor Emacs, which was installed on a student’s
virtual desktop [21]. In this case, the implementation of software access due to the
hybrid cloud deployment in Scenario 3 was organised.
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Fig. 3. The hybrid service model of the learning resources access.
In Fig.3, the configuration of the virtual hybrid cloud used in the pedagogical
experiment is shown. The model contains a virtual corporate (private) subnet and a
public subnet. The public subnet can be accessed by a user through the remote
desktop protocol (RDP). In this case, a user (student) refers to certain electronic
resources and a computing capacity set on a virtual machine of the cloud server from
any device, anywhere and at any time, using the Internet connection.
In this case, a user's computer is the RDP-client, while the virtual machine in the
cloud is the RDP-server. In the case of a corporate (private) subnet, a user cannot
apply to the RDP-server via desktop because it is not connected to the Internet
directly. Computers in the corporate subnet have Internet access via the VPN-
connection, i.e. the gateway. Thus, these computers cannot be accessed from any
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device, but only from the specially configured one (for example, a computer in the
educational institution or any other device where the VPN-connection is set up)
(Fig.3).
The advantage of the proposed model is that, in a learning process, it is necessary
to use both corporate and public learning resources for special purposes. In particular,
the corporate cloud contains limited access software; this may be due to the copyright
being owned by an author, or the use of licensed software products, personal data and
other information of corporate use. In addition, there is a considerable saving of
computational resources, as the software used in the distributed mode does not require
direct Internet access for each student. At the same time, there is a possibility of
placing some public resources on a virtual server so the learner can access them via
the Internet and use the server with the powerful processing capabilities in any place
and at any time. These resources are in the public cloud and can be supplied as
needed.
7 Implementation and Empirical Evaluation
In the joint research experiment held at Drohobych State Pedagogical University
named after I.Franko, 240 students participated. The aim was to test the specially
designed learning environment for training the operations research skills on the basis
of the Maxima system. During the study, the formation of students’ professional
competence by means of a special training method was examined. The experiment
confirmed the rise of the student competence, which was shown using the χ 2 –
Pearson criterion [21]. This result was achieved through a deepening of the research
component of training. The experiment was designed using a local version of the
Maxima system installed on a student’s desktop.
The special aspect of the study was the expansion of these results using the cloud
version of the Maxima system that was posted on a virtual desktop. In the first case
study (with the local version), this tool was applied only in special training situations.
In the second case study (the cloud version), the students’ research activity with the
system extended beyond the classroom time. This, in turn, was used to improve the
learning outcomes.
The cloud-based electronic learning resource used in the experiment has undergone
a quality estimation. The method of quality estimation in the joint laboratory of
educational quality management with the use of ICT was used for this study [29]. The
25 experts were specially selected as having experience in teaching professional
disciplines focused on the use of ICT and being involved in the evaluation process.
The experts evaluated the electronic resource with such parameters as “Ease of
access”, “Ease of use” and “Usefulness”. These parameters were chosen as they
contribute to the accessibility of the cloud resource and the cloud-based learning in
order to determine its feasibility and availability.
308
The problem was: is it reasonable and feasible to arrange the environment in a
proposed way? There were three questions part of the access realisation mode
(Table 1):
Table 1. The questionnaire.
Parameter Value
1 Ease of access Is the electronic 0 (no),
resource access easy 1 (low),
and convenient? 2 (good),
3 (excellent)
2 Ease of use Is the user 0 (no),
interface clear and 1 (low),
convenient? 2 (good),
3 (excellent)
3 Usefulness Is this resource 0 (no),
useful? 1 (low),
2 (good),
3 (excellent)
A four-point scale (0 (no), 1 (low), 2 (good), 3 (excellent)) was used for the
questions. The 25 experts estimated two parameters, “Ease of access” and “Ease of
use”, and were invited to examine the resource. Experience using this resource in the
learning process was not mandatory. The third parameter, “Usefulness”, was
estimated only by the seven experts who used the resource in the learning process.
The results of the evaluation are shown in Fig.4.
Fig. 4. The results of the cloud-based learning resource quality parameters evaluation.
The resulting average value was calculated for every parameter: “Ease of access” =
2.2, “Ease of use” = 1.86 and “Usefulness = 2.1. All criteria were weighted as one,
and the total value was 2.1. This characterises the resource accessibility as sufficient
for further implementation and use.
The advantage of the approach is the possibility to compare the different ways to
implement resources with regard to the learning infrastructure. Future research in this
area should consider different types of resources and environments.
309
8 Conclusion
The introduction of innovative technological solutions into the learning
environment of educational institutions contributes to unified learning infrastructure
formation and the growth of access to the best examples of electronic resources and
services. ICT use is promising regarding learning settings that can advance and
develop the tendencies of CC progress. For example, using the cloud-based models of
environment design, virtualising applications, unifying infrastructure, integrating
services, increasing the use of electronic resources, expanding collaborative forms of
work, widening the use of the hybrid models of ICT delivery and increasing the
quality of electronic resources.
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Methods and Technologies for the Quality Monitoring of
Electronic Educational Resources
Hennadiy Kravtsov1
1
Kherson State University
27, 40 rokiv Zhovtnya St., 73000, Kherson, Ukraine
kgm@ksu.ks.ua
Abstract. Support of the quality of training is one of the main objectives of the
university system. The results of modeling the quality management system of
electronic educational resources (EER) on the basis of the analysis of its elements
are presented. The subject of the study is the EER quality monitoring. Technolo-
gies for EER quality monitoring are based on the method of expert evaluations.
The criterion of EER quality is considered as the weighted average value of qual-
ity indicators. The weights of EER types and indicators of EER quality for their
types are evaluated in pedagogical experiment. Results of experiment confirmed
the assumption that the method of expert evaluations can be the basis for the EER
quality monitoring. Concordance method is used to assess the degree of consen-
sus of experts on the factors: weights of EER types, parameterization of EER
quality indicators, and weighted average criterion of EER quality. The model of
quality management system is shown in the example of assessing the quality of
the distance learning system resources.
Keywords. quality management system, electronic educational resources, moni-
toring of quality, distance learning system «Kherson virtual university».
Key Terms. QualityAssuranceMethodology, StandardizationProcess, Knowl-
edgeManagementMethodology, KnowledgeManagementProcess, Teaching-
Methodology.
1 Introduction
Electronic educational resources (EER) is object of quality management system of
the educational process with the use of ICT [1, 2]. There are two main approaches to
the concept of quality EER: compliance with standards and customer requirements.
Therefore it is necessary to take into account two aspects: compliance with educational
standards and meeting the requirements of students and teachers of the university. The
compatibility with international standards IMS, SCORM can be chosen as a criterion
for EER quality.
Improving the EER quality is the main purpose of the quality management system
(QMS) [3]. Implementation of QMS in institutions can improve processes by establish-
ing the effective and efficient management systems. Thus, EER quality management
312
provides tools, methods and technologies for the continuous improvement of the edu-
cational process. This improves performance, reduces the costs and ultimately increases
the competitive advantages of the institution.
Standards ISO 9000/9001 and ISO 29990 represent one of the models of manage-
ment of the institution to ensure the quality of the educational process [4]. Monitoring
is an essential tool of evaluating the quality of the educational process, in particular the
quality of the EER. The EER quality monitoring is understand as continuous process
of observation and recording EER parameters and their subsequent evaluation. Quality
monitoring provides expert advice according to the estimating procedure of the EER.
Because EER are classified as electronic educational editions and at the same time
they are software products then EER quality monitoring should be multilevel taking
into account their classifications.
The basic types of electronic educational resources for EER quality monitoring
should be assigned. For each EER type the weight factors and quality indicators should
be offered. The general criterion of quality electronic resources should be used to assess
their quality. It is average weighted characteristic of quality and takes into account the
weights of resource types and their relative quality indicators. The assessment of EER
quality monitoring is given by a corresponding university commission of experts [1].
Task of the present work is the analysis, calculation and optimization of parameters
of EER quality management system with use of methods for the analysis of complex
systems [5].
2 Model of EER Quality Management System
The EER quality management system is a structural element of architecture of edu-
cation quality management system in the higher educational institution. It plays a feed-
back role in EER quality management system of educational process.
The structure of EER quality management system is presented on figure 1 [1].
Let's list the basic elements of quality management system of electronic resources of
learning.
Assessment of EER quality underlies a quality management system of electronic
resources of learning. For an assessment of EER quality it is necessary:
to carry out monitoring for control of EER quality on a fixed basis;
to have a feedback with users of EER for the account of wishes in their improve-
ment from positions methodical and program-technology requirements.
It is necessary to develop these criteria of EER quality for carrying out of monitoring
of quality. The university council of experts confirms the criteria of EER quality devel-
oped by the methodical commissions. The university council of experts also confirms
the recommendations about improvement qualities of EER received as a result of the
analysis of users’ responses in Feedback system.
Results of an assessment of EER quality should be used on the one hand for im-
provement of their substantial part and satisfaction to technology requirements, and on
the other hand for publication of a rating of electronic learning resources that also pro-
motes the increase of their quality.
313
EER Quality management system
University coun- Monitoring of Standards and
cil of experts EER quality certification ISO
9000/9001
Assessment of
Feedback system Rating of EER
EER quality
Training of teach- EER Support Designing and
ers and employees and upgrade purchase of new
EER
Educational process
Fig. 1. Structure of EER quality management system.
Monitoring of EER quality has a leading role at their assessment of quality. The
analysis of electronic resources of learning shows, that they have the following classi-
fication: to a functional character they can be referred to learning editions, under the
form of representation they belong to a category of electronic editions, on the technol-
ogy of creation they represent software product [5]. Therefore the monitoring of quality
of electronic educational resources should be multi-criterion and multilevel according
to their classification. The satisfaction requirement to the universal international stand-
ards that are IMS, SCORM [6] is the uniting attribute of multilevel monitoring of EER
quality.
At monitoring of EER quality it is necessary to consider, the certain typological
model of system of educational editions for high schools which includes four groups of
the educational information resources differentiated to a functional sign, defining their
value and a place in educational process has affirmed [7]: learning-methodical, training,
auxiliary and supervising.
At monitoring of EER quality by criterion of compatibility with educational stand-
ards at definition of quality indicators it is possible to use specifications IMS which
describe information model of educational objects. These specifications define the
314
standardized set of information blocks which contains data about an educational re-
source. The IMS-package which contains educational object consists of two main ele-
ments [6]:
the IMS-manifesto – a special file which describes the base resources, the mainte-
nance and the organization of educational object (it is represented in language
XML);
the physical files which make educational object.
At monitoring of EER quality it is necessary to consider their typical classification:
electronic textbooks and methodical manuals, practical and virtual laboratory works,
tests and training simulators, etc.
Among all EER the special role is played by a distance learning course. It is the basic
educational object which is used in distance learning. It is compound training object
which unites various EER for the purpose of the organization of learning process with
use of special program environments – Distance Learning System (DLS). The example
of such program environment which allows to create, keep and use distance courses, is
DLS «Kherson Virtual University» [7].
The criterion of EER quality is considered as the average factor of quality K = (α1k1
+ α2k2 + … + αnkn)/n, where αi – average value of quality indicators, ki – value of weight
factor of i-type resource.
The general relative average criterion of EER quality can be calculated under the
formula [1]
K i1 aiti .
N
(1)
Here ai = ni∙γi – the quality metrics, i k /k – average factor of quality,
mi
iM
j 1 ij
ni – weight factor, mi – quantity of metric indicators of quality, kij – j-indicator of qual-
ity, kiM – the maximum value of an indicator of quality, ti – the generalized factor of
quality of i-type resource, N – quantity of EER.
The Feedback system serves as the tool for the organization of flexible and all-round
polls of opinions of students and teachers of university. Usually the system takes ques-
tioning in an automatic mode. The generalized assessment of EER quality was received
after statistical processing of results of questioning of users, it gives the opportunity to
consider the degree of their demand at quality monitoring.
Standards and certification ISO 9000/9001. Certification is a documentary
acknowledgement of conformity of production to certain requirements, concrete stand-
ards or specifications. It is necessary to notice, that conformity to standard ISO
9000/9001 does not guarantee high EER quality. However conformity to requirements
and recommendations of these standards is a necessary condition of high quality of
resources of training. The certificate of conformity ISO 9001 is acknowledgement of
satisfaction to standard requirements.
Standard ISO 9000/9001 is fundamental, the terms and definitions accepted in it are
used in all standards of a series 9000. This standard is a basis for understanding of base
elements of QMS according to ISO standards.
Requirements of standard ISO 9000/9001 can be used as criteria at the organization
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and carrying out of monitoring of EER quality.
University council of experts. In the control system of EER quality the university
advisory council is the body which is responsible for adequacy assessment of EER
quality taking into account all criteria and indicators of quality. It adopts the Regulation
about ERR quality management system, defines the criteria of their quality, forms rules
of carrying out and confirms results of an assessment of quality, and also plans actions
for improvement of EER quality.
The university advisory council defines the procedure of carrying out of monitoring
of EER quality. It confirms the list of criteria of quality, their weight factors and values
of indicators of quality according to (1).
Support and upgrade of EER is the important part of work in QMS for improvement
and optimization of EER software at its use in educational process. Support EER is one
of the phases of the software lifecycle. The software logs the detection correction, and
add new functionality to increase efficiency. Support software is defined by standard
IEEE Standard for Software Maintenance (IEEE 1219), and the life cycle standard is
specified ISO 12207.
The important factor of increase of efficiency usage of EER is training of users and
maintenance them with regular support at work with the current software version.
3 Integrated and differentiated approaches in modeling and use
of EER quality management system
The control system of EER quality is a model which describes the business process
including actions and activity of services of university according to functionality of
structure described above the scheme of EER quality management (fig. 2). It is neces-
sary to notice, that some elements of this system possess the property of close interre-
lation and have various degrees of influence on it. Thus some elements of the system
(for example, «University Advisory Council» and «Standards and Certification ISO
9000/9001» at monitoring of EER quality) can be united in groups which we will name
services. Therefore for the purpose of allocation of major factors of a quality control
system, influencing quality of its work, on the basis of its structure (fig. 2) we form
three main places of maintenance of EER quality: service of quality monitoring, service
of quality assessment and EER support and upgrade service. We will define structure,
primary goals, requirements and expected results of work of these services.
The Service of quality monitoring is intended for the organization and carrying out
of EER quality monitoring which are used in educational process, by criterion of their
conformity to the international educational standards. The University advisory council
defines the order and rules of carrying out of monitoring of EER quality.
Service tasks: the coordination of parameters and development of criteria of EER
quality, taking into account the requirements of standards, carrying out of analysis of
EER by the developed and coordinated criteria.
Requirements: carrying out monitoring on fixed basis, completeness of coverage of
all kinds of EER, objectivity of application of criteria of quality.
Expected results: data of the analysis of EER characteristics for their assessment of
316
quality.
The Service of an assessment of quality makes EER assessment on the basis of the
confirmed criteria taking into account the opinion of users – both students, and teachers.
Feedback system can be used for automation of carrying out polls and processing of
results.
Service tasks: to assess of EER quality by the developed and coordinated criteria on
the basis of the analysis of their characteristics for maintenance of formation of rating.
Requirements: objectivity, publicity, competitive character.
Expected results: on the basis of quality assessment to generate the list of reclama-
tions to electronic resources of learning for performance of works on their elimination
and to make rating of EER for increasing of motivation of authors of resources for
improvement of their quality.
The Service of EER support and upgrade carries out the organization, planning and
performance of works on improvement of their quality by correction of the noticed
lacks, realization of new didactic properties and possibilities of electronic resources of
learning. Experts of this service give consulting services in acquiring new EER, and
also take part in training of teachers and employees to use them.
Service tasks: on a constant basis taking into account an assessment of EER quality
to perform works on their upgrade and as much as possible to satisfy inquiries of users.
Requirements: operatively, qualitatively and full performance of works.
Expected results: upgrade and introduction new and improved EER in educational
process of university.
3.1 Analysis EER QMS by criteria of its elements importance
Services of control system of EER quality provide the consecutive process of their
monitoring, assessment of quality and support. Thus Feedback system plays a feedback
role in this process. On fig. 2 the function chart of work of services of EER QMS is
presented.
According to methods of the theory of automatic control we will designate through
Wi (p) - transfer functions of EER quality of corresponding services (i = 1,2,3) and Feed-
back system (i = 4) [8]. According to rules of calculation of consecutive connection of
links of system and taking into account Feedback system transfer function of opened
system W(p) is expressed through the transfer functions of corresponding links Wi (p)
under the formula
W1 ( p) W2 ( p) W3 ( p)
W ( p) . (2)
1 W2 ( p) W3 ( p) W4 ( p)
It is necessary to notice, that the Feedback system can play a role both local negative
(–), and local positive (+) feedback. Thus the role of a negative feedback is more sig-
nificant and more often is used in work of EER QMS as the main mission of EER QMS
consists in revealing of resources of poor quality and their upgrade. At the same time
the system can be in a status of action of a local positive feedback in case of a mode of
317
popularization of the best practices on creation qualitative EER.
1. Quality monitoring
service
2. Service of EER qual- 4. Feedback sys-
ity assessment tem
3. Service of EER sup-
port and upgrade
Fig. 2. The scheme of service functionality in the EER quality management system.
With sufficient degree of generality it is possible to consider the model of ideal
strengthening of links of system. Then Wi(p) = ki (i = 1,2,3,4), where ki-factors of im-
provement of EER quality of corresponding i-links of system. Generally for factor k
improvement of EER quality of all the QMS from (2) we have expression
k1 k2 k3
k . (3)
1 k2 k3 k4
Considering, that the control system of EER quality is a global feedback in architec-
ture of control system of learning quality, the condition performance suffices for
maintenance of improvement of electronic resources quality k > 1 or
k1∙ k2∙ k3 > 1 ± k2∙ k3∙ k4. (4)
The correlation (3) together with a condition (4) allows to apply the differentiated
approach to the account of degree of importance of elements of EER QMS, and also to
optimize parameters of this system.
3.2 Methods of calculation and optimization of parameters of EER QMS
For the purpose of optimization of parameters of EER QMS we will apply the
method of consecutive allocation of the major elements of system by criterion of their
influence on system from the point of view of EER quality. In considered above the
model of ideal strengthening of links of system the factors of improvement of EER
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quality can act as weight factors of the importance of elements of EER QMS of learn-
ing. The optimum combination of values of these factors will promote the optimization
of operating modes of all control system by quality of electronic resources. In practice
factors k1, k2, k3 and k4 are not the determined parameters, and have properties of ran-
dom variables with the known law of distribution therefore at modeling of optimum
statuses of EER QMS it is necessary to apply statistical methods of calculation and
optimization of parameters of system.
As example of use of statistical methods of calculation and optimization of parame-
ters of system the calculation of an average of distribution of factor k improvement of
EER quality depending on average of distributions of factors ki can serve. Optimization
of dispersion of values k is realized by imposing of restrictions on known values of
average of distributions and mean square deviations of factors ki.
4 Implementation and Empirical Evaluation of EER quality
management system
4.1 Method of expert evaluations of EER quality
In assessing the EER quality by the form of organization the method of collective
estimation is used with collective expert opinion. This method is used to obtain quanti-
tative estimates of the quality characteristics, parameters and properties. Analysis of
expert assessments involves filling each individual expert appropriate form, the results
of which are a comprehensive analysis of the problem situation and possible solutions.
The results of peer reviews are issued as a separate document.
The purpose of peer reviews of EER quality is an evaluation of EER quality indica-
tors with international, national and industry standards, the EER quality monitoring,
quality of the learning process through the use of qualitative EER and processing meth-
ods, criteria and forms for certification e-learning.
Objects and parameters of EER assessment:
Classification of EER types.
The weight factors of EER types (EER relative priority for their type).
Factors and criteria of EER quality for their types.
The following forms of expertise processing of EER quality are:
1. Definition of the competence of experts and the formation of the expert commit-
tee.
2. Evaluation of weight factors ranging of EER types.
3. Parameterization of EER quality indicators.
4. Expertise processing of EER quality.
5. Study the adequacy of the results of expertise.
Expert committee is created for the EER expertise with use of peer reviews method.
Delphi method is used in the formation of the expert committee and expertise pro-
cessing [9]. Top teachers, methodologists and researchers of higher education institu-
tions are involved in the commission of experts.
Since EER are classified as electronic publications for educational purposes and they
319
are software products, the examination of the quality of electronic educational resources
should be layered with regard to their classifications. Therefore, the EER quality should
be analyzed by the software and technological, psychological, pedagogical and ergo-
nomic features.
EER quality indicators are derivative of the requirements for them. Meeting the re-
quirements of program-technological, psychological, pedagogical and ergonomic ones
are a measure of EER quality assessment in determining their quality indicators
In this case the development of tools is based on modern fulfilled hygiene, ergo-
nomic and technical and technological standards to the use of computer technology and
is governed by existing regulations or standards. You can ask to have developed tech-
nology expertise of EER quality indicators that can be fully regulated in detail. How-
ever, there are problems of evaluating these indicators related to obsolescence of exist-
ing standards and the fact that definition of quality are not further developed.
4.2 The EER quality monitoring in educational institutions
Monitoring and evaluation (M&E) is a process that helps improving performance
and achieving results. Its goal is to improve current and future management of outputs,
outcomes and impact [10]. Consider the EER quality monitoring by the example of
DLS «Kherson Virtual University» [7].
Formation of the commission of experts. Determining the validity of each of the
three subjects of the educational process was made by expert evaluation method. 25
qualified experts (university teachers, graduate students, methodologists) was joined
the independent expert committee.
To define a point of evaluation for each subject Delphi method (for members of the
expert committee conditions for an independent individual work were created) was
used. The statistical processing of the results, which were presented to experts for final
approval, had been conducted.
Construction of weights ranging of EER types. The weight factor of EER type is
a numerical coefficient, a parameter that determines the value, the relative importance
of this EER type than other types that are classified EER on functional grounds.
Table 1 shows an example of a possible evaluation of EER weighting coefficients
values according to their types.
Table 1. The weighting factors of EER types.
# Name of EER Type Description Weighting
factor
1 Electronic textbooks and books Full course of lectures, encyclopedia 24,9
2 Lectures notes, laboratory and Lectures annotations, laboratory and 21,2
practical work notes practical work annotations
3 Lecture Presentation Author lecture in Power Point format 16,0
4 Video Lecture Author lecture in video format 19,5
320
5 Audio Resource Author EER in audio format 15,1
6 Learner's guide Electronic learner’s guide in discipline 26,9
7 Guidance for conducting semi- Full description of seminars, laboratory 18,8
nars and laboratory works and practical works
8 Laboratory work Virtual laboratory works in discipline 21,3
9 Test Full set of questions with indicating 17,6
correct answers
10 Library of electronic visual aids The library of visual learning objects in 26,3
a graphical format
11 Collection of tasks, exercises, Author's electronic resource 25,9
vocabulary
12 Training computer game Author's electronic resource 23,9
13 The work program of the course Approved author’s work program in 19,6
discipline
14 Questions to exam/credit, self- In accordance with the work program 17,2
control
15 Print and Internet resources Basic and advanced print and online re- 18,4
sources of discipline with active hyper-
links
16 Distance course in the discipline Correspond to international standards 98,1
Parameterization of EER quality indicators
The EER quality indicator is a numerical parameter that determines the evaluation
the EER under its qualitative characteristic (can be used a five point Likert's system).
Also the EER types are specified, which are measured by this indicator. Filling out the
list of EER quality indicators and their attachment to the EER types is held after ap-
proving the list of EER types.
Parameterization of EER quality indicators means evaluation of quality by scaling
method [11]. Table 2 shows an example of evaluation of EER quality indicators under
their quality point scale.
Table 2. The EER quality indicators.
Name of EER quality indicator. What EER types is Quality charac- Quality
Description applied to teristics indicator
Completeness of methodical support All types 1. Full 5
of discipline 2. Incomplete 4
3. Average 3
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4. Below Average 2
5. Inadequate 1
Authorship of EER All types 1. Full 5
2. collaboration 3
3. Plagiarism 0
EER compliance with state educa- All types 1. Full 5
tion standards 2. Incomplete 3
3. No 1
EER compliance with international 1, 6, 9, 16 1. Full 5
standards:IMS, SCORM, ІEEE etc. 2. Incomplete 3
3. No 1
EER compliance to work program All types 1. Full 5
content 2. Incomplete 3
3. No 1
Completeness of presenting educa- 1, 2, 3, 6, 16 1. Full 5
tional material 2. Short 4
3. Note 3
4. Plan 1
The use of resources with respect to All types 1. High 5
the maximum possible 2. Mediate 3
3. Low 1
Structuring and formatting of educa- 1, 2, 3, 6, 7, 8, 11, 16 1. Yes 5
tional material 2. Partially 3
3. No 1
Text ergonomics 1, 2, 3, 4, 5, 6, 7, 8, 9, 1. Quality 5
10, 11, 12, 16 2. Mediate 3
3. Poor 0
Hypertext links use 1, 2, 3, 6, 7, 10, 15, 16 1. Yes 5
2. No 0
Use of visual methods in material 1, 2, 3, 6, 7, 8, 10, 12, 1. Quality 5
15, 16 2. Mediate 3
3. Poor 0
Using multimedia 1, 2, 3, 4, 5, 6, 7, 8, 9, 1. Quality 5
10, 12, 15, 16 2. Mediate 3
3. Poor 0
The use of interactive systems and 1, 2, 3, 6, 7, 8, 9, 10, 1. Yes 5
modules, simulation 11, 12, 15, 16 2. No 0
322
Using testing, the ability to control 1, 2, 3, 6, 7, 8, 9, 11, 1. Yes 5
knowledge, self-control 12, 15, 16 2. No 0
Use file formats standard 1, 2, 3, 4, 5, 6, 7, 8, 9, 1. Yes 5
10, 11, 12, 13, 14, 15, 2. Partially 3
16 3. No 0
Use tables, charts, figures 1, 2, 3, 6, 7, 8, 9, 10, 1. Yes 5
11, 15, 16 2. No 0
Compliance learning material to All types 1. Yes 5
knowledge level of students 2. No 0
Purpose of educational material to an All types 1. Yes 5
appropriate audience 2. No 0
Free access to educational material All types 1. Yes 5
2. No 0
The stylistic correctness of teaching 1, 2, 3, 6, 7, 8, 10, 11, 1. Quality 5
learning material 15, 16 2. Mediate 3
3. Poor 0
The sequence of teaching learning 1, 2, 3, 4, 5, 6, 7, 8, 1. Quality 5
material 10, 11, 13, 14, 15, 16 2. Mediate 3
3. Poor 0
Validity of test, tutorial 1, 3, 6, 7, 8, 9, 16 1. Yes 5
2. No 0
Automatic processing of test results 1, 2, 3, 6, 7, 8, 9, 11, 1. Yes 5
and knowledge control 12, 16 2. No 0
Accessibility of used informational 1, 2, 3, 6, 7, 8, 11, 15, 1. Yes 5
resources 16 2. No 0
Matching of EER components to All types 1. Quality 5
psychological requirements 2. Mediate 3
3. Poor 0
The study of the adequacy of experiment results
Expert evaluation of the EER quality can be considered sufficiently reliable only
when a good consistency of expert answers. Therefore, the statistical processing of the
results of experts evaluations should include an analysis of consensus of experts. Con-
cordance method is used to assess the degree of consensus of experts on the factors:
weights of EER types, parameterization of EER quality indicators, and average factor
of EER quality [12].
Experts were asked to complete the table 1 for peer review weighting factors of EER
types. The values of the weighting factors were selected from 100 point scale. The re-
sults of the survey of experts are presented in Table 3.
323
Table 3. Expert data on weights of EER types.
Ex- ERR Types
pert #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16
1 2 11 14 7 9 4 5 3 6 12 8 10 13 15 16 1
2 2 11 14 4 8 9 10 5 6 16 3 7 12 13 15 1
3 3 10 12 7 8 2 6 4 5 11 9 13 14 15 16 1
4 4 7 10 6 8 2 5 3 9 12 11 14 13 15 16 1
5 2 10 14 9 8 3 12 4 5 6 7 11 13 15 16 1
6 3 9 10 8 7 2 6 4 5 11 12 14 15 13 16 1
7 2 12 11 8 10 5 4 3 7 13 6 9 14 15 16 1
8 3 8 13 4 7 2 6 9 5 12 10 11 16 14 15 1
9 4 10 11 6 8 2 3 5 7 12 9 13 14 15 16 1
10 2 5 13 8 7 3 6 4 10 11 9 12 16 14 15 1
11 2 11 12 6 10 5 4 3 8 13 7 9 14 15 16 1
12 2 9 11 7 8 3 4 5 6 10 12 13 14 15 16 1
13 3 10 9 8 13 2 5 4 6 12 7 11 14 16 15 1
14 3 12 13 7 9 2 4 5 6 11 8 10 14 16 15 1
15 2 8 12 6 10 3 5 4 7 13 9 11 14 15 16 1
16 5 10 11 8 6 2 3 9 4 12 7 13 14 15 16 1
17 2 9 10 7 8 4 14 3 6 12 5 11 13 16 15 1
18 2 13 11 8 10 5 4 3 7 14 6 9 12 15 16 1
19 2 6 13 11 9 3 4 5 8 12 7 10 14 15 16 1
20 4 11 10 7 8 2 3 5 6 13 9 12 15 16 14 1
21 2 12 7 8 13 3 4 5 6 11 10 9 14 15 16 1
22 5 14 13 9 2 3 6 4 7 11 8 12 16 10 15 1
23 3 11 14 7 9 5 4 2 6 10 8 13 12 16 15 1
24 2 12 13 8 7 3 6 4 5 11 9 10 16 14 15 1
Δi -138 37 77 -30 -2 -125 -71 -99 -51 77 -8 63 132 149 169 -180
Concordance coefficient W is calculated according to the formula proposed by Ken-
dall [12]
324
12S
W . (5)
m ( n 3 n)
2
x 12 m(n 1) , m – number of experts, n –
n n m 2
Here S
2
i 1 i i 1 j 1 ij
the number of objects of examination (e.g., EER types), xij – assessment of the i-object
by j-expert. Coefficient of concordance may vary between 0 and 1. If W = 1, all experts
gave the same evaluations for all objects, if W = 0, the evaluations of experts are not
coordinated.
Using the formula (5) we calculated that coefficient W = 0,872 and it is significantly
different from zero, so we can assume that among experts there is objective concord-
ance. Given that the value of m(n – 1)W is distributed according to χ2 with (n – 1) is the
12S
degree of freedom, then W
2
= 314,1. Comparing this value with the
m n (n 1)
tabulated value T for n – 1 = 15 degree of freedom and significance level α = 0,01,
2
we find W = 314,1 > T = 30,578. Therefore, the hypothesis of consistency of expert
2 2
evaluations confirmed according to Pearson.
Thus, the results of pedagogical experiment confirmed the assumption that the
method of expert evaluations can be the basis for the EER quality monitoring.
5 Conclusions and Outlook
The system of EER quality monitoring is based on the multi-criterion analysis of
conformity of these resources to the educational standards. Criterion of EER quality
compatibility with standards IMS, SCORM can be chosen.
Criteria of EER quality are described on a basis the multi-criterion analysis taking
into account EER compatibility with the international standards.
The basic types of electronic resources of educational appointment for carrying out
of monitoring of EER quality are allocated. For each type of EER their weight factors
and quality indicators are offered. The criterion of quality of an electronic training re-
source which is the average characteristic of quality is developed.
Technologies for EER quality monitoring is based on the method of expert evalua-
tions. The criterion of EER quality is considered as the weighted average value of qual-
ity indicators. The weights of EER types and indicators of EER quality for their types
are evaluated in pedagogical experiment. Results of experiment confirmed the assump-
tion that the method of expert evaluations can be the basis for the EER quality moni-
toring. Concordance method is used to assess the degree of consensus of experts on the
factors: weights of EER types, parameterization of EER quality indicators, and
weighted average criterion of EER quality. The model of quality management system
is shown in the example of assessing the quality of the distance learning system re-
sources.
325
The offered system of an assessment of ERR quality is not unique and supposes
additions and updating. The assessment of monitoring of EER quality is given by a
corresponding commission of experts of university.
The method of testing is used for the experimental verification of the results of expert
evaluation of the ERR quality. Electronic educational resources are subject to testing
by means of their actual use in the educational process. As a result of comprehensive
testing, a system of adjustments is formed to improve the ERR. The process of testing
and further development of electronic educational resources is an iterative cyclical pro-
cess. It should continue until achieving compliance with the ERR quality requirements.
Therefore, the process of testing is an element of the quality management system of
electronic educational resources. That study of ERR quality management system with
their testing in educational process is the prospect of further work.
References
1. Kravtsov H.M. Design and Implementation of a Quality Management System for Electronic
Training Information Resources / In: Ermolayev, V. et al. (eds.) Proc. 7-th Int. Conf. ICTERI
2011, Kherson, Ukraine, May 4-7, 2011, CEUR-WS.org/Vol-716, ISSN 1613-0073, P.88-
98, online CEUR-WS.org/Vol-716/ICTERI-2011-CEUR-WS-paper-6-p-88-98.pdf. – P. 88
– 98
2. H. Kravtsov. Structure of the Management System of Quality of Electronic Learning Re-
sources / Information Technologies in Education. 10th Issue. – Kherson. – 2011.– P. 94-101
3. Peris-Ortiz, M., Álvarez-García, J., Rueda-Armengot, C.: Achieving Competitive Ad-
vantage through Quality Management. Springer International Publishing Switzerland
(2015). – URL: http://www.springer.com/gp/book/9783319172507
4. ISO 9000 - Quality Management. – URL: http://www.iso.org/iso/home/standards/manage-
ment-standards/iso_9000.htm, Learning services for non-formal education and training
5. Bykov V. Yu. Models of the Open Education Organizational Systems: Monograph. – Kyiv:
Atika, 2009. – 684 p.: ill.
6. H. Kravtsov, D. Kravtsov. Knowledge Control Model of Distance Learning System on IMS
Standard / Innovative Techniques in Instruction Technology, E-learning, E-assessment, and
Education. – Springer Science + Business Media V.B. – 2008. – P.195 – 198.
7. H. Kravtsov. Evaluation Metrics of Electronic Learning Resources Quality / Information
Technologies in Education. 3d Issue. – Kherson. – 2009. – P. 141 – 147.
8. Jay C. Hsu, Andrew U. Meyer. Modern Control Principles and Applications. McGraw-Hill
(1968)
9. Rowe, G. & Wright, G. Expert Opinions in Forecasting: The Role of the Delphi Technique.
In: J.S. Armstrong (Ed.), Principles of Forecasting - A Handbook for Researchers and Prac-
titioners, pp. 125-144. Boston, MA; Kluwer Academic Publishers (2001)
10. Wikipedia – The Free Encyclopedia. – URL: https://en.wikipedia.org/wiki/Monitor-
ing_and_Evaluation
11. Kolen, Michael J., Brennan, Robert L. Test Equating, Scaling, and Linking. Methods and
Practices. Springer-Verlag New York (2004)
12. Kendall M. Rank Correlation Methods, Charles Griffen & Company, London (1948)
326
Realisation of “Black Boxes” Using Machines
Grygoriy Zholtkevych
Department of Theoretical and Applied Computer Science,
V.N. Karazin Kharkiv National University
4 Svobody Sqr, 61022, Kharkiv, Ukraine
g.zholtkevych@karazin.ua
Abstract. Modern engineering solutions attract attention of researchers
to well-known problems in the field of system theory and cybernetics in
general. The realisation problem of a “black box” is one among these
problems. In this paper the non-anticipation property for a “black box” is
generalised to the case of “black boxes”, whose behaviour admits deferred
decisions. Furthermore, for such “black boxes” it is shown that they can
be realised as pre-machines, which have been introduced by author jointly
with his co-authors in series of earlier papers.
Keywords: “black box”, deferred responses, sequential processing, pre-
machine, transfer function
Key Terms: Computation, Software Component, Specification Process,
Mathematical Model
1 Introduction
Let us suppose that two finite alphabets X and Y are given. The first of them
we identify as the alphabet of stimuli and the second one as the alphabet of
responses. Following to the general cybernetic concept [1, Chapter 6] we can
consider any mapping M : X ω → Y ∞ as the transfer function of some “black
box”, whose inputs belong to the set X ω of infinite sequences of stimuli and
outputs belong to the set Y ∞ of finite or infinite sequences of responses. The
realisation problem of such a mapping using a machine is the principal problem
that is solved by a system engineer. In other words a system engineer transforms
a “black” box into a “white box” or “glass box”.
The realisation problem had been studied in detail (see, for example, [6]) for
the mapping M : X ω → Y ω holding the following non-anticipation property1
if M (ux′ ) = y ′ , M (ux′′ ) = y ′′ for some finite sequence of stimuli
u = u1 u2 . . . un and x′ , x′′ ∈ X ω then y ′ = vz ′ and y ′′ = vz ′′ for (1)
some finite sequence of responses v = v1 v2 . . . vn and z ′ , z ′′ ∈ Y ω .
In this case there exists a Moore machine whose transfer function coincides with
the mapping M [4, 6].
1
This property informally means that a “black box” cannot use an information from
the future.
327
We should note the following: the previous formulation for the non-anticipa-
tion property implicitly implies that the “black box” responds immediately on
each stimulus. However there are systems having another reaction type. It is quite
possible such a system behaviour that requires to defer a response for as long as
the sufficient amount of the information will be received. For example, complex
event processing systems (see [7]) have such a reaction type. Therefore processes
of the specification and analysis for such systems require another models or at
least models, which generalise already existing ones. This paper is an attempt
to solve the realisation problem for “black boxes” with transfer function that
satisfies the generalisation being defined below of the non-anticipation property.
2 Prerequisites and Notation
The aim of this section is to give brief survey of some matters and explain the
basic notation used below.
At the paper we use the denotation N for the natural series with 0 .
For a set X (it is usually finite) we use the notation:
X ∗ denotes the set of all finite sequences (words) whose elements belong
to X ;
ε denotes the empty word;
X + denotes the set X ∗ r {ε} ;
X ω denotes the set of all (infinite) sequences whose elements belong to
X;
X ∞ denotes the union of the sets X ∗ and X ω .
Further, we use the denotation |u| for the length of the word u ∈ X ∗ and
assume that |x| = +∞ for any infinite sequence x ∈ X ω .
To refer to the k-th member of a word u ∈ X ∗ (or a sequence x ∈ X ω ) the
denotation u[k] (or x[k] respectively) is used.
For a word u ∈ X ∗ whose length is equal or greater than n (or a sequence
x ∈ X ω ) by u[1 : n] (or x[1 : n] respectively) we denote the word u[1] . . . u[n]
(or x[1] . . . x[n]).
Similarly, for a word u ∈ X ∗ whose length is greater than or equal to n (or
a sequence x ∈ X ω ) by u[n : ] (or x[n : ] respectively) we denote the word
u[n] . . . u[|u|] (or the sequence x[n]x[n + 1] . . .).
3 Non-anticipation Property
In Sec. 1 we have given the definition of the non-anticipation property for a
transfer function from X ω into Y ω under condition that the corresponding “black
box” reacts on each stimulus. Our nearest goal is to generalise the previous
definition for the case when a “black box” is capable to decide whether the
accumulated information is sufficient for the correct response and generates the
response if the decision positive otherwise postpones the response generation.
Firstly, it is needed to say that in this case the class of studied transfer
functions are being extended up to the class of mappings from X ω into Y ∞ .
328
Further, we should specify that the identity of prefixes for streams of stimuli
guarantees the identity of prefixes for the corresponding streams of responses.
The sequential character of processing streams of stimuli by a “black box” re-
quires that there exists a correspondence between word of stimuli u (as prefix of
the corresponding streams) and length N (u) of the response word (see Fig. 1).
u = x[1]x[2] . . . x[n] y[1]y[2] . . . y[N (u)]
“Black box”
N (u) ≤ n
Fig. 1. A sequential “black box”
The following definition is our attempt to present these considerations as a
formal specification.
Definition 1. We shall say that the non-anticipation property holds for a map-
ping M : X ω → Y ∞ if the following is true:
there exists a funtion N : X ∗ → N such that
1. N (u) ≤ |u| for any u ∈ X ∗ ;
2. if u′ ∈ X ∗ and u′′ = u′ x for some x ∈ X then
′ ′′ ′
N (u ) ≤ N (u ) ≤ N (u ) + 1 ;
(2)
′ ′′ ∗
3. if x , x ∈ u · X for some u ∈ X then
ω
(M x′ )[1 : N (u)] = (M x′′ )[1 : N (u)] ;
∗ ′ ′′
4. for any u ∈ X there exist x , x ∈ u · X such that
ω
′ ′′
(M x )[1 : N (u) + 1] 6= (M x )[1 : N (u) + 1] .
Remark 1. Informally, jump points for the function N introduced in Def. 1 de-
termine response instants of the “black box”. Items 3) and 4) ensure this inter-
pretation.
Remark 2. Item 2) ensures that the “black box” corresponding to a mapping
that holds the non-anticipation property generates at most one response at a
stimulus.
Remark 3. Item 3) and 4) of Def. 1 guarantee also that the existence of function
N for the mapping M : X ω → Y ∞ implies the uniqueness of N .
Remark 4. One can easy see that if N (u) = |u| then Def. 1 and the non-
anticipation property given in Sec. 1 specify the same class of mappings.
329
Now let us consider the partial mapping µ : X + 99K Y that is defined as
follows
µ(u) ↑ iff N (u) = N (u[1 : |u| − 1])
µ(u) ↓= M (uz)[N (u)] iff N (u) > N (u[1 : |u| − 1]) .
Item 3) of Def. 1 ensures the uniqueness of determining µ(u) .
Remark 5. Returning to Fig. 1, we note that µ(u) = y[N (u)] .
To determine the significance of the mapping µ let us consider the following
algorithm and proposition.
Require: a sequence of stimuli x ∈ X ω
Ensure: to print the corresponding sequence of responses
n=1
while True :
while µ(x[1 : n]) ↑ : n + = 1
print(µ(x[1 : n]))
n += 1
Algorithm 1: “Black box” algorithm for a mapping M : X ω → Y ∞ that holds
the non-anticipation property
Proposition 1. For any x ∈ X ω Algorithm 1 prints the sequence M x .
Proof. Taking into account (2) one can easy see that new response is printed only
if N (x[1 : n − 1]) 6= N (x[1 : n]) . In this case the printed symbol is (M x)[n] . ⊔
⊓
Definition 2. Let M : X ω → Y ∞ be a mapping that holds the non-anticipation
property then the corresponding partial mapping µ : X + 99K Y we shall call its
reaction function.
Conversely, we can consider a partial mapping µ : X + 99K Y and use Algorithm 1
to define the mapping M : X ω → Y ∞ .
Proposition 2. Let µ : X + 99K Y be a partial mapping then the correspondence
x ∈ X ω 7→ y ∈ Y ∞ , when y is the sequence printed by Algorithm 1 under han-
dling x , determines the mapping M : X ω → Y ∞ that holds the non-anticipation
property.
Proof. The key idea of the proof consists in the following recursive construction
of the function N : X ∗ → N :
base of recursion: N (ε) = 0 ;
step of recursion:
N (u), if µ(x) ↑
N (ux) = .
N (u) + 1, if µ(x) ↓
Now, easy seen that the mapping M holds the non-anticipation property. ⊔
⊓
330
4 Automata and Pre-automata
In this section we remind the definition of automata as the simplest discrete
systems that respond on external stimuli by changing their states. Automata are
actions of free finitely generated monoids on the state sets from the mathematical
standpoint. In [3] authors have introduced the notion of a pre-automaton using
a generalisation of the notion of an action known as a partial action. Taking
into account that these notions is used below and they are not widely used we
include this section to give the information necessary for understanding of the
further text.
4.1 Automata
We start our consideration reminding the definition of an automaton.
Definition 3. A triple A(X, SA , δA ) is called an automaton if X is a finite
alphabet of stimuli, SA is a set of states of the automaton, δA : SA × X → SA
is a mapping, which is called the transition function of the automaton.
An automaton behaviour is determined by a right action of the monoid X ∗ on
the state set SA [2].
Proposition 3. Let A(X, SA , δA ) be an automaton then the defined recursively
∗
defined mapping δA : SA × X ∗ → SA
∗
δA (s, ε) = s for any s ∈ SA ; (3)
∗ ∗
δA (s, ux) = δA (δA (s, u), x) for s ∈ SA , u ∈ X ∗ , x ∈ X (4)
is a right action of monoid X ∗ on the set SA .
Proof. To prove the proposition it is sufficient to check the equality
∗
δA (s, u′ u′′ ) = δA
∗ ∗
(δA (s, u′ ), u′′ )
for any s ∈ SA , u′ , u′′ ∈ X ∗ . Checking is a simple exercise in the application of
mathematical induction on the length of u′′ . ⊔
⊓
4.2 Pre-automata
The notion of a pre-automaton had been introduced in [3] by replacing the action
with the partial action in the definition.
∗
Definition 4. A triple P(X, SP , δP ) is called a pre-automaton if X is a finite
∗
alphabet of stimuli, SP is a set of states of the pre-automaton, δP is a right
331
partial action of the monoid X ∗ on the set SP , i.e. it is a partial mapping
∗
δP : SP × X 99K SP such that
∗
1. δP (s, ε) ↓= s for all s ∈ SP ;
∗
2. if δP (s, u′ ) ↓ and δP
∗ ∗
(δP (s, u′ ), u′′ ) ↓ then
∗
δP (s, u′ u′′ ) ↓= δP
∗ ∗
(δP (s, u′ ), u′′ ) ;
(5)
∗
3. if δP (s, u′ ) ↓ and δP
∗
(s, u′ u′′ ) ↓ then
∗ ∗
δP (δP (s, u′ ), u′′ ) ↓= δP
∗
(s, u′ u′′ ) .
4.3 Interrelations between Automata and Pre-automata
In this section we describe some method that allows us to construct a pre-
automaton using an automaton.
Suppose that we have taken some automaton A(X, SA , δA ) .
∗
Let us define the pre-automaton P(X, SP , δP ) in the following manner:
1. choose as SP an arbitrary subset of SA ;
2. define the partial mapping δP : SP × X 99K SP as follows for
∗ ∗
∗
s ∈ SP and u ∈ X let assign that (6)
∗
δP (s, u) ↑ if δA∗
(s, u) ∈
/ SP and
∗ ∗ ∗
δP (s, u) ↓= δA (s, u) if δA (s, u) ∈ SP .
Proposition 4. The triple defined by construction (6) is a pre-automaton.
Proof. Indeed, item (3) ensures that item 1) of (5) is satisfied.
Further, Prop. 3 implies that items 2) and 3) of (5) are satisfied. ⊔
⊓
The assertion just proved demonstrates that the method to obtain pre-
automata consists in hiding part of the states.
The converse assertion proved in [3] as Globalisation Theorem ensures that
the method considered above is the most general method to obtain pre-automata.
5 Moore Machines and Pre-machines
In this section we discuss the question about how a Moore machine or its gen-
eralisation, which we call a Moore pre-machine, can realise a “black box”.
5.1 Moore Machines
Usually, automata associate with “black boxes” in the following manner.
Firstly, the class of Moore machines is defined.
Definition 5. Let A(X, SA , δA ) be an automaton then the corresponding Moore
machine is a pentacle MA (X, SA , δA , s0M , λM ) where s0M is some fixed state of
A called the initial state of the machine and λM : SA → Y is a mapping called
the output function of the machine.
332
Then for a Moore machine is determined its reaction function.
Definition 6. Let MA (X, SA , δA , s0M , λM ) be a Moore machine then its reac-
tion function µM : X ∗ → Y is determined by the formula
µM (u) = λM (δA (s0M , u)) . (7)
Finally, we define the transfer function MM : X ω → Y ω for the machine MA
using its reaction function µM and Algorithm 1.
5.2 Moore Pre-machine
Here we repeat all constructions from the previous subsection substituting a
pre-automaton for an automaton.
Firstly, the class of Moore pre-machines is defined.
∗
Definition 7. Let P(X, SP , δP ) be a pre-automaton then the corresponding Mo-
ore pre-machine is a pentacle MP (X, SP , δP ∗
, s0M , λM ) where s0M is some fixed
state of P called the initial state of the pre-machine and λM : SP → Y is a
mapping called the output function of the pre-machine.
Then for a Moore pre-machine is determined its reaction function.
∗
Definition 8. Let MP (X, SP , δP , s0M , λM ) be a Moore pre-machine then its
+
reaction function µM : X 99K Y is determined in the following manner
∗
1. µM (u) ↑ if δM (s0M , u) ↑ and
(8)
∗
2. µM (u) ↓= λM (δP (s0M , u)) if δM
∗
(s0M , u) ↓ .
Finally, we define the transfer function MM : X ω → Y ∞ for the pre-machine
MP using its reaction function µM and Algorithm 1.
5.3 Posing of Synthesis Problem
The preceding arguments show that machines and pre-machines can be consid-
ered as “glass boxes”. It is known that machines are “glass boxes” for a proper
subclass of the class of all “black boxes” [4, 6]. Therefore we pose the following
problem.
Problem 1 (Synthesis Problem). Suppose we have a mapping M : X ω → Y ∞
that holds the non-anticipation property.
It is required to describe the properties of the mapping that ensure the existence
of a pre-machine MP such that MM ∼ =M.
6 Solving Synthesis Problem
Solving the problems posed at the end of the previous section is given in three
stages: firstly, some solution of the problem is constructed, secondly, this solution
is reduced, and, finally, the minimality of this reduced solution is proved.
Taking into account the fact that the hypothesis of the problem includes
the non-anticipation property for the mapping M we can consider the reaction
function µ of the “black box” instead its transfer function.
333
6.1 Existence of Solution
Thus we assume that two alphabets (the input alphabet X and the output
alphabet Y ) and a partial mapping µ : X + 99K Y are given.
Let us choose
SF = X ∗ ;
(9)
δF (u, x) = ux for x ∈ X and u ∈ X ∗ .
Now consider the triple F(X, SF , δF ) .
Lemma 1. The triple F(X, SF , δF ) is an automaton such that the right action
∗
δF : SF × X ∗ → SF associated with it satisfy the equation
∗
δF (u, v) = uv (10)
for all u, v ∈ X ∗ .
Proof. Checking is reduced to a simple application of the mathematical induc-
tion. ⊔
⊓
Now let us choose SF
µ
⊂ SF in the following manner:
S
SFµ
= {u ∈ X ∗ | µ(sequ) ↓} {ε} .
Now applying construction (6) and we obtain the pre-automaton F µ (X, SF , δF
µ
).
Theorem 1 (Existence of Solutions for the Synthesis Problem). Let us
µ∗ 0
consider the Moore pre-machine MµF (X, SF
µ
, δF sF , λµF ) , where
s0F = ε ;
λµF (u) = µ(u) if µ(u) ↓ ;
λµF (ε) is defined arbitrary ,
then µMµF ∼
= µ.
Proof. Really, MµF is a Moore pre-machine.
Hence we need to prove that µMµF (u) ↓ if and only if µ(u) ↓ and the equality
µMµF (u) = µ(u) holds on the common domain. But this follows immediately
from Lemma 1 and the specification of the pre-machine MµF . ⊔
⊓
6.2 Indistinguishability and Syntactic Pre-Machine
The solution that is given in the previous subsection for the Synthesis Problem
is too redundant because the state set of the corresponding pre-machine contains
too many indistinguishable states. In this subsection we demonstrate the method
to eliminate the lack of the construction.
Our consideration refers to some concepts of the theory of ordered sets. The
necessary information can be found in [5, Chapter 1].
334
Definition 9. We shall say that u′ ∈ X ∗ can not be distinct from u′′ ∈ X ∗ using
µ (this assertion is below written as u′ .µ u′′ ) if µ(u′ w) ↓ implies µ(u′′ w) ↓=
µ(u′ w) for any w ∈ X ∗ .
Proposition 5. The relation “ .µ ” is a quasi-order on X ∗ satisfying the fol-
lowing condition: if u′ .µ u′′ and w ∈ X ∗ then u′ w .µ u′′ w .
Proof. Reflexivity and transitivity of the relation is evident.
Now suppose that u′ ∈ X ∗ , u′′ ∈ X ∗ , w ∈ X ∗ , and u′ .µ u′′ .
If µ((u′ w)v) ↓ for some v ∈ X ∗ then u′ .µ u′′ ensures µ(u′′ (wv)) ↓= µ(u′ (wv))
and, therefore, µ((u′′ w)v) ↓= µ((u′ w)v) . ⊔
⊓
The following simple property of “ .µ ” is used below.
Proposition 6. The assertions u′ .µ u′′ and µ(u′ ) ↓ imply µ(u′′ ) ↓= µ(u′ ) .
Proof. To verify the validity of the proposition it is sufficient to put w = ε in
Def. 9. ⊔
⊓
Definition 10. Let u′ , u′′ ∈ X ∗ then we say that u′ and u′′ are µ-congruent
(this assertion is below written as u ≡µ u′′ ) if both u′ .µ u′′ and u′′ .µ u′ are
true.
Proposition 7. The relation “ ≡µ ” is a right congruence on X ∗ that satisfies
the following property: if u′ , u′′ ∈ X ∗ and u′ ≡µ u′′ then µ(u′ ) ↓ if and only if
µ(u′′ ) ↓ and in this case µ(u′ ) = µ(u′′ ) .
Proof. The fact that “ ≡µ ” is an equivalence relation follows from the properties
of a quasi-order [5, Sec. 1.3]. Its stability relative to the right multiplication
follows immediately from the similar property for the relation “ .µ ”. Finally,
the last assertion of the proposition follows from Prop. 6. ⊔
⊓
Let us define
SA
µ
= X ∗ / ≡µ ;
(11)
δA ([u]µ , x) = [ux]µ ,
µ
where [·]µ denotes a class of the µ-congruence, u ∈ X ∗ , and x ∈ X . Note that
the property to be a right congruence for the equivalence “ ≡µ ” ensures the
correctness of the definition of δA
µ
.
Now consider the triple Aµ (X, SA µ
, δA
µ
).
Lemma 2. The triple Aµ is an automaton such that the right action associated
µ∗
with it δA : SA
µ
× X ∗ → SA
µ
satisfies the equation
µ∗
δA ([u]µ , v) = [uv]µ (12)
for all u, v ∈ X ∗ .
Proof. The lemma is easy proved by induction on the length of v . ⊔
⊓
335
Now we can note that Prop. 7 ensures one of the alternatives:
T
either [u]µ ⊂ {v ∈ X ∗ | µ(v) ↓} or [u]µ {v ∈ X ∗ | µ(v) ↓} = ∅ .
This remark allows us to choose SSµ ⊂ SA
µ
in the following manner:
S
SSµ = {[u]µ | u ∈ X ∗ and µ(u) ↓} {[ε]µ } .
Hence we can again apply construction (6) and obtain the pre-automaton
S µ (X, SSµ , δSµ ∗ ) .
Theorem 2 (about Syntactic Pre-machine). Let us consider the Moore pre-
machine MµS (X, SSµ , δSµ ∗ , s0S , λµS ) , where
s0S = [ε]µ ;
λµS ([u]µ ) = µ(u) if µ(u) ↓ ;
λµS ([ε]µ ) is defined arbitrary ,
then µMµS ∼
= µ.
Proof. Let us note that Prop. 7 ensures the correctness for the definition of the
mapping λµS . Further, Lemma 2 guarantees the validity of µMµS ∼ = µ. ⊔
⊓
Remark 6. We shall call the Moore pre-machine built in the theorem the syn-
tactic pre-machine.
6.3 Syntactic Pre-machine as Minimal Solution of Synthesis
Problem
To complete the program indicated above, we need to establish the minimality
of the pre-machine MµS in any sense.
First of all, we note that the pre-machine MµS holds evidently the following
property called the reachability: one can obtain any state of the pre-machine
applying its partial action to the initial state.
Now let us formulate the main result.
Theorem 3 (about Minimality of Syntactic Pre-machine). For any reach-
∗
able Moore pre-machine MP (X, SP , δP , s0M , λM ) such that µM ∼
= µ there exists
a mapping ψ : SP → SS satisfying the following conditions
µ
1. for any s ∈ SP and u ∈ X ∗ the assertion δP
∗
(s, u) ↓ implies δSµ ∗ (ψ(s), u) ↓=
ψ(δP (s, u)) ;
2. ψ(s0M ) = s0S ;
3. µ ∼
= µS µ ◦ ψ .
Proof. The key item of the proof is the construction of the mapping ψ .
Let s ∈ SP and u′ , u′′ ∈ X ∗ such that δP
∗
(s0M , u′ ) ↓= s and δP (s0M , u′′ ) ↓= s
′ ′′
then we can show that u .µ u .
Indeed, suppose that µ(u′ w) ↓ for some w ∈ X ∗ . Taking into account that
336
µM ∼= µ we can write µ(u′ w) = λM (δM ∗
(s0M , u′ w)) .
Note that the previous equality ensures δM ∗
(s0M , u′ w) ↓ and therefore (5) leads
∗ ∗ 0 ′
to the conclusion that δP (δP (sM , u ), w)) ↓ .
Using the supposition δP∗
(s0M , u′ ) ↓= s and (5) we obtain
µ(u′ w) = λM (δP
∗ ∗
(δP (s0M , u′ ), w)) = λM (δP
∗
(s, w)) .
∗
This equation ensures δP (s, w) ↓ .
Hence the supposition δP (s0M , u′′ ) ↓= s implies δP
∗ ∗ ∗
(δP (s0M , u′′ ), w) ↓= δP
∗
(s, w) .
′′ ′ ′′ ′
Thus µ(u w) ↓= µ(u w) and, therefore, u .µ u .
Similar reasoning gives u′ .µ u′′ and, therefore, u′ ≡µ u′′ .
Now we can define ψ in the following manner:
∗
ψ(s) = [us ]µ where s = δP (s0M , us ) .
Checking the validity of items 1)–3) for the constructed mapping ψ is a simple
exercise now. ⊔
⊓
7 Conclusion
Thus, we can summarize that the paper gives the algebraic analysis for the prob-
lem of realisation “black boxes” by machines. The main results of the analysis
are
– the generalisation of the non-anticipation property for “black boxes” that
accumulate information for decision;
– the complete solution of the synthesis problem for such “black boxes”.
The machines that realise the corresponding transfer functions are based on
pre-automata. The class of such algebraic structures had been introduced by
author jointly with Prof. M. Dokuchaev and Prof. B. Novikov in earlier papers.
It should be emphasized that issues dealing with computational properties
of pre-machines has not considered in the paper. The coverage of these issues
requires a separate study.
References
1. Ashby, W.R.: An introduction to cybernetics. Chapman & Hall, London (1956)
2. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups, Volume 1.
AMS (1961)
3. Dokuchaev, M., Novikiov, B., Zholtkevych, G.: Partial actions and automata. Alg.
and Discr. Math. 11, 51–63 (2011)
4. Glushkov, V.M.: Some problems in the synthesis of digital automata. USSR Com-
putational Mathematics and Mathematical Physics. 1(3), 399–446 (1962)
5. Harzheim, E.: Ordered Sets. Springer Science+Business Media Inc., New York
(2005)
337
6. Trakhtenbrot, B.A., Barzdin, J.M.: Finite automata: behaviour and synthesis.
North-Holland Publishing Company, US (1973)
7. Zholtkevych, G., Novikov, B., Dorozhinsky, V.: Pre-automata and Complex Event
Processing. In: Ermolayev, V. et al (eds) ICT in Education, Research, and Indus-
trial Applications. CCIS, vol. 469, pp. 100–116. Springer International Publishing
(2014)
338
An Interleaving Reduction for Reachability Checking in
Symbolic Modeling
Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
1
Glushkov Institute of Cybernetics of National Academy of Sciences, Kyiv, Ukraine
{let,lit}@iss.org.ua
2
Kherson State University, Kherson, Ukraine
vladim@kspu.edu
Abstract. This paper is devoted to the whole problem of interleaving reduction
in modeling of concurrent processes. The main notions of insertional modeling
were described. The verification problem in terms of insertional modeling was
examined. General algorithm of interleaving reduction in terms of insertional
modeling was presented. A static and incremental algorithm of reduction for
reachability checking was presented. The proof of correctness of presented
algorithm was introduced. The results of experiments of such algorithm
application was described.
Keywords. Interleaving, predicate transformer, symbolic modeling.
Key Terms. MathematicalModel.
1 Introduction
Usually the multiagent distributed systems are high level non-deterministic. The
nature of this non-determinism is symbolic nature of models and concurrency (choice
of parallel process which should operate at each time of modeling). One of the main
problem of reachability checking in verification is exponential explosion of states
number. Some of the sources of such explosion is the number of parallel processes in
model and their interleaving[1] .
There are two different approaches for modeling: model checking and symbolic
modeling[2]. The model checking tool works with concrete states where state is
represented by values of its variables. A transition is occurred by assignment of new
values for the variables. The problem of exponential explosion could be solved by
using well known model checking methods: methods that introduce partial order to
reduce interleaving[3], methods for determining the symmetry when verifying the
equivalence of states[4], techniques of abstraction[5], approximation[6], data-flow
analyses[7], McMillan’s algorithm of unfolding[8].
A state of environment in symbolic modeling presents some formula in
corresponded theory (first order logic etc) which covers some set of concrete states. A
transition is occurred with a help of predicate transformers (weakest precondition,
strongest postcondition[9])[10]. Unfortunately not all methods of model checking for
339
2 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
reducing states space could be applied for symbolic case. The problem which was
described previously could be solved with a help of the next symbolic methods:
narrowing[11], unfolding concurrent well-structured transition systems[12].
This paper continues the work [13] where an algorithm with some restriction of
symbolic model was described. Here we present the algorithm for full symbolic case.
The algorithm bases on the McMillan’s algorithm adopted to symbolic modeling in
notion of insertion modeling [14]. This algorithm bases on notion of permutability
which is defined with help of predicate transformer (strongest postcondition, pt
function below). It was described in [10]. So, the paper is devoted to the solution of
the problem of interleaving reduction in insertion models with infinite number of
states.
The algebra of behaviors is presented in chapter Behavior Algebras, the
verification environments, corresponding insertion function, and predicate
transformer are considered in chapter Verification Environments. The normal form of
behavior is defined in chapter Behaviors Over Basis B. The problem of reachability
of the states is described in chapter Verification. The notion of partial unfolding is
examined in chapter Partial Unfolding. The optimization of partial unfolding by
statically permutable operators is reviewed in chapter Static Permutability Property.
The incremental algorithm for reducing of interleaving for transition systems is
presented in chapter Main Interleaving Reduction Algorithm. The static algorithm of
interleaving reduction is described in chapter Static Interleaving Reduction
Algorithm. The statistic of applying of such algorithm to few examples is presented in
chapter Examples of Application.
2 Behavior Algebras
One of the main notions of insertion modeling, which is used for describing
algorithm of interleaving reduction is behavior algebra. Behavior algebra [14] is a
kind of process algebra; it is used to express the behavior of agents (transition
systems) considered up to bisimilarity or trace equivalence. To make economic
unfolding we need to distinguish sequential and parallel behaviors. So we consider the
following modification of the notion of behavior algebra- it is a multisorted algebra
with three components: the algebra of actions, the algebra of sequential behaviors,
and the algebra of parallel behaviors.
The algebra of sequential behaviors has operations of prefixing:
. and one internal operation of nondeterministic
choice (()+()), which is associative, commutative, and idempotent operation with
neutral element 0. We also consider the constant behavior (successful termination),
which is a common element of the algebra of sequential and the algebra of parallel
behaviors. The operations of action algebra will be considered later.
The algebra of parallel behaviors has the parallel composition ()||() of sequential
behaviors as the main binary operation. It is associative commutative (but is not
idempotent) and has the neutral element . It also has the prefixing operation and
nondeterministic choice. The algebra of sequential behaviors is implicitly included to
the algebra of parallel behaviors by the identity u u || (parallel composition with
one component). Unfolding of parallel composition by interleaving will be considered
340
3 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
only after inserting of agents that are formed by parallel composition into the
environment.
3 Verification Environments
Verification environments of the form E E (U , P, B) are defined by the following
parameters: the set of conditional expressions U, the set of operators P, and the set of
basic behaviors B. The set of conditions and the set of operators are used to define
actions (it is a union of these two sets). The set of basic behaviors is used to define the
behaviors of agents inserted into environment in the way which will be explained
later. We also suppose that some logic language (first order or temporal) called basic
language is fixed to define the states of environment and checking conditions for
verification. The conditional expressions also belong to this language.
The state of environment is represented as E[u ] , where E is a statement of basic
language and u is a parallel composition of sequential behaviors of agents inserted
into environment. We suppose that operators are divided into the set of conditional
and unconditional operators. Conditional operator has the form a where is a
condition and a is an unconditional operator. Unconditional operator a is identified
with conditional operator 1 a . The associative product ()*() and the function
pt : U P U (predicate transformer) are defined by the set of actions so that the
following identities are valid:
pt ( , a) pt ( a)
pt ( pt ( , a), b) pt ( , a * b)
( a) * ( b) pt ( pt ( , a) , b)
*
Here and are conditions, a and b are unconditional operators.
Predicate transformer pt is supposed to be monotonic:
pt ( , a) pt ( , a)
In general case, the pt function is defined by some concrete syntax. An example of
such pair (syntax, pt) can be found in [16].
Example. The basic language is a first order language. Conditions are formulae
over simple attributes - symbols that change their values when a system changes its
state. Formally they are considered as function symbols with arity 0. Unconditional
operators are assignments (parallel assignments, sequences of assignments, if-then-
else operators, loops with finite number of repetitions, etc.). As usually in this case,
pt ( ( x), ( x1 : t1 ( x), x2 : t2 ( x), )) z( ( z) ( x1 t1 ( z) x2 t 2 ( z) ))
Actually this is the strongest postcondition for precondition .
Example of conditional operator. Let x be an integer variable,
u ( x 5) ( x : x 1) be an operator, x 3 is statement in basic language, u || u
is a behavior. For this case, U , P {u}, B {u ( x 5) ( x : x 1)} . The
equation u ( x 5) ( x : x 1) considered here as a basic behavior and it used for
definition of agent behavior u || u .
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4 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
In insertion modeling environment considered as agent with insertion function. So,
Insertion function is defined by the following identities and rules of operational
semantics.
1. E[u, v] E[u || v] , u,v are agents with sequential behavior (see sec. 1).
Identities for conditions.
2. E[ .u v] E[v] , if ( E ) 0 .
3. E[ . .u v] E[ .u v] , if ( E ) 0 (merging conditions).
4. E[. a.u v] E[ a.u v] , if ( E ) 0 . Special cases of
these identities are obtained when v=0 or 1 .
5. E[ . ] E [ ] , if ( E ) 0 .
Identities for operators.
6. E[a.u v] E[v] , if pt ( E, a) 0 .
7. E[a.u] a. pt ( E, a)[u || (a, E)] , if pt ( E, a) 0 , (a, E ) is a parallel
composition of sequential behaviors (it generates some new parallel branches). If
(a, E ) , then u || (a, E) u || u and u remains unchanged.
Nondeterministic choice.
8. E[a.u a.v w] E[a.(u v) w] . The use of left distributivity means that
environment considers behavior expressions up to trace equivalence. It also means
that a system uses delayed (angelic) choice.
9. E[u ] E[u] E[] . The states E[0] and E[] are called terminal states of
the environment. Formally, the states of the form E[0] are equivalent to 0, and states
of the form E[] are equivalent to (if E[] E[] is added). But from the
point of view of verification it is useful to distinguish syntactically different terminal
states.
Parallel behaviors.
10. E[u] E[v] E[u || w] E[v || w] . Therefore all identities for conditions and
operators can be applied within the parallel composition. A component
a1.u1 an .un of parallel composition is called degenerated relative to the state E,
if for all operators ai . pt ( E, ai ) 0 and for all conditions i it is true that
( E i ) 0 . Each component that is degenerated relatively to the state E is
equivalent to 0 relatively to this state.
11. E[u] F[v] F[v] , if parallel composition u contains degenerated component
relative to E. So all states of environment with degenerated components are
equivalent to 0.
12. E[u || v] E[u || v] E[v] .
13. E[a1.u1 a2 .u2 ] E[a1.u1 || v] E[a2 .u2 || v] , if all actions ai are
different, if ai is a condition then ui is terminal constant, and v does not contain
components degenerated relatively to the state E. The state of environment E[u ] is
called dead lock state, if there are no transitions from this state, but u is not a
successful termination. If there is at least one degenerated component in parallel
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5 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
composition, then the corresponding state is a dead lock state. All dead lock states are
equivalent to 0, but it is useful to distinguish them as well as terminal constants. The
rules (9), (12), and (13) are called unfolding of nondeterministic choice.
14. E[a1.u1 || || an .un ] i 1 ai .( || ai 1.ui 1 || ui || ai 1.ui 1 ||) ,
n
if all
components of parallel composition are non-degenerated. This relation is called a full
unfolding algorithm for a parallel composition. This is a complete unfolding and the
main result of this chapter shows that it is not needed to make the complete unfolding
at each step of verification. Let u a1.u1 || || an .un ,
unfold (u, i) ai .( || ai 1.ui 1 || ui || ai 1.ui 1 ||)
then identity (14) can be rewritten as
14a. E[a1 .u1 || || an .un ] i1 unfold (u, i) .
n
Environment does not distinguish trace equivalent behaviors and consequently,
bisimilar states of environment are trace equivalent[14]. The identity (14) defines the
main transition rule for the system:
a
E[u]
i E [u] ,
if u is a parallel composition with non-degenerated components and E [u ] is defined
by the identity (7).
4 Behaviors over Basis B
The set of symbols is given for the set B of behavior basis. These symbols are
called basic sequential behaviors. The expression of the algebra of sequential
behaviors constructed from these symbols and termination constants is called
sequential behavior over basis B. Suppose that for each symbol v B an equation of
the form v Fv (v1, v2 ,) is given with sequential behavior over basis B as a right
hand side. This equation is called the definition of a basic behavior v. The application
of this definition (the substitution of the left hand side by the right hand one) is called
the unfolding of this behavior. System of basic behaviors is called non-degenerated if
each path in the tree representation of the expression v Fv (v1, v2 ,) contains at
least one operator.
Normal form of sequential behavior is an expression of the form
a1.u1 a2 .u2 an .un where u1, u2 , are sequential behaviors. If ai is a
condition, then ui is a termination constant, n 0 , and all actions are different (not
equivalent with respect to the environment E), because of delayed (angelic) choice
(see sec. 2).
Each sequential behavior u over non-degenerated basis in a state E[u ] can be
reduced to a normal form v equivalent to u with respect to E.
Parallel behavior over B is a parallel composition of sequential behaviors over B.
Normal form of parallel behavior is a nondeterministic sum of behaviors of the
form a1.u1 a2 .u2 , where u1, u2 , are sequential behaviors over B, a1, a2 ,
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6 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
are operators or conditions such that if ai is a condition, then ui is a termination
constant.
Normal form of environment state is a term of the form iI ai .Ei [ui ] jJ or
0. Each environment state with non-degenerated system of basic behaviors is a trace
equivalent to some normal form.
5 Verification
A property of environment state is said to be correct if it does not distinguish
equivalent states. A property of environment state is monotonic if
E E ( E[u]) ( E[u]) .
5.1 Verification problem in terms of insertion modeling
Let S1 , S 2 be state of the model M . The problem of reachability checking is the
answer to the question if a path exists from the state S1 to the state S 2 on model M ,
or not. Usually models are highly non-deterministic. This non-determinism is based
on interleaving of parallel processes: a || b (a; b) (b; a) (here a,b are some
processes, “ | | ” is parallel composition, “ ; ” is sequential composition and “+” is non-
deterministic composition). From other side this non-determinism could produce
additional paths from S1 to S 2 and additional states. So, let call interleaving
reduction problem an answer to the question how to reduce non-determinism of the
model M to find the path from S1 to S 2 as quickly as possible.
For a given set of correct and monotonic checked properties, defined on the set
of environment states, the set of initial states defines which properties are reachable
(not reachable) from the initial states for a finite number of steps or a number of steps
bounded by some constant.
It is supposed that the set of properties to be checked contains the property of a state
“to be a dead lock” and a property “to be a state of successful termination”.
The simplest verification algorithm is exhaustive unfolding of initial states up to
saturation or depletion of a given number of steps. It uses the following formula of
unfolding: i1 E[unfold (u, i)] . Such algorithm was described in [14]. It builds all
n
states space for reachability checking which isn’t possible always. The properties to
be checked are checked in the process of unfolding and the states that satisfy checked
properties are collected. More economic unfolding algorithm can be constructed using
the following partial unfolding algorithm.
6 Partial Unfolding
Two operators a and a' are called permutable regarding the state of E if
E[a * a] E[a * a] and dynamically permutatable regarding the state E (denoted by
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7 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
a
E
a ) if E[a * a] E[a * a] 0 . Let E[u] E[a1.u1 || || an .un ] is a state of the
environment. Let’s select the component s ai .ui and build
nonp( E, ai ) {a j | i j (ai
E
a j )} . We obtain:
punfold ( E, u, i) A(i) B( E, i) C( E, i)
A(i) ai .( || ai 1.ui 1 || ui || ai 1.ui 1 ||)
B( E , i ) a .(...|| a j 1.u j 1 ||u j || a j 1.u j 1 || ...)
j
i j ( ai , a j )nonp( E , s )
C ( E, i) a .(...|| a .uk 1 || (( p; aw ); uk ) || ak 1.uk 1 || ...)
k
E
k 1
k i ( ak ,ai )nonp( E ,ai ) ak aw
In the last formula (( p; aw ); uk ) uk and p are sequences of compositions of actions
(behavior). Function punfold is called partial unfolding of parallel composition. Let’s
consider the following algorithm of reachability checking: we need to check the
properties on a current state of the environment and each state that is reachable from
this in one step. Partial unfolding is used for main function of unfolding states. This
algorithm is called partial unfolding algorithm of reachability checking.
In general, the punfold uses the notion of dynamic permutability of operators, but it
is not optimal, because it uses 4 times application of function predicate transformer pt
for each pair of operators. Using punfold can be optimized by using the concept of
static permutability of operators. Algorithm which uses punfold with some
optimization is considered in section 6.3.
6.1. Optimization of partial unfolding of states.
Theorem 1. If two operators p a, q b are permutable regarding the
states E1 , E2 , E3 then they are permutable regarding
any state [13].
The sufficient condition of permutability of two operators p a, q b
is valid under the following conditions:
1. pt ( pt ( , b), a) pt ( pt ( , a), b) ;
2. pt ( pt ( , b), a) 0 ;
3. pt ( pt ( , a), b) 0 .
Example 1. Let a,b:int and 1[init.(a1.good || b0 .bad b1.good )] is initial state and
behavior, where init, a1 , b0 , b1 - operators. Agent’s behavior could be represented by
the following list of equations: init (( a b) 1). AndFork ,
AndFork a1 || (b0 b1 ), a1 (( a 1) 1), b0 ((b 0) 1), b1 ((b 1) 1) .
Sufficient condition of permutability for operators a1 , b0 , b1 is performed in this
case, but there can be a case in the simulation where the state of the environment
includes some formula, which combines predicate memory of various parallel
processes (a=b). So, one of the operator will not be applicable, ie a pair of operators
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8 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
will be dynamically permutable regarding this state. Thus, the notion of sufficient
conditions of permutability of operators need to be strengthened.
To improve the usage of permutability for this example, we need
sat ( E ) 1 , otherwise operators will be dynamically permutable regarding
state E. Let’s try to obtain a sufficient condition for dynamic permutability of two
operators regarding some condition E.
The notion of dynamic permutability of two operators p, q regarding some state E
uses a condition:
E[ p * q] E[q * p] 0
So, let E pt ( pt ( , b), a) pt ( pt ( , a), b) 0 and try to apply
backward predicate transformer to the state E. We obtain:
pt 1 ( pt 1 ( E, , b), , a) E(q , p ) , pt 1 ( pt ( E, , a), , b) E(p ,q ) .
Theorem 2. If E pt ( pt ( , b), a) pt ( pt ( , a), b) 0 then
E(q , p ) E(p ,q ) 0 .
Proof.
Let’s assume the contrary that E(q , p ) E(p ,q ) 0 . Since the backward predicate
transformer turns back to its possible state transition set, it means that
( E(q , p ) ) ( E(p ,q ) ) . State E(p ,q ) ( E(q , p ) ) specifies a set of concrete
states from which transitions from state with operators p and q (q and p) exist,
which means that E(p ,q ) E(q , p ) E(p ,q ) E(q , p ) 0 . So, we got
a contradiction, because if E(q , p ) E(p ,q ) 0 then E 0 . The theorem is proved.
This condition means that if two operators were dynamically permutable regarding
E then it is necessary that current state of the environment should satisfy theorem 2.
Let E be some state of environment.
Theorem 3. If two operators p a, q b satisfy the sufficient condition
of permutability and E E(q , p ) E(p ,q ) 0 then E[ p * q] E[q * p] 0 .
Proof.
Let’s consider the condition of dynamic permutability regarding E:
E[ p * q] E[q * p] 0 .
E[ p * q] E[( a) * ( b)] pt ( E , a)[ b]
pt ( pt ( E , b), a) pt ( pt ( E ( ), b), a)
pt ( pt ( E E , a), b)
pt ( pt ( E ), a) pt ( E ), a), b)
pt ( pt ( E ), a), b) pt ( pt ( E ), a), b)
Next, let’s consider in details the sufficient condition permutability of operators
that satisfies the operators p, q:
E[ p * q] E[( a) * ( b)] pt ( E , a)[ b]
pt ( pt ( E , a), b) pt ( pt ( E ( ), a), b)
pt ( pt ( E, a) pt ( E, a), b) 0
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9 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
pt ( pt ( E, b), a) pt ( pt ( E, b), a) 0
pt ( pt ( E, a), b) 0 pt ( pt ( E, a), b) 0
Equality E[ p * q] E[q * p] shall be satisfied because otherwise the operators p,
q do not satisfy the sufficient condition permutability of operators (Theorem 1). Thus,
we have:
pt ( pt ( E ), a), b) pt ( pt ( E ), a), b)
pt ( pt ( E , b), a) pt ( pt ( E , b), a)
pt ( pt ( E ), a), b) pt ( pt ( E , b), a)
Let’s consider opposite:
pt ( pt ( E ), a), b) pt ( pt ( E , b), a) 0
Let’s continue to consider sufficient conditions of permutability:
pt ( pt ( , b), a) pt ( pt ( , a), b) 0
pt ( pt ( ( E E), b), a) pt ( pt ( ( E E), a), b) 0
pt ( pt ( E E), b), a)
pt ( pt ( E E), a), b) 0
pt ( pt ( E), b), a) pt ( pt ( E), b), a)
pt ( pt ( E), a), b) pt ( pt ( E), a), b) 0
pt ( pt ( E), b), a) pt ( pt ( E), a), b) 0
This means that the condition E E(q, p ) E(p,q ) 0 should be satisfied.
But we have the following condition E E(q , p ) E(p ,q ) 0 . Thus, both conditions
must be satisfied, however:
E E(q , p ) E(p ,q ) E E(q, p ) E(p ,q ) 0
So we got a contradiction. The theorem is proved.
If there are two operators p a, q b that satisfy the sufficient
condition of permutability. Condition E E(q , p ) E(p ,q ) 0 is called sufficient
condition of dynamic permutability of operators p, q regarding the environment E.
From a practical point of view, let’s try to identify requirements for operators with
which we can determine statistically whether they satisfy the sufficient condition of
dynamic permutability or not.
Let E be a state of the environment, and p - an operator. The set A(E) is called the
set of all attributes from state E and A(p) is called the set of all attributes in the
statement p[15].
Two operators p a, q b are called statically permutable if they
satisfy the following conditions:
A( p) A(q) pt ( , a) 0 pt ( , b) 0
Theorem 4. If two operators p a, q b are statically permutable then
they are dynamically permutable.
Proof.
To prove the theorem we need to show that these operators satisfy necessary
condition of permutability of operators in this case.
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10 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
Since A( p) A(q) pt ( , a) 0 pt ( , b) 0 and theorem 1 then
pt ( pt ( , a), b) pt ( pt ( , a), b) 0
pt ( pt ( , b), a) pt ( pt ( , b)) 0
pt ( pt ( , b), a) pt ( pt ( , a), b)
pt ( pt ( , b), a) pt ( pt ( , a), b)
pt ( pt ( , b), a) pt ( pt ( , a), b)
pt ( , a) pt ( , b) pt ( , a) pt ( , b)
The theorem is proved.
This theorem means that if a predicate that combines memory in a state of
environment with different operators is absent then checking the necessary condition
of dynamic permutability is not required. Since in this case a usage of one of these
operators does not affect the applicability of another operator. The appearance and
disappearance of such predicates can be defined statically and syntactically.
Thus, in Example 1 operators are statically permutable, but after applying init
operator formula will contain predicate that combines memory of operators a1 , b0
and a1 , b1 . So, we have to use sufficient condition for dynamic permutability of pairs
of operators, a1 , b0 and a1 , b1 regarding the state of the environment after
application of init operator . So, E (a b) . Let’s statically compute sufficient
condition of permutability of operators:
(a1 , bo ) : E(a ,b ) E(b ,a ) (a 1) (b 0)
1 0 0 1
(a1 , b1 ) : E(a ,b ) E(b ,a ) (a 1) (b 1)
1 1 1 1
Next let’s try to apply sufficient condition of dynamic permutability of operators
regarding the condition E for both pairs of operators:
(a1 , bo ) : E E(a ,b ) E(b ,a ) (a b) (a 1) (b 0) 0
1 0 0 1
(a1 , b1 ) : E E(a ,b ) E(b ,a ) (a b) (a 1) (b 1) 0
1 1 1 1
Thus, operators (a1 , bo ) will be dynamically permutable regarding the condition E,
and operators (a1 , b1 ) will be dynamically permutable. This means that interleaving
will be removed in correct way for this problem.
6.2. The Problem of Reachability of Some State
The approach proposed in the previous sections can be applied to the problem of
finding deadlocks in a given model, but if the user specifies a state of environment
you want to check coverage, whereas previously proposed approach should be
strengthened.
Example 2. Let a,b:int and 1[init.(a1 || b1 )] be initial behavior and a state of the
environment, where init, a1 , b1 - operators. Agent’s behavior could be represented by
the following list of equations:
init (( a 0) (b 0) 1), AndFork , AndFork a1 || b1 ,
a1 (1 (a : 1)), b1 (1 (b : 1))
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11 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
Let’s check recheability of the state F (a 0) (b 1) .
After applying the operator init obtains the state of the environment
E (a 0) (b 0) . Operators a1 , b1 are statically permutable and can be applied
to the state E, which means that they are dynamically permutable regarding E. So,
E[a1 || b1 ] E[a1.b1 ] , which means that the operator b1 never will be applied before
the operator a1 and user defined state F will be unreachable after interleaving
reduction. Let’s try to enhance sufficient condition of operators permutability
regarding some state E with some conditions related to formula F.
F ( E[a1 * b1 ]) F ( E[b1 * a1 ]) 0 for this example then we consider conditions for
operators separately (not for pairs of operators).
Let p a be an operator.
Theorem 5. If pt 1 ( pt ( , a), , a) 0 then pt ( , a) 0 .
Proof.
Let’s consider the opposite pt 1 ( pt ( , a), , a) 0 and pt ( , a) 0 . In this
case by performed substitution it can be easily obtained the following:
pt 1 ( pt ( , a), , a) 0 pt 1 (0, , a) 0 0 0
So we got a contradiction. The theorem is proved.
The operator p a is called permutable regarding some user defined state F,
if the following conditions are satisfied:
1) pt 1 ( pt ( , a), , a) 0 ;
2) F pt 1 ( pt ( , a), , a) F pt ( , b) .
This permutability means that an operator does not change the state of the
environment in order to reach the user defined state changed. From reachability point
of view we are interested in two cases (if pt 1 ( pt ( , a), , a) 0 ):
1) F pt 1 ( pt ( , a), , a) 0 F pt ( , b) 0 ;
2) F pt 1 ( pt ( , a), , a) 0 F pt ( , b) 0 .
In first case, the reachability of user defined state should be checked immediately
before application of an operator, and in the second case - after.
If operators satisfy the sufficient condition of dynamic permutability, but at least
one of them is not permutable regarding a user defined state then this operator should
be applied first.
This approach can be applied to any algorithm of unfolding.
So, for checking of reachability of the user defined state F the notion of
permutability regarding the user defined state could be used. You can’t consider a pair
of operators if both of them do not satisfy this condition.
Coming back to example 2. Operator a1 will not be permutable regarding the user
defined state F:
1 pt 1 ( pt (1, a : 1),1, a : 1) 1 E1
pt (1, a : 1) (a 1) E2
F E1 F E2 (a 0) (b 1) 1 (a 0) (b 1) (a 1) 0
Operator b1 is permutable regarding F:
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12 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
1 pt 1 ( pt (1, b : 1),1, b : 1) 1 E1
pt (1, b : 1) (b 1) E2
F E1 F E2 (a 0) (b 1) 1 (a 0) (b 1) (b 1) 1
From other side operators a1 , b1 are statically permutable since
E (a 0) (b 0) has no predicates that combine memory of these operators.
This means that in this case you should first apply an operator b1 , then you need to
check reachability of F (since F E1 (a 0) (b 1) 1 0 ) before applying a1 .
And after that you can try to apply a1 . So,
pt (( a 0) (b 0), b : 1) (a 0) (b 1)
Then let’s check the reachability of user defined state:
(a 0) (b 1) (a 0) (b 1) 1
So, reachability of user defined state is proved.
6.3. The Main Interleaving Reduction Algorithm
Let E[u ] be a model (an initial state of the environment and behavior), where u is
behavior, and F is some user defined state which reachability should be checked. So,
we need to check reachability of F in the model E[u ] and all its deadlocks.
The main interleaving reduction algorithm for reachability checking is represented
in fig. 1.
Fig. 1. The main interleaving reduction algorithm for reachability checking
Static Analyses. In the initial behavior u we look for set Opn (set of operators of a
n-th parallel process) on each parallel process. Next, for each pair of operators from
different parallel processes we build a table: H : N OpN N OpN G Bool . This
table by a pair (parallel process identifier and operator) returns four (number of
parallel process that is not equal to the previous one, and the operator which is
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13 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
permutable to current one, the last two parameters are sufficient condition for
permutability of operators and flag for static permutability of operators).
For each pair of operators that does not satisfy the sufficient condition of
permutability of operators the table is filled: D : N OpN {N , OpN } , where
{N , Op N } is a set of pairs: the number of parallel process and an operator, which does
not satisfy the sufficient condition of permutability.
Each operator is constructed Flt : Op N Bool Bool Bool , which defines the
triple for each operator in set: value of reachability of user defined state before and
after application of an operator, the third value is 1 if all operators from other
processes are statically permutable with this one, and 0 if not.
Checking Reachability. Checking reachability of user defined state F. If the filter is
reachable then saving corresponded trace and stop modeling.
Choosing Component. We build normal form (section 4). From list of components
we should choose one to continue working. Here we propose to select first component
from the list, but in general case here some heuristics could be applied (it’s out of
scope of this paper). If there is no component left then finishing.
Choosing Operator. In a chosen component we select operators in the following
order. First we check the applicability of operators for which the third option from the
table Fpl is 1. If there are no operators or they can’t be applied, then we choose other
operators. If the flag state of the reachability of user defined state is 1 then we first try
to apply such operators that are permutable regarding a user defined condition for
both operators in the table Flt being 1. If the flag state of user defined state equals 0
then we choose to consider operators whose value pairs in the table Flt are (0,1). If
one of such operators is applicable then after his application we need to check the
reachability of user defined state. If user defined state is reachable then finishing. If
no such operators left then deadlock is obtained and we get new component.
Otherwise, finishing.
Cycle/Visited. Checking cycle/visited filters. If the filter is reachable then we
choose a next operator to work. If no operator left then we choose other component.
Partial Unfolding. We try to build B and C if it is required, using notion of
sufficient condition of static and dynamic permutability. If the last operators satisfy
the sufficient condition of static (dynamic) permutability then B=0. Starting delayed
to build C. In general, this problem is formulated as follows. It is given: current state
of environment E, operator a one of the parallel processes u1 (other processes are
delayed to use some operators in this process, including the process by which it was
taken the operator a), and delayed parallel processes. In the set of parallel processes it
is needed to find the operator b, which does not satisfy the sufficient condition of
permutability (table D) or does not satisfy the condition of sufficient dynamic
permutability regarding the E. In order to check whether these operators are in a given
process, you generally build all states space. If these operators are not found then all
resulting state of the search should be removed from storage cycle/visited filters. This
is necessary because subtrace which leads to the required operator can modify the
current state of the environment and a sufficient condition for dynamic permutability
can not be performed, although for state E a sufficient condition for dynamic
permutability is performed. But in some cases the search for these operators do not
need to spend a dynamically performance of all subtrace. If the state of the
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14 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
environment does not contain predicates that combine memory of these operators and
the set of attributes operators intersect, then we can use the concept of
specialization[16] in order to break into several operators and sufficient condition will
check only those suboperator memory that belongs to the operator. If such operator
was found then we add result of it insertion into the list of components.
For trace equivalence each trace for deadlock should be checked additionally
because of used normal form. Each cycle/visited trace should be checked for
reachability of user defined state in the following way: turning back with a help of
backward predicate transformer until operator doesn’t have value 1 as first and second
parameters in the table Flt.
Theorem 6. punfold ( E, u, i) Function which was represented in fig. 1 saves
property of reachability checking.
Proof.
Let’s suppose opposite that the function punfold ( E, u, i) does not save the property
of reachability checking. This means that for some state of environment E such
operator a exists, which is applied to the E( E
a
E ) and doesn’t exist as first
action in components A(i), B( E, i), C( E, i) . So, the operator will be dynamically
permutable regarding the environment E and all other operators resulting behavior
components A(i), B( E, i), C( E, i) (according to Choosing Operator, Partial
Unfolding). In addition, operator a can be applied after the application of the first
operators in the resulting behavior of components A(i), B( E, i), C( E, i) .
This means that the required state of the environment is reachable, but after
applying the operator a on the next step these operators are dynamically permutable
regarding the environment E. From other point of view we do not take into account
E . If value of pair for the operator in the table Flt is (0,1) then according to step 5
we have to take it into consideration and in this case it will be the first operator in the
behavior of components A(i), B( E, i), C( E, i) . If the value of such pair is (1,1) then
the state of the environment is reachable in the next step, as defined Flt. If the value is
(1,0) then before application of the operator a we need to check the reachability of the
environment E and definitions in Flt. If the value is (0,0) then required state is not
reached in E . That means that the required state of the environment is not unreached
at all states of the environment as a result of unfolding application punfold ( E, u, i) .
So we got contradiction. The theorem is proved.
The main problem of proposed algorithm is complicity to find component C ( E, i) .
One of the ways to speed up such algorithm is delayed computation. The idea of this
method contains the following:
1) To collect all such special states from Partial Unfolding, where we should find
component C ( E, i) and finding the required states with a help of different methods:
all states coverage, invariants etc.
2) To continue algorithm with built states of component C ( E, i) .
Such algorithm is called incremental algorithm of reachability checking.
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15 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
6.4. The Static Interleaving Reduction Algorithm
If operators and initial environment state of model do not contain predicates which
connected to the memory of different parallel processes then general algorithm in
previous section could be simplified. Such algorithm is called static interleaving
reduction algorithm.
For the component C ( E, i) of punfold ( E, u, i) we should check reachability of
application of operator which is not dynamically permutable for ai (see section 5).
For elimination of such reachability checking we could build additional interleaving
according to checking of reachability of corresponded operator in behavior. For
example, let a || b.c || d and (a c) (b d ) , E be some environment state. So,
punfold ( E, a || b.c || d ,1) E[a.(b.c) || d ] E[b.c.(a || d )] E[d.(a || b.c)]
Here we take into account b.c.(a || d ) , because (a c) ; d .(a || b.c) , because we
have taken b.c.(a || d ) and (b d ) .
6.5. Examples of Application
In Table 1 information about few big examples run with our static interleaving
reduction algorithm are presented. All of them give out of memory error (PC with 8
Gb of RAM) if we try to obtain all states space. So, we try to run them on
implementation of proposed algorithm in Insertion Modeling System.
Table 1. Experiments result for static interleaving reduction algorithm
No. Total number of Number of non-permutable Time
operators pairs operator’s pairs
1 660 30 25 min (on prototype)
2 780 14 47 min 4 sec
3 12882 225 1 min 42 sec
Here “on prototype” means that this experiment was done on the algorithm which
was implemented in language of Insertion Modeling System[17]. Other experiments
were run on the algorithm which was implemented on C++. “Total number of
operators pairs” is number of pairs of operators which were detected in parallel
behavior of the model. “Number of non-permutable operator’s pairs” is a number of
detected non-permutable pairs of operators. Example 2 works slower because it has
four parallel processes and each sequential process more non-deterministic, example 1
has only 2 parallel processes.
7 Conclusion
Described algorithm of interleaving reduction was implemented in Insertional
Modeling System. Its restriction for usage of static permutability condition was good
account in set of big examples. In any case, the main interleaving reduction algorithm
depends on reachability checking problem (component C ( E, i) , section 6).
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16 Alexander Letichevsky1, Oleksandr Letychevskyi1, Vladimir Peschanenko2
Notoriously this problem is algorithmically unsolvable. It means that you could
always prepare example where interleaving reduction will be impossible (for
example, all operators will be non-permutable etc).
References
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Doron A. Peled, and Lenore D. Zuck (Eds.), Berlin, Heidelberg, pp. 68-82, Springer-Verlag
(2008)
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180-195, Springer (1995)
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354
Abstracting an operational semantics to finite
automata
Nadezhda Baklanova, Wilmer Ricciotti, Jan-Georg Smaus, Martin Strecker
IRIT (Institut de Recherche en Informatique de Toulouse)
Université de Toulouse, France
firstname.lastname @irit.fr ⋆,⋆⋆
Abstract. There is an apparent similarity between the descriptions of
small-step operational semantics of imperative programs and the seman-
tics of finite automata, so defining an abstraction mapping from seman-
tics to automata and proving a simulation property seems to be easy.
This paper aims at identifying the reasons why simple proofs break,
among them artifacts in the semantics that lead to stuttering steps in
the simulation. We then present a semantics based on the zipper data
structure, with a direct interpretation of evaluation as navigation in the
syntax tree. The abstraction function is then defined by equivalence class
construction.
Keywords: Programming language semantics; Abstraction; Finite Au-
tomata; Formal Methods; Verification
Key Terms: FormalMethod, VerificationProcess
1 Introduction
Among the formalisms employed to describe the semantics of transition systems,
two particularly popular choices are abstract machines and structural opera-
tional semantics (SOS). Abstract machines are widely used for modeling and
verifying dynamic systems, e.g. finite automata, Büchi automata or timed au-
tomata [9,4,1]. An abstract machine can be represented as a directed graph
with transition semantics between nodes. The transition semantics is defined by
moving a pointer to a current node. Automata are a popular tool for modeling
dynamic systems due to the simplicity of the verification of automata systems,
which can be carried out in a fully automated way, something that is not gener-
ally possible for Turing-complete systems.
This kind of semantics is often extended by adding a background state com-
posed of a set of variables with their values: this is the case of timed automata,
which use background clock variables [2]. The Uppaal model checker for timed
⋆
N. Baklanova and M. Strecker were partially supported by the project Verisync
(ANR-10-BLAN-0310).
⋆⋆
W. Ricciotti and J.-G. Smaus are supported by the project Ajitprop of the Fonda-
tion Airbus.
355
automata extends the notion of background state even further by adding inte-
ger and Boolean variables to the state [7] which, however, do not increase the
computational power of such timed automata but make them more convenient
to use.
Another formalism for modeling transition systems is structural semantics
(“small-step”, contrary to “big-step” semantics which is much easier to handle
but which is inappropriate for a concurrent setting), which uses a set of reduction
rules for simplifying a program expression. It has been described in detail in [14]
and used, for example, for the Jinja project developing a formal model of the
Java language [10]. An appropriate semantic rule for reduction is selected based
on the expression pattern and on values of some variables in a state. As a result
of reduction the expression and the state are updated.
s′ = s(v 7−→ eval expr s)
[Assignment]
(Assign v expr, s) → (U nit, s′ )
This kind of rules is intuitive; however, the proofs involving them require
induction over the expression structure. A different approach to writing a struc-
tural semantics was described in [3,12] for the CMinor language. It uses a notion
of continuation which represents an expression as a control stack and deals with
separate parts of the control stack consecutively.
(Seq e1 e2 · κ, s) → (e1 · e2 · κ, s) (Empty · κ, s) → (κ, s)
Here the “·” operator designates concatenation of control stacks. The se-
mantics of continuations does not need induction over the expression, something
which makes proof easier; however it requires more auxiliary steps for maintain-
ing the control stack which do not have direct correspondance in the modeled
language.
For modeling non-local transfer of control, Krebbers and Wiedijk [11] present
a semantics using (non-recursive) “statement contexts”. These are combined
with the above-mentioned continuation stacks. The resulting semantics is situ-
ated mid-way between [3] and the semantics proposed below.
The present paper describes an approach to translation from structural op-
erational semantics to finite automata extended with background state. All the
considered automata are an extension of Büchi automata with background state,
i.e. they have a finite number of nodes and edges but can produce an infinite
trace. The reason of our interest in abstracting from structural semantics to
Büchi automata is our work in progress [6]. We are working on a static analysis
algorithm for finding possible resource sharing conflicts in multithreaded Java
programs. For this purpose we annotate Java programs with timing information
and then translate them to a network of timed automata which is later model
checked. The whole translation is formally verified. One of the steps of the trans-
lation procedure includes switching from structural operational semantics of a
Java-like language to automata semantics. During this step we discovered some
problems which we will describe in the next section. The solutions we propose
356
extend well beyond the problem of abstracting a structured language to an au-
tomaton. It can also be used for compiler verification, which usually is cluttered
up with arithmetic adress calculation that can be avoided in our approach.
The contents of the paper has been entirely formalized in the Isabelle proof
assistant [13]. We have not insisted on any Isabelle-specific features, therefore
this formalization can be rewritten using other proof assistants. The full Isabelle
formal development can be found on the web [5].
2 Problem Statement
We have identified the following as the main problems when trying to prove the
correctness of the translation between a programming language semantics and
its abstraction to automata:
1. Preservation of execution context: an abstract machine always sees all the
available nodes while a reduced expression loses the information about pre-
vious reductions.
2. Semantic artifacts: some reduction rules are necessary for the functionality of
the semantics, but may be missing in the modeled language. Additionally, the
rules can produce expressions which do not occur in the original language.
These problems occur independently of variations in the presentation of se-
mantic rules [14] adopted in the literature, such as [10] (recursive evaluation of
sub-statements) or [3,12] (continuation-style).
We will describe these two problems in detail, and later our approach to
their solution, in the context of a minimalistic programming language which only
manipulates Boolean values (a Null value is also added to account for errors):
datatype val = Bool bool | Null
The language can be extended in a rather straightforward way to more com-
plex expressions. In this language, expressions are either values or variables:
datatype expr = Val val | Var vname
The statements are those of a small imperative language:
datatype stmt =
Empty — no-op
| Assign vname val — assignment: var := val
| Seq stmt stmt — sequence: c1 ; c2
| Cond expr stmt stmt — conditional: if e then c1 else c2
| While expr stmt — loop: while e do c
2.1 Preservation of execution context
Problem 1 concerns the loss of an execution context through expression reduc-
tions which is a design feature of structural semantics. Let us consider a simple
example.
357
Assume we have a structural semantics for our minimal imperative language
(some rules of a traditional presentation are shown in Figure 1): we want to
translate a program written in this language into an abstract machine. Assume
that the states of variable values have the same representation in the two systems:
this means we only need to translate the program expression into a directed
graph with different nodes corresponding to different expressions obtained by
reductions of the initial program expression.
s′ = s(v 7−→ eval expr s)
[Assign]
(Assign v expr, s) → (Empty, s′ )
eval bexp s = T rue eval bexp s = F alse
[CondT] [CondF]
(Cond bexp e1 e2, s) → (e1, s) (Cond bexp e1 e2, s) → (e2, s)
Fig. 1. Semantic rules for the minimal imperative language.
On the abstract machine level the Assign statements would be represented
as two-state automata, and the Cond as a node with two outgoing edges directed
to the automata for the bodies of its branches.
Consider a small program in this language Cond bexp (Assign a 5) Empty
and its execution flow.
a:=5
Cond bexp (Assign a 5) Empty (Assign a 5) Empty
Empty
The execution can select any of the two branches depending on the bexp
value. There are two different Empty expressions appearing as results of two
different reductions. The corresponding abstract machine would be a natural
graph representation for a condition statement with two branches (Figure 2).
a:=5
Cond bexp (Assign a 5) Empty Assign a 5 Empty
Cond bexp (Assign a 5) Empty
...
...
Fig. 2. The execution flow and the corresponding abstract machine for the program
Cond bexp (Assign a 5) Empty.
358
During the simple generation of an abstract machine from a program expres-
sion the two Empty statements cannot be distinguished although they should be
mapped into two different nodes in the graph. We need to add more information
about the context into the translation, and it can be done by different ways.
A straightforward solution would be to add some information in order to
distinguish between the two Empty expressions. If we add unique identifiers
to each subexpression of the program, they will allow to know exactly which
subexpression we are translating (Figure 3). The advantage of this approach is
its simplicity, however, it requires additional functions and proofs for identifier
management.
a:=5
Cond n1 bexp (Assign n2 a 5) (Empty n3 ) Assign n2 a 5 Empty n2
Cond n1 bexp (Assign n2 a 5) Empty n3 n2
...
n3
...
Fig. 3. The execution flow and the corresponding abstract machine for the program
with subexpression identifiers Cond n1 bexp (Assign n2 a 5) (Empty n3 ).
Another solution for the problem proposed in this paper involves usage of a
special data structure to keep the context of the translation. There are known ex-
amples of translations from subexpression-based semantics [10] and continuation-
based semantics [12] to abstract machines. However, all these translations do not
address the problem of context preservation during the translation.
2.2 Semantic artifacts
The second problem appears because of the double functionality of the Empty
expression: it is used to define an empty operator which does nothing as well as
the final expression for reductions which cannot be further reduced. The typical
semantic rules for a sequence of expressions look as shown on Figure 4.
(e1, s) → (e1′ , s′ )
[Seq1] [Seq2]
(Seq e1 e2, s) → (Seq e1′ e2, s′ ) (Seq Empty e2, s) → (e2, s)
Fig. 4. Semantic rules for the sequence of two expressions.
359
Here the Empty expression means that the first expression in the sequence
has been reduced up to the end, and we can start reducing the second expression.
However, any imperative language translated to an assembly language would not
have an additional operator between the two pieces of code corresponding to the
first and the second expressions. The rule Seq2 must be marked as a silent
transition when translated to an automaton, or the semantic rules have to be
changed.
3 Zipper-based semantics of imperative programs
3.1 The zipper data structure
Our plan is to propose an alternative technique to formalize operational se-
mantics that will make it easier to preserve the execution context during the
translation to an automata-based formalism. Our technique is built around a
zipper data structure, whose purpose is to identify a location in a tree (in our
case: a stmt) by the subtree below the location and the rest of the tree (in our
case: of type stmt-path). In order to allow for an easy navigation, the rest of the
tree is turned inside-out so that it is possible to reach the root of the tree by
following the backwards pointers. The following definition is a straightforward
adaptation of the zipper for binary trees discussed in [8] to the stmt data type:
datatype stmt-path =
PTop
| PSeqLeft stmt-path stmt | PSeqRight stmt stmt-path
| PCondLeft expr stmt-path stmt | PCondRight expr stmt stmt-path
| PWhile expr stmt-path
Here, PTop represents the root of the original tree, and for each constructor
of stmt and each of its sub-stmts, there is a “hole” of type stmt-path where a
subtree can be fitted in. A location in a tree is then a combination of a stmt and
a stmt-path:
datatype stmt-location = Loc stmt stmt-path
Given a location in a tree, the function reconstruct reconstructs the original
tree reconstruct :: stmt ⇒ stmt-path ⇒ stmt, and reconstruct-loc (Loc c sp) =
reconstruct c sp does the same for a location.
fun reconstruct :: stmt ⇒ stmt-path ⇒ stmt where
reconstruct c PTop = c
| reconstruct c (PSeqLeft sp c2 ) = reconstruct (Seq c c2 ) sp
| reconstruct c (PSeqRight c1 sp) = reconstruct (Seq c1 c) sp
| reconstruct c (PCondLeft e sp c2 ) = reconstruct (Cond e c c2 ) sp
| reconstruct c (PCondRight e c1 sp) = reconstruct (Cond e c1 c) sp
| reconstruct c (PWhile e sp) = reconstruct (While e c) sp
fun reconstruct-loc :: stmt-location ⇒ stmt where
reconstruct-loc (Loc c sp) = reconstruct c sp
360
3.2 Semantics
Our semantics is a small-step operational semantics describing the effect of the
execution a program on a certain program state. For each variable, the state
yields Some value associated with the variable, or None if the variable is unas-
signed. More formally, the state is a mapping vname ⇒ val option. Defining the
evaluation of an expression in a state is then standard.
Before commenting the rules of our semantics, let us discuss which kind
of structure we are manipulating. The semantics essentially consists in moving
around a pointer within the syntax tree. As explained in Section 3.1, a position
in the syntax tree is given by a stmt-location. However, during the traversal of
the syntax tree, we visit each position at least twice (and possibly several times,
for example in a loop): before executing the corresponding statement, and after
finishing the execution. We therefore add a Boolean flag, where True is a marker
for “before” and False for “after” execution.
↓W hile W hile W hile W hile W hile
=⇒ =⇒ =⇒ =⇒
Seq ↓Seq Seq Seq Seq
x := T y := F x := T y := F ↓x := T y := F x := T↑ y := F x := T ↓y := F
Fig. 5. Example of execution of small-step semantics
As an example, consider the execution sequence depicted in Figure 5 (with
assignments written in a more readable concrete syntax), consisting of the ini-
tial steps of the execution of the program While (e, Seq(x := T , y := F )).
The before (resp. after) marker is indicated by a downward arrow before (resp.
an upward arrow behind) the current statement. The condition of the loop is
omitted because it is irrelevant here. The middle configuration would be coded
as ((Loc (x := T ) (PSeqLeft (PWhile e PTop) (y := F ))), True).
Altogether, we obtain a syntactic configuration (synt-config) which combines
the location and the Boolean flag. The semantic configuration (sem-config) ma-
nipulated by the semantics adjoins the state, as defined previously.
type-synonym synt-config = stmt-location × bool
type-synonym sem-config = synt-config × state
The rules of the small-step semantics of Figure 7 fall into two categories:
before execution of a statement s (of the form ((l , True), s)) and after execution
(of the form ((l , False), s)); there is only one rule of this latter kind: SFalse.
Let us comment on the rules in detail:
– SEmpty executes the Empty statement just by swapping the Boolean flag.
– SAssign is similar, but it also updates the state for the assigned variable.
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fun next-loc :: stmt ⇒ stmt-path ⇒ (stmt-location × bool ) where
next-loc c PTop = (Loc c PTop, False)
| next-loc c (PSeqLeft sp c 2 ) = (Loc c 2 (PSeqRight c sp), True)
| next-loc c (PSeqRight c 1 sp) = (Loc (Seq c 1 c) sp, False)
| next-loc c (PCondLeft e sp c 2 ) = (Loc (Cond e c c 2 ) sp, False)
| next-loc c (PCondRight e c 1 sp) = (Loc (Cond e c 1 c) sp, False)
| next-loc c (PWhile e sp) = (Loc (While e c) sp, True)
Fig. 6. Finding the next location
[SEmpty]
((Loc Empty sp, True), s) → ((Loc Empty sp, False), s)
[SAssign]
((Loc (Assign vr vl ) sp, True), s) → ((Loc (Assign vr vl ) sp, False), s(vr 7→ vl ))
[SSeq]
((Loc (Seq c 1 c 2 ) sp, True), s) → ((Loc c 1 (PSeqLeft sp c 2 ), True), s)
eval e s = Bool True
[SCondT]
((Loc (Cond e c 1 c 2 ) sp, True), s) → ((Loc c 1 (PCondLeft e sp c 2 ), True), s)
eval e s = Bool False
[SCondF]
((Loc (Cond e c 1 c 2 ) sp, True), s) → ((Loc c 2 (PCondRight e c 1 sp), True), s)
eval e s = Bool True
[SWhileT]
((Loc (While e c) sp, True), s) → ((Loc c (PWhile e sp), True), s)
eval e s = Bool False
[SWhileF]
((Loc (While e c) sp, True), s) → ((Loc (While e c) sp, False), s)
sp 6= PTop
[SFalse]
((Loc c sp, False), s) → (next-loc c sp, s)
Fig. 7. Small-step operational semantics
– SSeq moves the pointer to the substatement c 1 , pushing the substatement
c 2 as continuation to the statement path.
– SCondT and SCondF move to the then- respectively else- branch of the
conditional, depending on the value of the condition.
– SWhileT moves to the body of the loop.
– SWhileF declares the execution of the loop as terminated, by setting the
Boolean flag to False.
362
– SFalse comes into play when execution of the current statement is finished.
We then move to the next location, provided we have not already reached
the root of the syntax tree and the whole program terminates.
The move to the next relevant location is accomplished by function next-loc
(Figure 6) which intuitively works as follows: upon conclusion of the first sub-
statement in a sequence, we move to the second substatement. When finishing
the body of a loop, we move back to the beginning of the loop. In all other cases,
we move up the syntax tree, waiting for rule SFalse to relaunch the function.
4 Target language: Automata
4.1 Syntax
As usual, our automata are a collection of nodes and edges, with a distinguished
initial state. In this general definition, we will keep the node type ′n abstract.
It will later be instantiated to synt-config. An edge connects two nodes; moving
along an edge may trigger an assignment to a variable (AssAct), or have no
effect at all (NoAct).
An automaton ′n ta is a record consisting of a set of nodes, a set of edges and
an initial node init-s. An edge has a source node, an action and a destination
node dest. Components of a record are written between (| ... |).
4.2 Semantics
An automaton state is a node, together with a state as in Section 3.2.
type-synonym ′n ta-state = ′n ∗ state
Executing a step of an automaton in an automaton state (l , s) consists
of selecting an edge starting in node l, moving to the target of the edge and
executing its action. Automata are non-deterministic; in this simplified model,
we have no guards for selecting edges.
e ∈ set (edges aut)
l = source e l ′ = dest e s ′ = action-effect (action e) s
[Action]
aut ⊢ (l , s) → (l ′, s ′)
5 Automata construction
The principle of abstracting a statement to an automaton is simple; the novelty
resides in the way the automaton is generated via the zipper structure: as nodes,
we choose the locations of the statements (with their Boolean flags), and as edges
all possible transitions of the semantics.
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To make this precise, we need some auxiliary functions. We first define a
function all-locations of type stmt ⇒ stmt-path ⇒ stmt-location list which gath-
ers all locations in a statement, and a function nodes-of-stmt-locations which
adds the Boolean flags.
As for the edges, the function synt-step-image yields all possible successor
configurations for a given syntactic configuration. This is of course an over-
approximation of the behavior of the semantics, since some of the source tree
locations may be unreachable during execution.
fun synt-step-image :: synt-config ⇒ synt-config list where
synt-step-image (Loc Empty sp, True) = [(Loc Empty sp, False)]
| synt-step-image (Loc (Assign vr vl ) sp, True) = [(Loc (Assign vr vl ) sp, False)]
| synt-step-image (Loc (Seq c1 c2 ) sp, True) = [(Loc c1 (PSeqLeft sp c2 ), True)]
| synt-step-image (Loc (Cond e c1 c2 ) sp, True) =
[(Loc c1 (PCondLeft e sp c2 ), True), (Loc c2 (PCondRight e c1 sp), True)]
| synt-step-image (Loc (While e c) sp, True) =
[(Loc c (PWhile e sp), True), (Loc (While e c) sp, False)]
| synt-step-image (Loc c sp, False) = (if sp = PTop then [] else [next-loc c sp])
Together with the following definitions:
fun action-of-synt-config :: synt-config ⇒ action where
action-of-synt-config (Loc (Assign vn vl ) sp, True) = AssAct vn vl
| action-of-synt-config (Loc c sp, b) = NoAct
definition edge-of-synt-config :: synt-config ⇒ synt-config edge list where
edge-of-synt-config s =
map(λ t. (|source = s, action = action-of-synt-config s, dest = t|))(synt-step-image s)
definition edges-of-nodes :: synt-config list ⇒ synt-config edge list where
edges-of-nodes nds = concat (map edge-of-synt-config nds)
we can define the translation function from statements to automata:
fun stmt-to-ta :: stmt ⇒ synt-config ta where
stmt-to-ta c =
(let nds = nodes-of-stmt-locations (all-locations c PTop) in
(| nodes = nds, edges = edges-of-nodes nds, init-s = ((Loc c PTop), True) |))
6 Simulation Property
We recall that the nodes of the automaton generated by stmt-to-ta are labeled by
configurations (location, Boolean flag) of the syntax tree. The simulation lemma
(Lemma 1) holds for automata with appropriate closure properties: a successor
configuration wrt. a transition of the semantics is also a label of the automaton
(nodes-closed ), and analogously for edges (edges-closed ) or both nodes and edges
(synt-step-image-closed ).
The simulation statement is a typical commuting-diagram property: a step of
the program semantics can be simulated by a step of the automaton semantics,
364
for corresponding program and automata states. For this correspondence, we use
the notation ≈, even though it is just plain syntactic equality in our case.
Lemma 1 (Simulation property).
Assume that synt-step-image-closed aut and (((lc, b), s) ≈ ((lca, ba), sa)). If
((lc, b), s) → ((lc ′, b ′), s ′), then there exist lca ′, ba ′, sa ′ such that (lca ′, ba ′)
∈ set (nodes aut) and the automaton performs the same transition: aut ⊢ ((lca,
ba), sa) → ((lca ′, ba ′), sa ′) and ((lc ′, b ′), s ′) ≈ ((lca ′, ba ′), sa ′).
The proof is a simple induction over the transition relation of the program se-
mantics and is almost fully automatic in the Isabelle proof assistant.
We now want to get rid of the precondition synt-step-image-closed aut in
Lemma 1. The first subcase (edge closure), is easy to prove. Node closure is
more difficult and requires the following key lemma:
Lemma 2.
If lc ∈ set (all-locations c PTop) then set (map fst (synt-step-image (lc, b)))
⊆ set (all-locations c PTop).
With this, we obtain the desired
Lemma 3 (Closure of automaton). synt-step-image-closed (stmt-to-ta c)
For the proofs, see [5].
Let us combine the previous results and write them more succinctly, by using
the notation →∗ for the reflexive-transitive closure for the transition relations
of the small-step semantics and the automaton. Whenever a state is reachable
by executing a program c in its initial configuration, then a corresponding (≈)
state is reachable by running the automaton generated with function stmt-to-ta:
Theorem 1.
If ((Loc c PTop, True), s) →∗ (cf ′, s ′) then ∃ cfa ′ sa ′. stmt-to-ta c ⊢ (init-s
(stmt-to-ta c), s) →∗ (cfa ′, sa ′) ∧ (cf ′, s ′) ≈ (cfa ′, sa ′).
Obviously, the initial configuration of the semantics and the automaton are
in the simulation relation ≈, and for the inductive step, we use Lemma 1.
7 Conclusions
This paper has presented a new kind of small-step semantics for imperative
programming languages, based on the zipper data structure. Our primary aim is
to show that this semantics has decisive advantages for abstracting programming
language semantics to automata. Even if the generated automata have a great
number of silent transitions, these can be removed.
We are currently in the process of adopting this semantics in a larger for-
malization from Java to Timed Automata [6]. As most constructs (zipper data
365
structure, mapping to automata) are generic, we think that this kind of seman-
tics could prove useful for similar formalizations with other source languages.
The proofs (here carried out with the Isabelle proof assistant) have a pleasingly
high degree of automation that are in sharp contrast with the index calculations
that are usually required when naming automata states with numbers.
Renaming nodes from source tree locations to numbers is nevertheless easy
to carry out, see the code snippet provided on the web page [5] of this paper.
For these reasons, we think that the underlying ideas could also be useful in the
context of compiler verification, when converting a structured source program to
a flow graph with basic blocs, but before committing to numeric values of jump
targets.
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https://bitbucket.org/Martin_Strecker/abstracting_op_sem_to_automata.
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tion. MIT Press, Cambridge, MA, USA, 1993.
366
The Static Analysis of Linear Loops
Michael Lvov1, Yulia Tarasich1,
1
Kherson State University, 40 rokiv Zhovtnya St. 27
73000, Kherson, Ukraine
{Lvov, YuTarasich}@ksu.ks.ua
Abstract. In the first part of the paper, we consider the problem of generation
of polynomial invariants of iterative loops with operator of initialization of loop
and non-singular linear operator in the loop body. In the article we also show
the algorithm for calculating the basic invariants for linear operator of the
Jordan cell, and an algorithm for calculating the basic invariants of
diagonalizable linear operator with an irreducible minimal characteristic
polynomial. The second part presents a new method for proving the invariance
of the system of linear inequalities and of termination of certain linear iterative
loops of imperative programs whose data are elements of the constructive
linearly ordered field. The theoretical material of the paper is illustrated by
examples.
Keywords. Static program analysis, polynomial invariant of a loop, invariant
system of linear inequalities, eigenpolynomial of a linear operator.
Key Terms. VerificationProcess, Method, FormalMethod
1 Introduction
As for now, methods of program statistical analysis are being studied intensely.
One of the important problems is a problem of the automatic generation of program
invariants. Invariants of program are used particularly in methods of programs
verification.
The problem of searching for loop invariants in imperative programs was offered
by R. Floyd [1] and C. Hoare [2].
A correctness property of the program is formulated in terms of its total or partial
correctness. Often, the proof of termination of the program should be implemented
separately from the proof of its partial correctness. The algorithmic unsolvability of
the termination problem shows that the general algorithm of proof of termination of
the program does not exist. To prove the partial correctness of programs, Р. Floyd and
S. Hoare offered the idea of building loop invariants [1] and invariant relations in
control points of programs [2], which allows to prove programs by method of math
induction.
Thus, there is a problem of finding the invariants of the program as a key problem
of analysis of programs properties.
367
Now, the main attention is paid to the problem of constructing polynomial
invariant equalities. A set of invariant equalities forms the polynomial ideal, a finite
basis of which one must build. Note that in a general case, the problem of
constructing this basis has not been solved.
The existence and efficiency of algorithms to generate program invariants depend
on the subject domain, i.e., on the properties of the data algebras the program deals
with. Problems of automatic generation of program invariants for various data
algebras have been being analyzed since beginning of 1970s at the Institute of
cybernetics of NAS of Ukraine. Their main results are represented in [3,4].
Numerical data algebras are the most important from the practical point of view.
The paper [5] outlines two methods of constructing polynomial invariant equalities
types in programs whose data algebra is the domain of integrity (polynomially
determinate programs) or a field (rationally determinate programs).
This idea used in [6] to generate polynomial invariants of bounded degree for
polynomially determined programs. Program conditions such as f ( X ) 0 were
taken into account, where f (X ) are polynomials of program variables. In [7] they
proposed a method to generate polynomial program invariants of bounded degree in
linearly determinate (affine) programs containing recursive procedure calls.
In [8] they proposed a method to generate polynomial loop invariants as template
polynomials with the use of the algorithm for computing Grobner bases. In [9] they
described a method to generate nonlinear and, generally speaking, nonpolynomial
invariant relation for linear loops. The method uses eigenvalues and eigenvectors of
the linear operator in the loop body.
The paper [10] is devoted to the algebraic fundamentals of the problem of
generating polynomial loop invariants. The main result of the study is an algorithm
for generating all polynomial invariants for loops with so-called solvable assignment
operators. In particular, affine operators with positive real eigenvalues are solvable.
The same authors [11] proposed a method to generate polynomial loop invariants,
including enclosed loops, as well as program conditions in the form of both
polynomial equalities and inequalities. The paper considers a great number of
examples and presents tables for the algorithm time depending on technical
parameters of the program being analyzed.
In [12] they proposed an algorithm to search for loop invariants based on a system
of recurrent relations with loop variables and parameter n, which is the loop index.
The algorithm searches for the solution of this system not depended on n. It is
implemented in Theorema software system and is illustrated with examples in detail.
The problem of the description of invariant inequalities is less studied. The main
intricacy lies in the infinity of the basis of the metaideal [13] of polynomial
inequalities [13, 14]. Iterative methods for solving the problem of the description of
linear invariant inequalities were considered in [15-18]. In [15], the problem of
generation of the simplest invariant inequalities is solved. In [16-17], general iterative
methods are used to solve the problem of searching for linear invariant inequalities.
In [19] they described a method of proving the invariance of the system of linear
inequalities for a class of linear iterative loops with real eigennumbers of linear
368
operators in the loop body. This method can be applied to the entire class of linear
iterative loops and it can also be applied to prove their termination. The paper with
description of it is under preparation for a publication.
2 The Static Analysis of Polynomial Invariant Equations
2.1 L-invariants of Linear Maps and Invariants of Linear Loops.
Definition 1. Let W be an n-dimensional vector space over the field of rational
_
numbers Q and let Q be the algebraic closure of the field Q . Let X ( x1 ,....xn )
_
be an n -dimensional vector of variables. A rational function p( X ) Q( X ) is
called L-invariant of a linear operator A : W W if, for any vector b W the
following relationship holds:
p( A b) p(b) (1)
Example 1. (a linear operator with characteristic polynomial x 2 )
3
Let us consider a linear operator with the matrix
0 1 0
A 0 0 1 , X ( x, y, z ) .
2 0 0
It's easy to calculate [26], that the rational expression
(12 x 1 y z )(32 x 3 y z )
p( x, y, z ) (2)
(22 x 2 y z ) 2
2 2
where 1 2 , 2 2 , 3 2 , and cos( ) i sin( ) is the
3 3 3 2
3 3
primitive third root of unity, is the L-invariant of this operator.
Definition 2. Let X ( x1 ,..., xn ) and b (b1 ,..., bn ) - be two collections of
variables. The following fragment of an imperative program is called a linear loop:
X := b;
While Q(X, b) do X := A*X
Remark 1. Operators X:=b and X:=A*X are interpreted as simultaneous
assignments of the values of the variables of the right sides to the variables on the left
sides. In what follows, we ignore the condition Q(X, b) and consider that the linear
loop is infinite and that its execution is nondeterministic. Thus, we consider loops of
the form
369
X := b;
While True|False do X := A*X (3)
Definition 3. Let a vector b( 0) (b1( 0) ,..., bn( 0) ) W be chosen as initial.
( j 1)
Sequence of vectors, set by recurrent correlation b Ab , will be called the
( j)
orbit of linear operator A .
A loop sets the orbit of linear operator A in space W . Obviously, an orbit A lies
in some one-dimensional variety, and the system of invariants characterizes this
variety as algebraic.
Definition 4. Polynomial P(b, X ) is called loop invariant if, for any natural j
and any b
(0)
P(b(0) , b( j ) ) 0 .
Theorem 1. If p( X ) r ( X ) q( X ) is an L-invariant of a linear operator A ,
then the polynomial r ( X )q(b) q( X )r (b) is an invariant of a linear loop over the
_
field Q .
We call such loop invariants L-invariants (of linear loops).
Example 2. (a linear loop with operator from example 1)
The linear loop corresponding to the operator A , has the form
(x, y, z) := (a, b, c);
While True|False do (x, y, z) := (y, z, 2*x)
L-invariant of this loop is defined by formula (2):
P( x, y, z, a, b, c) (12 x 1 y z )(32 x 3 y z )(22 a 2 b c) 2
(4)
(22 x 2 y z ) 2 (12 a 1b c)(32 a 3b c)
Note that L-invariant of the loop P( x, y, z, a, b, c) is defined over a field
_
Q(1 , 2 , 3 ) . However, it has a set of L-invariants with coefficients from the field
Q , which can be constructed, they are shown in (4) the canonical form to the
polynomial from 1 , 2 , 3 , and then - to the polynomial from 2 with using the
relation 13 2 and Vieta's relation. Technique for computing L-invariants over a
2
field Q is demonstrated in [20]. Note that if the variables a, b, c are the assigned
numeric values, L-invariant is converted into a loop invariant.
In [22] they described the results, that link L-invariants to eigenvalues and
T
eigenvectors of the operator A . The main result of this work:
Theorem 2 (about the multiplicative relations). Let 1 ,..., m be eigenvalues of a
T
linear operator A and let s1 ,..., sm be eigenvectors of the conjugate operator A
370
that correspond to these eigenvalues. We assume that there are integers k1 ,..., k m
such that
1k ... m k 1 .
1 m
(5)
Then
p( X ) (s1 , X ) k1 ... (sm , X ) km (6)
is L-invariant of the linear operator A .
Proof of the theorem 2 can be found in [21]
Example 3 (continuation of example 2). Apply the theorem 2 to the example 2.
Calculate the eigennumbers of operator A.
0 1 0 1 0
A 0 0 1 , h ( ) A E 0 1 3 2 .
2 0 0
2 0
A characteristic polynomial has the form b h( x) x 2 . Its roots are
3
1 3 2 , 2 3 2 , 3 3 2 2 , where exp(i 2 3) is the primitive cube
root of unity.
0 0 2
Calculate the eigenvectors s1 , s2 , s3 of matrix A 1 0 0 :
T
0 1 0
s1 (12 , 1 , 1), s2 (22 , 2 , 1), s3 (32 , 3 , 1) .
It is easy to check that 1 2 3 1 . By the theorem 2 the operator A has a L-
2
invariant (2).
Corollary 1. If the minimum characteristic polynomial h(x) of linear operator
A has a free term equal to 1 (i.e. det( A) 1 ), then the linear operator A has
a L-invariant.
Example 4. A loop of the points rotation of a plane (a, b) at an angle
arctan(4 3) .
(x,y) := (a,b);
While True do (x, y):= (4/5*x - 3/5*y, 3/5*x + 4/5*y)
Calculate the eigenvalues and eigenvectors of the operator A :
371
4 / 5 3 / 5 8
A . h( ) A E 2 1 .
3/ 5 4 / 5 5
4 3 4 3
1 i , 2 i . s1 (i, 1), s2 (i, 1) .
5 5 5 5
Since 12 1 , L-invariant of the operator A is
p( x, y) (ix y)(ix y) x 2 y 2 .
And the loop invariant is x y a b .
2 2 2 2
Example 5. Loop of Fibonacci sequence calculation, starting with a pair of (a, b) .
(x,y) := (a,b);
While True|False do (x, y):= (x + y, x)
Calculate the eigenvalues and eigenvectors of the operator A :
1 1
A . h( ) A E 2 1 .
1 0
1 1 1 1
1 5 , 2 5.
2 2 2 2
1 1 1 1
s1 (1 , 1) ( 5 , 1), s2 (2 , 1) ( 5 , 1) .
2 2 2 2
Since 12 1 , L-invariant of the operator A is
p( x, y) ((1 x y)(2 x y)) 2 ( x 2 xy y 2 ) 2 .
The invariant relation of loop is ( x xy y ) (a ab b ) .
2 2 2 2 2 2
Corollary 2. If the characteristic (minimum) polynomial h(X ) of linear operator
A is x m a , then linear operator has an L-invariants.
Proofs of corollaries 1 and 2 are in [21]
Theorem 3. Let h(x) be an polynomial from variable x with rational
coefficients and (1 ,..., m ) are all its roots in an algebraic closure Q of the
field Q . Consider the set G(h) {x1 1 ... xmm : 11 ... mm 1} that is the set of
k k k k
monomials of the field of rational expressions Q(X ) (possibly with negative
degrees), who receive a value of 1 when we substitute i instead of xi . Then G (h)
is a multiplicative abelian group with a finite number of generators.
The proof of theorem 3 is obvious, since the subgroup of an abelian group with a
finite number of generators has a finite number of generators.
372
It follows from theorem 3 that the main problem for the generation of L-invariants
is the problem of finding an algorithm for constructing a set that generate the groups
G(h) .
Example 6 (continuation of example 3). It is easy to see that we have the following
multiplicative relations for the polynomial h( x) x 2 between its roots:
3
12 2 3 , 12 32 , 13 22 , 32 33
These relations have relevant binomials
x12 x2 x3 , x1 x2 x32 , x1 x3 x22 , x23 x33 ,
that form a Gröbner basis of the ideal I (GB ) I (G(h)) .
Corollary 3. The set of all L-invariant of operator A defines the field of rational
expressions.
Proof of corollary 3 is in [21]
Theorem 4 Let f (x) be irreducible over the field Q and reduced polynomial and
_
{1, 2 ,...m} is the set of its roots over the field Q . If we have a nontrivial
multiplicative relationship 11 ...mm 1 with integer indices k1 ,..., km between his
k k
m
roots, then the free term am f (x) equal to 1 or k i 0 .
i 1
The proof is in [21]
Definition 5. L-invariants of operator A , defined of multiplicative relation
between the roots of the characteristic polynomial 1 ... m 1, will be called
whole. L-invariants of operator A , defined of multiplicative relation
... 1, ki 0 , will be called rational.
k1
1
km
m
Theorem 5. If the characteristic polynomial of operator A is h( x ), k 1 , then
k
operator A has a rational L-invariants.
The proof of theorem 5 is in [21]
2.2 L-invariants of Jordan Cells
A nondegenerate linear operator A can be represented in a suitable basis by the
following Jordan form of its matrix [18, 22].
J 1 (1 ) 0 ... 0
0 J 2 ( 2 ) ... 0
A , (7)
. . ... .
0 0 ... J m (m )
where J i (i ) are Jordan cells of different sizes. Jordan cell is of the form
373
1 ... 0
0 ... 0
J ( ) (8)
0 ... 1
0 ... 0
Thus, theorem 2 is applied only to the rows of the matrix of the linear operator A ,
that correspond to the eigenvectors of A , i.e., to the collection of the last rows of
Jordan cells J i (i ) , i 1,..., m . Below, we will extend this theorem to arbitrary
nondegenerate linear operators by considering Jordan cells on the whole.
Transformation J : J * X , where X ( x1 ,..., xk ) , in the coordinate form is
x1 : x1 x2 ;...; xk 1 : xk 1 xk ; xk : xk
df df
Introduce the following notation: xk 1 y, xk z .
For each Jordan cell J k (k ) of the Jordan form of the operator A its own
sequence of subspaces of eigenpolynomials is determined.
The main theory of the eigenpolynomials of Jordan cells as well as of the
relationship between eigenpolynomials and L-invariants of linear operators is
formulated in [23, 24].
The concept of eigenpolynomial of a linear operator can be of an independent
interest for linear algebra applications.
If all eigennumbers of linear operator A are rational numbers, then the problem of
constructing this basis is an algorithmically solvable with the help of
theoretical&number algorithm.
In the [25] a direct method of finding invariants of Jordan cells is described. The
main results of this work are discussed below.
Theorem 6 (about the structure of the ideal of invariants). Let A be an arbitrary
nondegenerate linear operator, presented in a suitable basis of matrix (7),
I J1 ( A),..., I J k ( A) are ideals of his invariants, presented in homogeneous
coordinates
uij xij zi , ui yi / zi eij aij c i , ei bi c i
by basis of the form
u j q j ( , u,1) , j 1,..., n 2
and I (A) is an ideal of invariants of the operator Ared , and I ( A) is an ideal of
invariants of the operator A (of the loop (3)). Then
GBase( I ( A)) GBase( I J1 ( A)) ... GBase( I J k ( A)) GBase( I ( A))
Theorem 7. If a group of multiplicative relations of roots of an irreducible
polynomial f (x) is nontrivial ( MR( f ) (e)) , there may be two situations:
374
1. The set of roots (1 ,..., n ) is divided into certain number l of equally-
powerful classes 1,..., l ; j {( j 1) d 1,... jd }; j 1,..., l.
wherein d len ( j ), n ld . Multiplicative relations from MR( f ) in this
situation have the form j j , j 1,..., l , where j are roots from 1.
2. The equally-powerful classes 1 ,..., l , i {(i 1) d 1 ,...id }; i 1,..., k.
Wherein d len ( j ), n kd . Multiplicative relations from MR( f ) MR( f )
in this situation have the form i ij j , i 1,..., l , where j are roots from 1.
Both situations may occur simultaneously.
For the proof of theorem 7, take a look in [25]. This theorem has a key role for the
algorithm of calculation of the system generators of the group MR( f ) .
Theorem 8. Let f ( x) Q[ x] is an irreducible polynomial and 1 ,..., m are its
roots. The problem of constructing a basis of a set of generating the group
GU (h) {x1k1 ...xmkm : 1k1 ...kmm U }, where U is a group of all roots from 1 is
algorithmically solvable.
The proof of theorem 8 is in [25].
Thus, by theorem 6, the invariants of a linear operator can be classified as
intracellular - that are inherent to each Jordan cell of linear operator, and intercellular
- those that are inherent in its diagonalisable part.
Intracellular invariants are computed directly from the formulas of [25]
cy bz cy bz
C1 ( ) C n j ( )
z cz cz
x j (a j a j 1 ... a ).
n j
n
c
The existence of intercellular invariants depend on the existence of nontrivial
multiplicative relations between the eigenvalues of the linear operator (theorem 2).
For linear operators with an irreducible minimum characteristic polynomial
problem of constructing a basis of set of multiplicative relations between its
eigenvalues is algorithmically solvable, but the algorithm of theorem 8 is ineffective
due to a very large degree of the polynomial S (x) , which is be necessary to
decompose into factors.
The problem of constructing a basis of set of multiplicative relations for arbitrary
linear operators is still open.
3 The Static Analysis of Linear Inequalities.
Let W K n be an n-dimensional vector space over a linearly ordered and
_
constructive field K and K is an algebraic closure of K .
375
Definition 6. As a linear semi-algebraic set M ( x1 ,..., xn ) is called the area W ,
that is defined by a quantifier-free formula in the signature of the logical connectives
,&, with linear inequalities in the variables x1 ,..., xn as atoms. If the field
M is given by the formula F (X ) , i.е. М {X : F(X)} , We shall denote it by
M ( F ( X )) .
Definition 7. Let X ( x1 ,..., xn ), and b (b1 ,..., bn ) be two vectors of
variables. The linearly loop with the precondition is a fragment of imperative program
in the form
X := b; // S (b ) - a precondition
While U(X, b) do X := A*X (9)
where S (b ) , and U ( X , b ) are quantifier-free formulas of applied logic of linear
semi-algebraic sets, A is a matrix of the linear operator W W .
Non-deterministic and associated with loop (9) we call the loop of the form
X := b; // S (b ) - a precondition
While True|False do X := A*X (10)
whose number of repeats is nondeterministic.
Remark 2. Definition 7 of loops differs from the definitions 2 and 3 because of its
precondition S (b ) that limited the initial values of the loops variables by a linear
semi-algebraic set and an introduction to the consideration of the conditions of the
loop U ( X , b ) .
Definition 8. Linear inequality P( X , b) K [ X , b] is called an invariant for the
1
loop (9) with a precondition S (b) , if it is executed whenever the loop body is
executed.
df
P( X , b) a1 x1 ... an xn a1' b1 ... an' bn
Thus, the invariance means performing of a sequence of formulas
S (b) P(b, b) , // Invariant is executed in the input in the loop
U (b, b) P( Ab, b) , // Invariant is executed after the first iteration
U ( Ab, b) P( A2 b, b) , // Invariant is executed after the second iteration
…
U ( Ak b, b) P( Ak 1b, b) , // Invariant is executed after the k-th iteration
U ( Ak b, b) P( Ak b, b) // Invariant is executed at the completion of the
loop
376
Theorem 9. If all eigenvalues (1 ,..., n ), i K of operator A are real,
the problem of proving of the invariance P( X , b) for the loop (9) is algorithmically
solvable.
The main content of the proof of theorem 9 is formulated in lemmas 1-5 [13].
Definition 9. The linearly defined loop (10) is called completed if for any
b M (S ( X )) the sequence
b (0) b , b ( m 1) Ab ( m) , m 0,1,... (11)
for some natural m* m * (b ) satisfies the relationship U (b
( m*)
,b ) .
Thus, if the loop is completed, for each b M ( S ( X )) is the smallest positive
integer m * (b ) , on which the loop (9) is completed.
Definition 10. Let a , c K . A linear inequality
n
df
L(a , c , X , b ) (a , X ) (c , b ) (12)
is called conditional invariant of linear certain loop (9) (with a precondition
S (b ) ), if for any b M ( S ( X )) Orbit( A, b ) (11) is satisfies to relations
S (b ) L(a , c , b , b ) , U (b ( m1) , b ) L(a , c , b ( m) , b ), m 1,2,..., m * (b ) .
Remark 3. If the loop (10) is not completed (is branched) at some point b ,
m * (b ) it should be considered equal to infinity.: m * (b ) .
Example 7.
S ( x, y) (0 x 1) & (0 y 1) ,
U ( x, y, b1 , b2 ) (| x b1 | ) & (| y b2 | ) ,
3 / 5 4 / 5
A .
4 / 5 3 / 5
L x y 2b1 2b2 // a (1,1), c (2, 2) .
377
b
L(a, c , X , b )
U ( X , b )
Fig. 2. Geometric illustration of the linear defined loop.
In this example, the linear operator A is an operator of rotation for
angle arctg (4 / 3) . A starting point b belongs to the unit square. The orbit of a
linear operator A is a sequence, each point of which lies on the loop
x y b b22 . The condition of repeating of the loop is a «point ( x, y) that
2 2
1
2
lies outside the square with side 2 and center at (b1 ,b2 ) ». Therefore, a loop is
completed when the point gets inside this square, i.e. a point will make the rotation by
angle 2k with accuracy equal to . Since the angle is incommensurate
with , the orbit of the operator A is a dense set on the circle x y b1 b2 ,
2 2 2 2
therefore, the loop is complete. In this example, the basic algorithm is used to prove
that L x y 2b1 2b2 is a conditional invariant of loop.
Let f (x) be a minimal characteristic polynomial of the operator A ,
{1,..., n } is a set of its roots (spectrum A ). Suppose further that, 1 ,..., 2 k
is a set of complex eigenvalues, and 2 k 1 ,..., n is a set of real eigennumbers
and 1 2 ,..., 2 k 1 2 k than we obtain a representation of a linear operator in
the so-called real Jordan form:
B1 0 . 0 . . 0
0 B2 . 0 . . 0
. . . . . . .
A 0 ... 0 Bk . ... 0
0 . . 0 2 k 1 ... 0
. . . . . . .
0 ... n
. . . 0
378
j j
B j rj
j .
Where
j
Remark 4. After the transition to a basis of eigenvectors the coefficients of
inequality will be changed. If S () is a transition matrix, then the new values of the
1 1
vectors a, b calculated by the formulas a Sa S , b Sb S . But in order
(S ) (S )
not to overload the text by new notations, we will use the old notations.
df
Note, that the matrix of the form B , where 1 is a matrix
2 2
of rotation of vector of two-dimensional space on the angle , that is defined by
ratios cos( ) , sin( ) . That is why
cos( j ) sin( j )
B j rj
sin( j ) cos( j ) , r j j j 2 j 2 .
inequality (12), whose invariance is regarded by a loop (11) with a specific initial
value b , indicates that X Orbit( A, b )(a , X ) (c , b ) . Algorithm of prove of
the invariance of (12) will be formulated in the equivalent form:
Sup ( a , X ) (c , b ) .
X Orbit( A, b )
df
Let us consider the linear form a1 x1 a2 x2 ... an xn (a , X ) . The
transformation X : A * X converting this form in (a, AX ) , and m is a multiple
m
iteration of loop, that is described by the transformation X : A * X - in
(a, Am X ) .
X1 ( x1, x2 ),..., X k ( x2k 1, x2k ) a1 (a1, a2 ),..., ak (a2k 1, a2k )
Let , .
Then
(a , X ) (a1, X1 ) ... (ak , X k ) a2k 1x2k 1 ... an xn
(13)
Conversion (a , AX ) of a linear form can be written as
(a , AX ) (a1 , B1 X 1 ) ... (ak , Bk X k ) 2k 1a2k 1 x2k 1 ... n an xn
(14)
And its m -th iteration can be written as
(a , Am X ) (a1 , B1m X 1 ) ... (ak , B km X k ) m2 k 1 a2k 1 x2k 1 ... mn an xn (15)
Passing in (14) to the representation in the form B j r j B j , we obtain:
(a , Am X ) r1m (a1 , B1m X 1 ) ... rkm (ak , B km X k ) m2 k 1 a2 k 1 x2k 1 ... mn an xn
379
Consider the question of the set of values of the operator orbit
(a1 , B1 X 1 ) ... (ak , B k X k ) for the initial value b
m m ( 0)
(b ,..., b ) , where
1
( 0)
k
( 0)
b j (b2 j 1, b2 j ) , j 1,..., k . The interpreted pair X j shall be as points on the two-
df cos( j ) sin( j )
dimensional plane, and the conversion of B j - as a
sin( j ) cos( j )
rotations of points X j on the angle j .
The proof is formulated in lemmas 1-7 in [20].
Theorem 10. The problem of proving the invariance of inequality L(a , c , X , b )
for the loop (9) with diagonalizable linear operator A and with an initial point b is
algorithmically solvable.
Theorem 11. The problem of proving the invariance of inequality L(a , c , X , b )
for the loop (9) (i.e., with the precondition S (b) ) is algorithmically solvable.
Theorem 12. The problem of termination of the loop (9) is algorithmically
solvable. Proof of theorems 10-12 is in [20].
4 Conclusion
This review represents main results of several works of one of the authors of the
theory of program invariants. Subject of the research is an invariant of linear iteration
loops. A new approach to the problems of static analysis of linear loops is
represented: the problem of generating of polynomial invariance equations and the
problem of proving the invariance of linear inequalities. This approach uses the
representation of a linear operator in the loop body in the Jordan form and is based on
the analysis of the spectrum of this operator.
The main results about invariant equality are the theorem 2 about multiplicative
relations, a formula of invariant equations for the Jordan cell, a theorem 6 of the
structure of a basis of the ideal of polynomial invariants, and, also, the algorithm of
constructing of the basis of ideal of polynomial invariants for operators with
irreducible over the field of rational numbers characteristic polynomial. Thus, for a
given problem the problem of constructing of the basis of ideal of polynomial
invariants for operators with a reducible characteristic polynomial remains open.
From the practical view, the interest is in constructing the corresponding effective
algorithms.
Unlike polynomial equations, the set of linear invariant inequalities does not have a
finite basis. Therefore, a method of generating the basis is not applicable to this task.
This paper represents the basic idea of the direct method of proof of the invariance of
linear inequalities. There is a need to note, that the key role in the method is played by
the set of maximal (from the modulus) eigenvalues of operator A . In this case, the
case of maximal real eigenvalues and the maximal complex eigenvalues are
significantly different. In the second case, the method uses the original method of
380
finding the maximum of the linear form in the orbit of a linear operator, and various
algorithms of computation in the field of algebraic number.
There is a need to assume that this method can be used as a basis for a general
algorithm of proving the invariance of a system of linear inequalities for linear-certain
programs, similar to the method of proof of invariance of polynomial equations [5, 6],
and to prove the invariance of polynomial inequalities for linear-certain programs.
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382
Defining Finitely Supported Mathematics
over Sets with Atoms
Andrei Alexandru and Gabriel Ciobanu
Romanian Academy, Institute of Computer Science, Iaşi
andrei.alexandru@iit.academiaromana-is.ro
gabriel@info.uaic.ro
Abstract. This paper presents some steps of defining a finitely sup-
ported mathematics by using sets with atoms. Such a mathematics gen-
eralizes the classical Zermelo-Fraenkel mathematics, and represents an
appropriate framework to work with (infinite) structures in terms of
finitely supported objects. We focus on the techniques of translating
the Zermelo-Fraenkel results to this finitely supported mathematics over
sets with atoms.
Keywords: Fraenkel-Mostowski set theory, invariant sets, finite support prin-
ciple, Finitely Supported Mathematics.
Key-Terms: FormalMethod, MathematicalModel, Research.
1 Introduction
Since the experimental sciences are mainly interested in quantitative aspects,
and since there exists no evidence for the presence of infinite structures, it be-
comes useful to develop a mathematics which deals with a more relaxed notion
of (in)finiteness. We present our attempt of building the necessary concepts and
structures for a finitely supported mathematics. What we call Finitely Sup-
ported Mathematics is a mathematics which is consistent with the axioms of
the Fraenkel-Mostowski (FM) set theory. The FM axioms represents an “ax-
iomatization” of the FM permutation model of the Zermelo-Fraenkel set theory
with atoms; in this way, these axioms transform this model into an independent
set theory. The axioms of the FM set theory are precisely the Zermelo-Fraenkel
with atoms (ZFA) axioms over an infinite set of atoms [16], together with the
special property of finite support which claims that for each element x in an
arbitrary set we can find a finite set supporting x. Therefore in the FM universe
only finitely supported objects are allowed. The original purpose of the FM set
theory was to provide a mathematical model for variables in a certain syntax.
Since they have no internal structure, atoms can be used to represent names.
The finite support axiom is motivated by the fact that syntax can only involve
finitely many names. The FM set theory provides a balance between rigorous
formalism and informal reasoning. This is discussed in [23], where principles of
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structural recursion and induction are explained in the FM framework. We can
use this theory in order to manage infinite structures in a finitary manner, that
is, in the FM framework we try to model the infinite using a more relaxed notion
of finite, i.e, the notion of finite support.
Although a set of axioms for describing sets with atoms (or FM-sets) was
introduced in [16], an earlier idea of using atoms in computer science belongs to
Gandy [17]. Gandy proved that any machine satisfying four physical ‘principles’
is equivalent to some Turing machine. Gandy’s four principles define a class of
computing machines, namely the ‘Gandy machines’. Gandy machines are rep-
resented by classes of ‘states’ and ‘transition operations between states’. States
are represented by hereditary finite sets built up from an infinite set U of atoms,
and transformations are given by restricted operations from states to states. The
class HF of all hereditary finite sets over U introduced in Definition 2.1 from [17]
is described quite similar to the von-Neumann cumulative hierarchy of FM-sets,
F MA presented in [16]. The single difference between these approaches is that
each HFn+1 is defined inductively involving ‘finite subsets of U ∪ HFn ’, whilst
each F Mα+1 (A) is defined inductively by using ‘the disjoint union between A
and the finitely supported subsets of F Mα (A)’; HF is the union of all HFn
(with the mention that the empty set is not used in this construction), and the
family of all FM-sets is the union of all F Mα from which we exclude the set A
of atoms. The support of an element x in HF , obtained according to Definition
2.2(1) of [17], coincides with supp(x) (with notations from Definition 2(4)) if we
see x as an FM-set. Also, the effect of a permutation π on a structure x described
in Definition 2.3 from [17] is defined analogue as the application of the SA -action
on F MA to the element (π, x) ∈ SA × F MA . Obviously, the Gandy’s principles
can also be presented in the FM framework because any finite set is well defined
in FM; however, an open problem regards the consistency of Gandy’s principles
when ‘finite’ is replaced by ‘finitely supported’.
The construction of the universe of all FM-sets [16] is inspired by the con-
struction of the universe of all admissible sets over an arbitrary collection of
atoms [6]. The hereditary finite sets used in [17] are particular examples of ad-
missible sets. The FM-sets represent a generalization of hereditary finite sets
because any FM-set is an hereditary finitely supported set.
In the literature there exist various approaches regarding the FM framework.
We try to clarify the differences between these approaches.
– The FM permutation model of the ZFA set theory.
This model was introduced by Fraenkel [14] and extended by Lindenbaum
and Mostowski [21]. Its original aim was to establish the independence of the
axiom of choice from the other axioms of the ZFA set theory. There also exist
some other permutation models of ZFA presented in [20] which are defined
by using countable infinite sets of atoms.
– The FM axiomatic set theory. This set theory was presented in [16]. It is
inspired by the FM permutation model of the ZFA set theory. However, the
FM set theory, the ZFA set theory and the Zermelo-Fraenkel (ZF) set theory
are independent axiomatic set theories. All of these theories are described by
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axioms, and all of them have models. For example, the Cumulative Hierarchy
Fraenkel-Mostowski universe F MA presented in [16] is a model of the FM
set theory, while some models of the ZF set theory can be found in [19], and
the permutation models of the ZFA set theory can be found in [20]. The sets
defined using the FM axioms are called FM-sets. A ZFA set is an FM-set if
and only if all its elements have hereditarily finite supports. Note that the
infinite set of atoms in the FM set theory does not necessary be countable.
The Fraenkel-Mostowski set theory is consistent whether the infinite set of
atoms is countable or not. In [16] it is used a countable set of atoms in
order to define a model of the Fraenkel-Mostowski set theory for new names
in computer science, while in [7] there are described FM-sets over a set of
atoms which do not represent a homogeneous structure. Also, in [12] the
authors use non-countable sets of atoms (like the set of real numbers) in
order to study the minimization of deterministic timed automata.
– Nominal sets. These sets can be defined both in the ZF framework [24] and
in the FM framework [16]. In ZF, a fixed infinite set A is considered as a set of
names. A nominal set is defined as a usual ZF set endowed with a particular
group action of the group of permutations over A that satisfies a certain
finiteness property. Such a finiteness property allows us to say that nominal
sets are well defined according to the axioms of the FM set theory whenever
the set of names is the set of atoms in the FM set theory. There exists also
an alternative definition for nominal sets in the FM framework. They can be
defined as sets constructed according to the FM axioms with the additional
property of being empty supported (invariant under all permutations). These
two ways of defining nominal sets finally lead to similar properties. According
to the previous remark we use the terminology “invariant” for “nominal” in
order to establish a connection between approaches in the FM framework and
in the ZF framework. Moreover, we can say that any set defined according
to the FM axioms (any FM-set) can be seen as a subset of the nominal
(invariant) set F MA . However, an FM-set is itself a nominal set only if it
has an empty support. The theory of nominal sets makes sense even if the set
of atoms is infinite but not countable. Informally, since the ZFA set theory
collapses into the ZF set theory when the set of atoms is empty, we can
say that the nominal sets represent a natural extension of the usual sets.
In computer science, nominal sets offer an elegant formalism for describing
λ-terms modulo α-conversion [16]. They can also be used in algebra [5, 2],
in proof theory [27], in domain theory [26], in topology [22], semantics of
process algebras [4, 15] and programming [25]. A survey on the applications
of nominal sets in computer science emphasizing our contributions can be
found in [3].
– Generalized nominal sets. The theory of nominal sets over a fixed set A
of atoms is generalized in [10] to a new theory of nominal sets over arbitrary
(unfixed) sets of data values. This provides the generalized nominal sets. The
notion of ‘SA -set’ (Definition 2) is replaced by the notion of ‘set endowed
with an action of a subgroup of the symmetric group of D’ for an arbitrary set
of data values D, and the notion of ‘finite set’ is replaced by the notion of ‘set
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with a finite number of orbits according to the previous group action (orbit-
finite set)’. This approach is useful for studying automata on data words [10],
languages over infinite alphabets [8], or Turing machines that operate over
infinite alphabets [11]. Computations in these generalized nominal sets are
presented in [9, 13].
As their names say, the nominal sets are used to manage notions like renaming,
binding or fresh name. However, this theory could be studied deeper from an
algebraically viewpoint, and it could be used in order to characterize some infinite
structures in terms of finitely supported objects.
Finitely Supported Mathematics (FSM) is introduced to prove that
many finiteness ZF properties still remain valid if we replace the term ‘finite’
with ‘infinite, but with finite support’. Such results have already been presented
in [5] where we proved that a class of multisets over infinite alphabets (inter-
preted in the nominal framework) has similar properties to the classical multisets
over finite alphabets. FSM is the mathematics developed in the world of finitely
supported objects where the set of atoms has to be infinite (countable or not
countable). Informally, FSM extends the framework of the ZF set theory without
choice principles; ZF set theory is actually the Empty Supported Mathematics.
In FSM, we use either ‘invariant sets’ or ‘finitely supported sets’ instead of
‘sets’. As an intuitive rule, we are not allowed to use in the proofs of the results
of FSM any construction that does not preserve the property of finite support.
That means we cannot obtain a property in FSM only by using a ZF result
without an appropriate proof using only the finite support condition. Since the
invariant sets can also be defined in the ZFA framework similarly as in the ZF
framework (see the first paragraph in Section 2), the definition of the finitely
supported mathematics also makes sense over the ZFA axioms.
To summarize, FSM represents the ZF theory rephrased in terms of finitely
supported objects; this means that FSM presents the theory of invariant sets,
including invariant algebraic structures. FSM is not at all the theory of nominal
sets from [24] presented in a different manner; actually the theory of nominal
sets [24] could be considered as a tool for defining FSM. The main aim of FSM
is to characterize the infinite algebraic structures by using their finite supports.
2 Sets with Atoms
Let A be a fixed infinite (countable or non-countable) ZF-set. The following
results make also sense if A is considered to be the set of atoms in the ZFA
framework (characterized by the axiom “y ∈ x ⇒ x ∈ / A”) and if ‘ZF’ is replaced
by ‘ZFA’ in their statements. Thus, we mention that the theory of invariant sets
makes sense both in ZF and in ZFA. Several results of this section are similar to
those in [24], but without assuming the set of atoms to be countable.
Definition 1. A transposition is a function (a b) : A → A defined by (a b)(a) =
b, (a b)(b) = a, and (a b)(n) = n for n 6= a, b. A permutation of A is generated
by composing finitely many transpositions.
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Definition 2. Let SA be the set of all permutations of A.
1. Let X be a ZF set. An SA -action on X is a function · : SA × X → X having
′ ′
the properties that Id·x = x and π ·(π ·x) = (π ◦π )·x for all π, π ′ ∈ SA and
x ∈ X. An SA -set is a pair (X, ·) where X is a ZF set, and · : SA × X → X
is an SA -action on X.
2. Let (X, ·) be an SA -set. We say that S ⊂ A supports x whenever for each
π ∈ F ix(S) we have π · x = x, where F ix(S) = {π | π(a) = a, ∀a ∈ S}.
3. Let (X, ·) be an SA -set. We say that X is an invariant set if for each x ∈ X
there exists a finite set Sx ⊂ A which supports x. Invariant sets are also
called nominal sets if we work in the ZF framework [24], or equivariant sets
if they are defined as elements in the cumulative hierarchy F MA [16].
4. Let X be an SA -set and let x ∈ X. If there exists a finite set supporting
x, then there exists a least finite set supporting x [16] which is called the
support of x and is denoted by supp(x). An element supported by the empty
set is called equivariant.
Proposition 1. Let (X, ·) be an SA -set and π ∈ SA . If x ∈ X is finitely sup-
ported, then π · x is finitely supported, and supp(π · x) = π(supp(x)).
Example 1.
1. The set A of atoms is an SA -set with the SA -action · : SA × A → A defined
by π · a := π(a), ∀π ∈ SA , a ∈ A. Moreover, supp(B) = B, ∀B ⊂ A, B finite.
2. Any ordinary ZF set X (like N or Z) is an SA -set with the trivial SA -action
· : SA × X → X defined by π · x := x for all π ∈ SA and x ∈ X.
3. If (X, ·) is an SA -set, then ℘(X) = {Y | Y ⊆ X} is also an SA -set with
the SA -action ⋆ : SA × ℘(X) → ℘(X) defined by π ⋆ Y := {π · y | y ∈ Y }
for all π ∈ SA , and all subsets Y of X. For each invariant set (X, ·) we
denote by ℘f s (X) the set formed from those subsets of X which are finitely
supported according to the action ⋆ . (℘f s (X), ⋆|℘f s (X) ) is an invariant set,
where ⋆|℘f s (X) represents the action ⋆ restricted to ℘f s (X).
4. Let (X, ·) and (Y, ⋄) be SA -sets. The Cartesian product X × Y is also an
SA -set with the SA -action ⋆ : SA ×(X ×Y ) → (X ×Y ) defined by π ⋆(x, y) =
(π · x, π ⋄ y) for all π ∈ SA and all x ∈ X, y ∈ Y . If (X, ·) and (Y, ⋄) are
invariant sets, then (X × Y, ⋆) is also an invariant set.
5. The FM cumulative hierarchy F MA described in [16] is an invariant set with
SA -action · : SA × F MA → F MA defined inductively by π · a := π(a) for all
atoms a ∈ A and π · x := {π · y | y ∈ x} for all x ∈ F MA \ A. An FM-set is a
finitely supported element in F MA ; additionally an FM-set has the recursive
property that all its elements are also FM-sets. An FM-set which is empty
supported as an element in F MA is an invariant set.
Definition 3. Let (X, ·) be an invariant set. A subset Z of X is called finitely
supported if and only if Z ∈ ℘f s (X) with the notations of Example 1 (3).
Definition 4. Let X and Y be invariant sets, and let Z be a finitely supported
subset of X. A function f : Z → Y is finitely supported if f ∈ ℘f s (X × Y ).
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Proposition 2. [5] Let (X, ·) and (Y, ⋄) be invariant sets, and let Z be a finitely
supported subset of X. The function f : Z → Y is finitely supported in the sense
of Definition 4 if and only if there exists a finite set S of atoms such that for all
x ∈ Z and all π ∈ F ix(S) we have π · x ∈ Z and f (π · x) = π ⋄ f (x).
3 Reformulating the Classical ZF Results in FSM
The main idea of translating a classical ZF result (depending on sets and rela-
tions) into FSM is to analyze if there exists a valid result obtained by replac-
ing “set” with ”invariant/finitely supported set” and “relation” with “invari-
ant/finitely supported relation” in the ZF result. If this is possible, then things
go smoothly; however, this is not always so simple.
Every ZF set is a particular invariant set equipped with a trivial permutation
action (Example 1(2)). Therefore, the general properties of invariant sets lead
to valid properties of ZF sets. The converse is not always valid, namely not
every ZF result can be directly rephrased in the world of invariant sets, terms
of finitely supported objects according to arbitrary permutation actions. This
is because, given an invariant set X, there could exist some subsets of X (and
also some relations or functions involving subsets of X) which fail to be finitely
supported. A classical example (presented also in Subsection 2.2.3.6 of [26]) is
represented by the powerset of the invariant set A. A subset of A which is in the
same time infinite and coinfinite could be defined in some models of ZF (or of
ZFA is we consider A to be the set of atoms in ZFA), but it can not be defined in
FSM because it is not finitely supported. Therefore the remark that everything
that can be done in ZF can also be done in FSM is not valid. That means there
may exist some valid results depending on several ZF structures which fail to be
valid in FSM if we simply replace “ZF structure” with “FSM structure” in their
statement.
We present few examples regarding these aspects. There exist some valid ZF
results that cannot be translated into FSM. According to Remark 1, the following
examples are particularly interesting because they do not overlap neither on
some known properties of permutative models of ZFA, nor on some properties
of nominal sets [24].
Example 2.
– There exist models of ZF without choice that satisfy the ordering principle
“Every set can be totally ordered”. More details about such models are
in [19], where there are mentioned Howard-Rubin’s first model N38 and
Cohen’s first model M1. Therefore the ordering principle is independent from
the axioms of the ZF set theory.
– In FSM the following result fails “For every invariant set X there exists a
finitely supported total order relation on X”. Therefore the ordering prin-
ciple is inconsistent with the axioms of the FM set theory. Indeed, suppose
that there exists a finitely supported total order < on the invariant set A. Let
a, b, c ∈
/ supp(<) with a < b. Since (a c) ∈ F ix(supp(<)) we have (a c)(a) <
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(a c)(b), so c < b. However, we also have (a b), (b c) ∈ F ix(supp(<)), and so
((a b) ◦ (b c))(a) < ((a b) ◦ (b c))(b), that is, b < c. We get a contradiction,
and so the translation of the ordering principle in FSM realized by replacing
“structure” with “finitely supported structure” leads to a false statement.
Example 3.
– There exist models of ZF without choice that satisfy the partial countable
choice principle: “Given any countable family (sequence) of non-empty sets
F = (Xn )n , there exists an infinite subset M of N such that it is possible
to select a single element from each member of the family (Xm )m∈M , i.e.
there exist a choice function on (Xm )m∈M ”. More details about such models
are in [19], where there are mentioned Pincus-Solovay’s First Model M27,
Shelah’s Second Model M38 and Howard-Rubin’s first model N38. Therefore
the partial countable choice principle is independent from the axioms of the
ZF set theory.
– In FSM the following result fails: “Given any invariant set X, and any count-
able family F = (Xn )n of subsets of X such that the mapping n 7→ Xn is
finitely supported, there exists an infinite subset M of N with the property
that there is a finitely supported choice function on (Xm )m∈M ”. Therefore
the partial countable choice principle is inconsistent with the axioms of the
FM set theory. Indeed, for the invariant set A we consider the countable
family (Xn )n where Xn is the set of all injective n-tuples from A. Since A
is infinite, it follows that each Xn is non-empty. In the FM framework, each
Xn is equivariant because A is an invariant set and each permutation is a bi-
jective function. Therefore the family (Xn )n is equivariant, and the mapping
n 7→ Xn is also equivariant. Suppose that there exists an infinite subset M of
N and a finitely supported choice function f on (Xm )m∈M . Let f (Xm ) = ym
with each ym ∈ Xm . Let π ∈ F ix(supp(f )). According to Proposition 2,
and because each element Xm is equivariant according to its definition, we
obtain that π · ym = π · f (Xm ) = f (π · Xm ) = f (Xm ) = ym . Therefore,
each element ym is supported by supp(f ), and so supp(ym ) ⊆ supp(f ) for
all m ∈ M . Since ym is a finite tuple of atoms which has exactly m ele-
ments for each m ∈ M , we have that supp(ym ) = ym , ∀m ∈ N (see Example
1(1)). Thus ym ⊆ supp(f ) for all m ∈ M . However, because M is infinite,
we contradict the finiteness of supp(f ). Therefore the translation of the par-
tial countable choice principle in FSM realized by replacing “structure” with
“finitely supported structure” leads to a false statement.
Remark 1. Examples 2 and 3 show us that there exist some choice
principles which are independent from the axioms of the ZF set theory, but
inconsistent in FSM. Since FSM is consistent even if the set of atoms is not
countable, such results do not overlap on some related properties in the basic
or in the second Fraenkel modes of the ZFA set theory (which are defined using
countable sets of atoms) [20]. Also, the previous results do not follow immediately
from [24] because the nominal sets are defined over countable sets of atoms, while
we define invariant sets over possible non-countable sets of atoms; in [24] where
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the set of atoms is countable, Example 3 would be trivial. Moreover, we claim
that all the choice principles from [18] rephrased in terms of invariant sets are
inconsistent in FSM. Note that it is not easy to prove such a result in FSM,
even if various relationship results between several forms of choice hold in the
ZF framework. This is because nobody guarantees that ZF results remain valid
in FSM. Therefore, all the possible relationship results between various choice
principles in FSM have to be independently proved in terms of finitely supported
object. Details regarding the consistency of various choice principles in the world
of invariant sets defined over possibly non-countable sets of atoms are presented
in another paper.
Other results which fail in FSM are given by the Stone duality [22], by the
determinization of finite automata and by the equivalence of two-way and one-
way finite automata [10]. There also exist some valid ZF results that can be
translated into FSM only in a weaker form.
Example 4. We define an invariant complete lattice as an invariant set (L, ·)
together with an equivariant order relation ⊑ on L satisfying the property that
every finitely supported subset X ⊆ L has a least upper bound with respect to
the order relation ⊑.
– Let L be a ZF complete lattice and f : L → L a ZF monotone function.
Then there exists a greatest e ∈ L such that f (e) = e and a least e ∈ L such
that f (e) = e (weak form of Tarski theorem).
– Let (L, ⊑, ·) be an invariant complete lattice and f : L → L a finitely
supported monotone function. Then there exists a greatest e ∈ L such that
f (e) = e, and a least e ∈ L such that f (e) = e (the proof is similar to
Theorem 3.2 in [1]).
These results show that the weak form of the Tarski theorem can be naturally
translated into FSM. However, as it is presented below, the strong form of the
Tarski theorem cannot be naturally translated into FSM; it holds in FSM only for
a particular class of finitely supported monotone functions, i.e, the equivariant
monotone functions.
– Let L be a ZF complete lattice and f : L → L a ZF monotone function over
L. Let P be the set of fixed points of f . Then P is a complete lattice (strong
form of Tarski theorem).
– Let (L, ⊑, ·) be an invariant complete lattice and f : L → L an equivariant
monotone function over L. Let P be the set of fixed points of f . Then (P, ⊑, ·)
is an invariant complete lattice.
The result does not hold if f is finitely supported, but not equivariant (the
proof is similar to Theorem 3.3 in [1]).
4 Limits of the Equivariance / Finite Support Principle
In order to translate a general ZF result into FSM, one must prove that several
structures are finitely supported. There exist two general methods of proving
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that a certain structure is finitely supported. The first method is a constructive
one: by using some intuitive arguments, we anticipate a possible candidate for the
support and prove that this candidate is indeed a support. The second method
is based on a general finite support principle which is defined using the higher-
order logic. However the use of this second method has some limits, as we present
in the paragraphs below.
According to [23], we have the following equivariance/finite support principle
which works over invariant sets.
Theorem 1.
– Any function or relation that is defined from equivariant functions and rela-
tions using classical higher-order logic is itself equivariant.
– Any function or relation that is defined from finitely supported functions and
relations using classical higher-order logic is itself finitely supported.
In applying this equivariance/finite support principle, one must take into account
all the parameters upon which a particular construction depends. We think that
the formal involvement of the equivariance/finite support principle, i.e. the pre-
cise verification if the conditions for applying the equivariance/finite support
principle are properly satisfied is sometimes at least as difficult as a constructive
proof. Moreover, in many cases we need to construct effectively the support, and
it is not enough to prove only that a certain structure is finitely supported.
Example 5. An invariant monoid (M, ·, ⋄) is an invariant set (M, ⋄) endowed with
an equivariant internal monoid law · : M × M → M . If (Σ, ⋄) is an invariant set,
then the free monoid Σ ∗ on Σ is an invariant monoid [5].
1. For each monoid M and each function f : Σ → M , there exists a unique
homomorphism of monoids g : Σ ∗ → M with g ◦ i = f , where i : Σ → Σ ∗
is the standard inclusion of Σ into Σ ∗ which maps each element a ∈ Σ into
the word a (ZF universality theorem for monoids).
2. i) Let (Σ, ⋄Σ ) be an invariant set. Let i : Σ → Σ ∗ be the standard in-
clusion of Σ into Σ ∗ which maps each element a ∈ Σ into word a. If
(M, ·, ⋄M ) is an arbitrary invariant monoid and ϕ : Σ → M is an ar-
bitrary finitely supported function, then there exists a unique finitely
supported homomorphism of monoids ψ : Σ ∗ → M with ψ ◦ i = ϕ.
This result can be proved directly by involving the equivariance/finite
support principle.
ii) Let (Σ, ⋄Σ ) be an invariant set. Let i : Σ → Σ ∗ be the standard in-
clusion of Σ into Σ ∗ which maps each element a ∈ Σ into the word a.
If (M, ·, ⋄M ) is an arbitrary invariant monoid and ϕ : Σ → M is an
arbitrary finitely supported function, then there exists a unique finitely
supported homomorphism of monoids ψ : Σ ∗ → M with ψ ◦ i = ϕ.
Moreover, if a finite set S supports ϕ, then the same set S supports ψ.
The last sentence of this theorem cannot be proved by involving the
equivariance/finite support principle.
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Proof. If (M, ·, ⋄M ) is an invariant monoid, then (M, ·) is a monoid. From the
general ZF theory of monoids, we can define a unique homomorphism of monoids
ψ : Σ ∗ → M with ψ ◦ i = ϕ.
In [5] we proved that the free monoid Σ ∗ on Σ is an invariant monoid when-
ever (Σ, ⋄) is an invariant set. The SA -action e ⋆ : SA × Σ ∗ → Σ ∗ is defined by
πe⋆x1 x2 . . . xl = (π ⋄ x1 ) . . . (π ⋄ xl ) for all π ∈ SA and x1 x2 . . . xl ∈ Σ ∗ \ {1}, and
πe⋆1 = 1 for all π ∈ SA .
In order to prove that ψ is finitely supported it is sufficient to apply Theo-
rem 1 because ψ is defined from the finitely supported functions ϕ and i using
the higher-order logic. However, Theorem 1 is not sufficient to prove that if a
finite set S supports ϕ, then the same set S supports ψ. In order to prove the
previous statement we proceed as follows.
Let us consider S = supp(ϕ). Thus, by Proposition 2 we have ϕ(π ⋄Σ x) =
π ⋄M ϕ(x) for all x ∈ Σ and π ∈ F ix(S). We have to prove that S supports
ψ. Let π ∈ F ix(S). According to Proposition 2 it is sufficient to prove that
ψ(πe ⋆x1 x2 . . . xn ) = π ⋄M ψ(x1 x2 . . . xn ) for each x1 x2 . . . xn ∈ Σ ∗ . However,
ψ is a monoid homomorphism between Σ ∗ and M , and ψ ◦ i = ϕ. This means
ψ(x1 x2 . . . xn ) = ϕ(x1 )·ϕ(x2 )·. . .·ϕ(xn ). Since (M, ·, ⋄M ) is an invariant monoid
we have π ⋄M ψ(x1 x2 . . . xn ) = π ⋄M (ϕ(x1 ) · ϕ(x2 ) · . . . · ϕ(xn )) =(π ⋄M ϕ(x1 )) ·
(π ⋄M ϕ(x2 )) · . . . · (π ⋄M ϕ(xn )) = ϕ(π ⋄Σ x1 ) · ϕ(π ⋄Σ x2 ) · . . . · ϕ(π ⋄Σ xn ).
However, πe ⋆x1 x2 . . . xn = (π ⋄Σ x1 ) . . . (π ⋄Σ xn ) and ψ(πe⋆x1 x2 . . . xn ) = ψ((π ⋄Σ
x1 ) . . . (π⋄Σ xl )) = ϕ(π⋄Σ x1 )·ϕ(π⋄Σ x2 )·. . .·ϕ(π⋄Σ xn ). Hence ψ(πe ⋆x 1 x 2 . . . x n ) =
π ⋄M ψ(x1 x2 . . . xn ) for each π ∈ F ix(S), which means S supports ψ.
Example 5(2) shows us that by using the equivariance/finite support prin-
ciple we can obtain a universality property for invariant monoids which is sim-
ilar to the one described in Example 5(1). However, in order to prove that
supp(ψ) ⊆ supp(ϕ) in the second item of Example 5(2), we need to present a
constructive method of defining a set supporting ψ (see also Theorem 6 from [5]).
Other related examples regarding the equivariance/finite support principle are
Theorems 4, 9 and 11 from [5], or Theorem 3.7 from [2]. In these theorems we are
able to prove a precise characterization for the support of some structures which
could not be obtained by a direct application of the equivariance/finite support
principle in the form from Theorem 1. In these results we do not prove only that
some structures are finitely supported, but we also found a relationship between
the supports of the related structures.
In some cases we can prove stronger properties without involving the equiv-
ariance/finite support principle. For example, each function fx in the proof of
Theorem 7 of [5] has a non-empty finite support. Using the equivariance/finite
support principle one can say that the function T from that theorem has also
a finite support. We were able to prove something stronger using a constructive
method: the function T is equivariant.
A constructive method of defining the support is also necessary in order to
assure that some structures are uniformly finitely supported (i.e. supported by
the same finite set of atoms). Some related examples regarding the uniform
support are presented in [2] (Section 5), where we should assume that some
392
structures are uniformly supported in order to obtain some embedding properties
for invariant (nominal) groups. Also, note that a chain is finitely supported if and
only if all its elements are finitely supported and have the same support, i.e., all
its elements are uniformly finitely supported. Therefore, in order to prove that
a chain is finitely supported, we must present a constructive method of defining
the support of its elements. More exactly, we cannot use the equivariance/finite
support principle which would not assure the uniformity of the support of its
elements. Suggestive examples regarding finitely supported chains are presented
in Chapter 4 of [25].
We conclude that the equivariance/finite support principle is not useful when
we want to obtain a relationship between the supports of several constructions
(and we do not want only to prove that these constructions are finitely sup-
ported). This is because, in its actual form, the second part of Theorem 1 allows
to prove that a certain structure is finitely supported, but it do not provide any
information about the structure of the support. However, the first part of Theo-
rem 1 helps when we want to prove the equivariance of some constructions. Note
that we do not claim that the finite support principle is not useful. Obviously,
it can be used to give simpler proofs for the fact that functions and relations
defined from finitely supported functions and relations via classical higher-order
formulas are finitely supported. However, a concrete calculation for the supports
of some structures is able to provide more informations about the related sup-
ports; we justify this viewpoint in Example 5. Also, such a method is useful in
order to find the uniform supports.
Note that, often in practice, it is not sufficient to prove only that a certain
structure is finitely supported without giving any information about the struc-
ture of support. A more precise characterization of the support is useful. For
example, let us consider an α-equivalence class [t] of a λ-term t. The support
of [t] is represented by the set of free names of t [16]; the support of [t] is finite
because any λ-term has a finite numbers of free names. However, the precise
description of the free names of t is an aspect that matters. Therefore, we sug-
gest to use a constructive method of defining the support of a certain structure
instead of the finite support part (the second part) of Theorem 1, because in
this way we can obtain more informations about the support.
5 Conclusion
Our goal is to develop a mathematics for experimental science which deals with
a more relaxed notion of finiteness. We call it the ‘Finitely Supported Mathe-
matics’. Informally, in Finitely Supported Mathematics we can model infinite
structures after a finite number of observations. More precisely, we intend to re-
state some parts of algebra by replacing ‘(infinite) sets’ with ‘invariant sets’. This
allows to model some infinite structures by using their finite supports. In order
to sustain our viewpoint, we involve the axiomatic theory of FM-sets presented
in [16]. Rather than using a non-standard set theory, we could alternatively work
with invariant sets, which are defined within ZF as usual sets endowed with some
393
group actions satisfying a finite support requirement. The properties of invari-
ant sets are similar to those presented in [24], with the mention that we assume
invariant sets to be defined over possible non-countable sets of atoms. Our paper
presents the basic steps requested in order to provide an extension of the theory
of invariant sets to a theory of invariant algebraic structures. Although the initial
purpose of defining invariant sets was to formulate a semantics for syntax with
variable binding, we consider that such sets can also be used from an algebraic
perspective in order to characterize infinite structures modulo finite supports,
and thus in order to provide more informations about infinite objects.
The category of invariant sets has a very rich structure, and so the definitions
of many structures given in the usual category of sets can be reformulated within
the invariant sets framework. A natural question is which classical theorems
about these structures hold internally in the world of invariant sets. Until now
(or, more precisely, until we would be able to solve the open problem presented
below), there does not exist a standard algorithm to translate any classical ZF
result into FSM. This is because there may exist some subsets of an invariant set
which fail to be finitely supported, and thus there may exist some ZF results that
fail in the universe of invariant sets. Related examples regarding the previous
statement are presented in Section 3. Therefore, reformulating the ZF theorems
into FSM should be done for each case separately. For example, the theory of
monoids is studied in FSM in [5], the theory of groups is rephrased in FSM in
[2], and the theory of posets and domains is reformulated within invariant sets
framework in [24, 25]. In order to prove that a structure is finitely supported,
one could use either the finite support principle of [24] (e.g. Theorem 1), or a
more “constructive” method. To employ such a “constructive method” means
that we anticipate a possible candidate for a support, and then prove that this
candidate is indeed a support. The benefit of this method is that we are able
to obtain more informations about the related support than by using the finite
support principle. Related examples can be found in Section 4.
An Open Problem: The main task in order to define a finitely supported
mathematics is to prove that certain subsets of an invariant set are finitely
supported. We already know that given an invariant set X, there could exist
some subsets of X which fail to be finitely supported. Some related examples
are presented in [24] and [26]. However, all these examples are described by using
choice principles or consequences of choice principles (like the assertion that the
set A can be non-amorphous in ZFA) in order to construct some structures which
later fail to be finitely supported. We conjecture that all the choice principles
presented in [18] are inconsistent in FSM. We did not find yet any example of a
non-finitely supported subset of an invariant set defined without using a choice
principle from [18] or a consequence of a form of choice (like the construction
of an infinite and coinfinite subset of an infinite set). Therefore, the question
regarding the validity of the following assertions naturally appears.
– If we consider the ZF set theory (or the ZFA set theory) without any choice
principle, then every subset of an invariant set is finitely supported?
394
– For what kind of atoms the previous question has an affirmative answer?
If we get an affirmative answer (even for a particular set of atoms), then the
mathematics developed in the ZF (or ZFA) set theory without any choice prin-
ciple would be somehow equivalent to FSM, namely we could model any infinite
structure by using its finite support.
Acknowledgements. The work was supported by a grant of the Romanian
National Authority for Scientific Research, CNCS-UEFISCDI, project number
PN-II-ID-PCE-2011-3-0919.
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396
On a Strong Notion of Viability for Switched
Systems
Ievgen Ivanov
Taras Shevchenko National University of Kyiv, Ukraine
ivanov.eugen@gmail.com
Abstract. We propose a strong notion of viability for a set of states
of a nonlinear switched system. This notion is defined with respect to
a fixed region of the state space and can be interpreted as a condition
under with a system can be forced to stay in a given safe set by applying
a specific control strategy only when its state is outside the fixed region.
When the state of the system is inside the fixed region, the control can
be kept constant without the risk of driving the system into unsafe set
(the complement of the safe set).
We investigate and give a convenient sufficient condition for strong vi-
ability of the complement of the origin for a nonlinear switched system
with respect to a fixed region.
Keywords. dynamical system, switched system, viability, global-in-time
trajectories, control system.
Key Terms. Mathematical Model, Specification Process, Verification
Process
1 Introduction
A subset of the state space of a control system is called viable, if for any initial
point in this set there exists a solution of the control system which stays for-
ever in this set. Usual problems associated with viability are checking if a given
set is viable, finding a solution (and/or the corresponding control input) which
stays forever in this set (viable solution), designing a viable region [2]. Viability
was studied in many works on the theory of differential equations and inclusions
and the control theory [20, 5, 2, 3, 9, 19, 24, 21, 7, 10, 1, 16, 6]. The corresponding
results can be straightforwardly applied to control and verification problems
for hybrid (discrete-continuous) systems [11] and other models of cyber-physical
systems [22, 4, 17, 23], assuming that viable sets are interpreted as safety re-
gions. However, this interpretation suggests certain natural generalizations of
the notion of viability. We propose and investigate one such generalization in
this paper.
Let n ≥ 1 be a natural number, I be a non-empty finite set, and fi : R → Rn ,
i ∈ I be an indexed family of vector fields.
397
Let T = [0, +∞), I be the set of all functions from T to I which are piecewise-
constant on each compact segment [a, b] ⊂ T , and k∙k denote the Euclidean norm
on Rn . Consider a switched dynamical system [18] of the form
ẋ(t) = fσ(t) (t, x(t)) (1)
where, σ ∈ I, t ≥ 0.
Assume that for each i ∈ I:
1. fi is continuous and bounded on [0, +∞) × Rn ;
2. there exists a number L > 0 such that kfi (t, x1 ) − fi (t, x2 )k ≤ L kx1 − x2 k
for all x1 , x2 ∈ Rn , t ∈ T , and i ∈ I (Lipschitz-continuity).
Under these conditions Caratheodory existence theorem [8] implies that for
each t0 ∈ T and x0 ∈ Rn , and σ ∈ I the problem
d
x(t) = fσ(t) (t, x(t)) (2)
dt
x(t0 ) = x0 (3)
has a Caratheodory solution defined for all t ≥ t0 , i.e. a function t 7→ x(t; t0 ; x0 ; u)
which is absolutely continuous on every segment [a, b] ⊂ [t0 , +∞), satisfies
the equation (2) a.e. (almost everywhere in the sense of Lebesgue measure),
and satisfies (3). Moreover, this solution is unique in the sense that for any
function x : [t0 , t1 ) → Rn , which is absolutely continuous on every segment
[a, b] ⊂ [t0 , t1 ), satisfies (2) a.e. on [t0 , t1 ) and satisfies (3), x(t) = x(t; t0 ; x0 ; u)
holds for t ∈ [t0 , t1 ).
For any X ⊆ Rn and x0 ∈ X denote by V S(X, x0 ) (set of viable switchings)
the set of all σ ∈ I such that x(t; 0; x0 ; σ) ∈ X for all t ≥ 0;
If V S(X, x0 ) 6= ∅ for each x0 ∈ X, then X is a viable set of (1) and functions
t 7→ x(t; 0; x0 ; σ), σ ∈ V S(X, x0 ) are viable solutions for X.
Let Y ⊆ Rn be a set. Let us say that a set X ⊆ Rn is Y -strongly viable, if
for each x0 ∈ X there exists σ ∈ V S(X, x0 ) such that σ(t) is constant on each
interval (t1 , t2 ) ⊂ [0, +∞) such that x(t; 0; x0 ; σ) ∈ Y for all t ∈ (t1 , t2 ).
In particular, X is viable if and only if X is ∅-strongly viable. Thus strong
viability is a generalization of viability.
This notion has the following natural interpretation: the state of the system
(1) can be forced to stay in a given “safe” set X by applying a specific control
strategy (σ) only when its state is outside Y . When the state of the system is
inside Y , one can keep the control constant (i.e. do not make any switchings)
without the risk of driving the system into the “unsafe” region Rn \X. Then Y
can be interpreted as a set of states where “nothing specific needs to be done”
to ensure safety of the system and the complement of Y can be interpreted as
a set of states upon reaching which “something may need to be done” to ensure
safety.
In this paper we will consider the case when X is the complement of the origin
(i.e. the origin may be interpreted as a safety hazard) and propose a convenient
398
sufficient condition which can be used to verify that for a given system, X, and
Y , X is Y -strongly viable.
To do this we will use the notion of a Nondeterministic Complete Markovian
System (NCMS) [14] which is based on the notion of a solution system by O.
Hájek [12]. More specifically, we will represent the system (1) using a suitable
NCMS and reduce the problem of Y -strong viability of a set X to the problem
of the existence of global-in-time trajectories of NCMS which was investigated
in [14, 15] and apply a theorem about the right dead-end path in NCMS [15] in
order to obtain a condition of Y -strong viability.
To make the paper self-contained, in Section 2 we give the necessary defi-
nitions and facts about NCMS. In Section 3 we formulate and prove the main
result of the paper.
2 Preliminaries
2.1 Notation
We will use the following notation: N = {1, 2, 3, ...}, N0 = N ∪ {0}, R is the set
of real numbers, R+ is the set of nonnegative real numbers, f : A → B is a total
function from a set A to a set B, f : A→B ˜ denotes a partial function from a
set A to a set B. We will denote by 2A the power set of a set A and by f |A the
restriction of a function f to a set A.
If A, B are sets, then B A will denote the set of all total functions from A to
B and A B will denote the set of all partial function from A to B.
For a function f : A→B ˜ the symbol f (x) ↓ (f (x) ↑) mean that f (x) is
defined, or, respectively, undefined on the argument x.
We will not distinguish the notions of a function and a functional binary
relation. When we write that a function f : A→B ˜ is total or surjective, we
mean that f is total on the set A specifically (f (x) is defined for all x ∈ A), or,
respectively, is onto B (for each y ∈ B there exists x ∈ A such that y = f (x)).
We will use the following notations for f : A→B:˜ dom(f ) = {x | f (x) ↓}, i.e.
the domain of f (note that in some fields like category theory the domain of a
partial function is defined differently), and range(f ) = {y | ∃x f (x) ↓ ∧ y =
f (x)}. We will use the same notation for the domain and range of a binary
relation: if R ⊆ A × B, then dom(R) = {x | ∃ y (x, y) ∈ R} and range(R) =
{y | ∃ x (x, y) ∈ R}.
We will denote by f (x) ∼= g(x) the strong equality (where f and g are partial
functions): f (x) ↓ if and only if g(x) ↓, and f (x) ↓ implies f (x) = g(x).
We will denote by f ◦ g the functional composition: (f ◦ g)(x) ∼ = f (g(x)).
For any set X and a value y we will denote by X 7→ y a constant function
defined on X which takes the value y.
Also, we will denote by T the non-negative real time scale [0, +∞) and assume
that T is equipped with a topology induced by the standard topology on R.
The symbols ¬, ∨, ∧, ⇒, ⇔ will denote the logical operations of negation,
disjunction, conjunction, implication, and equivalence respectively.
399
2.2 Nondeterministic Complete Markovian Systems (NCMS)
The notion of a NCMS was introduced in [13] for studying the relation between
the existence of global and local trajectories of dynamical systems. It is close
to the notion of a solution system by O. Hájek [12], however there are some
differences between these two notions [14].
Denote by T the set of all intervals (connected subsets) in T which have the
cardinality greater than one.
Let Q be a set (a state space) and T r be some set of functions of the form
s : A → Q, where A ∈ T. The elements of T r will be called (partial) trajectories.
Definition 1. ([13, 14]) A set of trajectories T r is closed under proper restric-
tions (CPR), if s|A ∈ T r for each s ∈ T r and A ∈ T such that A ⊆ dom(s).
Definition 2. ([13, 14])
(1) A trajectory s1 ∈ T r is a subtrajectory of s2 ∈ T r (denoted as s1 ⊑ s2 ), if
dom(s1 ) ⊆ dom(s2 ) and s1 = s2 |dom(s1 ) .
(2) A trajectory s1 ∈ T r is a proper subtrajectory of s2 ∈ T r (denoted as s1 ⊏
s2 ), if s1 ⊑ s2 and s1 6= s2 .
(3) Trajectories s1 , s2 ∈ T r are incomparable, if neither s1 ⊑ s2 , nor s2 ⊑ s1 .
The set (T r, ⊑) is a (possibly empty) partially ordered set.
Definition 3. ([13, 14]) A CPR set of trajectories T r is
(1) Markovian (Fig. 2), if for each s1 , s2 ∈ T r and t ∈ T such that t =
sup dom(s1 ) = inf dom(s2 ), s1 (t) ↓, s2 (t) ↓, and s1 (t) = s2 (t), the following
function
( s belongs to T r:
s1 (t), t ∈ dom(s1 )
s(t) =
s2 (t), t ∈ dom(s2 )
(2) complete, if each non-empty chain in (T r, ⊑) has a supremum.
Fig. 1. Markovian property of NCMS. If one trajectory ends and another begins in the
state q at time t, then their concatenation is a trajectory.
400
Definition 4. ([13, 14]) A nondeterministic complete Markovian system
(NCMS) is a triple (T, Q, T r), where Q is a set (state space) and T r (trajectories)
is a set of functions s : T →Q
˜ such that dom(s) ∈ T, which is CPR, complete,
and Markovian.
An overview of the class of all NCMS can be given using the notion of an LR
representation [13–15].
Definition 5. ([13, 14]) Let s1 , s2 : T →Q.
˜ Then s1 and s2 coincide:
(1) on a set A ⊆ T , if s1 |A = s2 |A and A ⊆ dom(s1 ) ∩ dom(s2 ) (this is denoted
.
as s1 =A s2 );
(2) in a left neighborhood of t ∈ T , if t > 0 and there exists t′ ∈ [0, t) such that
. .
s1 =(t′ ,t] s2 (this is denoted as s1 =t− s2 );
.
(3) in a right neighborhood of t ∈ T , if there exists t′ > t, such that s1 =[t,t′ ) s2
.
(this is denoted as s1 =t+ s2 ).
Let Q be a set. Denote by ST (Q) the set of pairs (s, t) where s : A → Q for
some A ∈ T and t ∈ A.
Definition 6. ([13, 14]) A predicate p : ST (Q) → Bool is
.
(1) left-local, if p(s1 , t) ⇔ p(s2 , t) whenever {(s1 , t), (s2 , t)} ⊆ ST (Q) and s1 =t−
s2 hold, and, moreover, p(s, t) holds whenever t is the least element of dom(s);
(2) right-local, if p(s1 , t) ⇔ p(s2 , t) whenever {(s1 , t), (s2 , t)} ⊆ ST (Q) and
.
s1 =t+ s2 hold, and, moreover, p(s, t) holds whenever t is the greatest el-
ement of dom(s).
Let LR(Q) be the set of all pairs (l, r), where l : ST (Q) → Bool is a left-local
predicate and r : ST (Q) → Bool is a right-local predicate.
Definition 7. ([14]) A pair (l, r) ∈ LR(Q) is called a LR representation of a
NCMS Σ = (T, Q, T r), if
T r = {s : A → Q | A ∈ T ∧ (∀t ∈ A l(s, t) ∧ r(s, t))}.
The following theorem gives a representation of NCMS using predicate pairs.
Theorem 1. ([14, Theorem 1])
(1) Each pair (l, r) ∈ LR(Q) is a LR representation of a NCMS with the set of
states Q.
(2) Each NCMS has a LR representation.
401
2.3 Existence global-in-time trajectories of NCMS
The problem of the existence of global trajectories of NCMS was considered in
[13, 14] and was reduced to a more tractable problem of the existence of locally
defined trajectories. Informally, the method of proving the existence of a global
trajectory in NCMS consists of guessing a “region” (subset of trajectories) which
presumably contains a global trajectory and has a convenient representation
in the form of (another) NCMS and proving that this region indeed contains
a global trajectory by finding or guessing certain locally defined trajectories
independently in a neighborhood of each time moment.
Below we briefly state the main results about the existence of global trajec-
tories of NCMS described in [15].
Let Σ = (T, Q, T r) be a fixed NCMS.
Definition 8. ([15]) Σ satisfies
(1) local forward extensibility (LFE) property, if for each s ∈ T r of the form
s : [a, b] → Q (a < b) there exists a trajectory s′ : [a, b′ ] → Q such that
s′ ∈ T r, s ⊑ s′ and b′ > b.
(2) global forward extensibility (GFE) property, if for each trajectory s of the
form s : [a, b] → Q there exists a trajectory
s′ : [a, +∞) → Q such that s ⊑ s′ .
Definition 9. ([15]) A right dead-end path (in Σ) is a trajectory s : [a, b) → Q,
where a, b ∈ T , a < b, such that there is no s′ : [a, b] → Q, s ∈ T r such that
s ⊏ s′ (i.e. s cannot be extended to a trajectory on [a, b]).
Definition 10. ([15]) An escape from a right dead-end path s : [a, b) → Q (in
Σ) is a trajectory s′ : [c, d) → Q (where d ∈ T ∪ {+∞}) or s′ : [c, d] → Q
(where d ∈ T ) such that c ∈ (a, b), d > b, and s(c) = s′ (c). An escape s′ is called
infinite, if d = +∞.
Definition 11. ([15]) A right dead-end path s : [a, b) → Q in Σ is called strongly
escapable, if there exists an infinite escape from s.
Definition 12. ([15])
(1) A right extensibility measure is a function f + : R × R→R ˜ such that A =
{(x, y) ∈ T × T | x ≤ y} ⊆ dom(f + ), f (x, y) ≥ 0 for all (x, y) ∈ A, f + |A
is strictly decreasing in the first argument and strictly increasing in the second
argument, and for each x ≥ 0, f + (x, x) = x , limy→+∞ f + (x, y) = +∞.
(2) A right extensibility measure f + is called normal, if f + is continuous on
{(x, y) ∈ T × T | x ≤ y} and there exists a function α of class K∞ (i.e. the
function α : [0, +∞) → [0, +∞) is continuous, strictly increasing, and α(0) = 0,
limx→+∞ α(x) = +∞) such that α(y) < y for all y > 0 and the function y 7→
f + (α(y), y) is of class K∞ .
An example of a right extensibility measure is f1+ (x, y) = 2y − x.
Let f + be a right extensibility measure.
402
Definition 13. ([15]) A right dead-end path s : [a, b) → Q is called f + -escapable,
if there exists an escape s′ : [c, d] → Q from s such that d ≥ f + (c, b).
Theorem 2. ([15], About right dead-end path) Assume that f + is a normal
right extensibility measure and Σ satisfies LFE. Then each right dead-end path
is strongly escapable if and only if each right dead-end path is f + -escapable.
Lemma 1. ([15]) Σ satisfies GFE if and only if Σ satisfies LFE and each right
dead-end path is strongly escapable.
Theorem 3. ([15], Criterion of the existence of global trajectories of NCMS)
Let (l, r) be a LR representation of Σ. Then Σ has a global trajectory if and
only if there exists a pair (l′ , r′ ) ∈ LR(Q) such that
(1) l′ (s, t) ⇒ l(s, t) and r′ (s, t) ⇒ r(s, t) for all (s, t) ∈ ST (Q);
(2) ∀t ∈ [0, ǫ] l′ (s, t) ∧ r′ (s, t) holds for some ǫ > 0 and a function s : [0, ǫ] → Q;
(3) if (l′ , r′ ) is a LR representation of a NCMS Σ ′ , then Σ ′ satisfies GFE.
3 Main result
Let I, I, and fi , i ∈ I, and x(t; t0 ; x0 ; σ) be defined as in Section 1. Let X =
Rn \{0} and Y ⊂ Rn be a set. Let denote D = Rn \Y .
Let us state the main result:
Theorem 4. Assume that:
(1) for each t ∈ T there exist i1 , i2 ∈ I such that fi1 (t, 0) and fi2 (t, 0) are
noncollinear;
(2) {0} is a path-component of {0} ∪ Y .
Then X is Y -strongly viable.
We will need several lemmas to prove this theorem.
Let us fix an element x∗0 ∈ X.
Let Q = Rn × I. Denote by pr1 : Q → Rn , pr2 : Q → I the projections on
the first and second component, i.e. pr1 ((x0 , i)) = x0 and pr2 ((x0 , i)) = i.
Let T r be the set of all functions s : A → Q, where A ∈ T, such that the
following conditions are satisfied, where x = pr1 ◦ s and σ = pr2 ◦ s:
1) σ is piecewise-constant on each segment [a, b] ⊆ A (a < b);
2) x is absolutely continuous on each segment [a, b] ⊆ A (a < b) and satisfies
d
the equation dt x(t) = fi (t, x(t)) a.e. on A;
3) x(t) 6= 0 for all t ∈ A;
4) for each non-maximal t ∈ A such that x(t) ∈ / D there exists t′ ∈ (t, +∞)∩A
such that σ(t ) = σ(t) for all t ∈ [t, t );
′′ ′′ ′
5) for each non-minimal t ∈ A such that x(t) ∈ / D there exists t′ ∈ (0, t) ∩ A
such that σ(t ) = σ(t) for all t ∈ (t , t];
′′ ′′ ′
6) if 0 ∈ A, then x(0) = x∗0 .
It follows straightforwardly from this definition that Σ(x∗0 ) = (T, Q, T r) is a
NCMS (i.e. T r is a CPR, Markovian, and complete set of trajectories).
Let us find a sufficient condition which ensures that Σ has a global trajectory.
403
Lemma 2. (1) Σ(x∗0 ) satisfies the LFE property.
(2) There exists s ∈ T r and ε > 0 such that dom(s) = [0, ε].
Proof. (1) Let s : [a, b] → Q be a trajectory, x = pr1 ◦ s, and u = pr2 ◦ s.
Let σ ′ : [a, +∞) → I be a function such that σ ′ (t) = σ(t), if t ∈ [a, b] and
σ ′ (t) = σ(b), if t > b. Then σ = σ ′ |[a,b] , σ ′ is piecewise-constant on each segment
in its domain, and x(t) = x(t; a; x(a); σ ′ ) for all t ∈ [a, b]. Let b′ = b + 1 and
x′ : [a, b′ ] → Rn be a function such that x′ (t) = x(t; a; x(a); σ ′ ) for t ∈ [a, b′ ].
Then x = x′ |[a,b] . Because x′ (t) 6= 0 for all t ∈ [a, b] and x′ is continuous, there
exists b′′ ∈ (b, b′ ] such that x′ (t) 6= 0 for all t ∈ [a, b′′ ]. Let s′ : [a, b′′ ] → Q
be a function such that s′ (t) = (x′ (t), σ ′ (t)) for all t ∈ [a, b′′ ]. Then it follows
immediately that s′ ∈ T r. Besides, s⊑s′ . Thus Σ satisfies LFE.
(2) Let us choose any i0 ∈ I and define x : T → Rn as x(t) = x(t; 0; x∗0 ; σ0 )
for all t ∈ T , where σ0 (t) = i0 for all t. Then x is continuous and x(0) = x∗0 6= 0,
so there exists ε > 0 such that x(t) 6= 0 for all t ∈ [0, ε]. Let s : [0, ε] → Q be a
function s(t) = (x(t), i0 ), t ∈ [0, ε]. Then s ∈ T r. ⊔
⊓
Lemma 3. Assume that:
(1) for each t ∈ T there exist i1 , i2 ∈ I such that fi1 (t, 0), fi2 (t, 0) are (nonzero)
noncollinear vectors, i.e. k1 fi1 (t, 0) + k2 fi2 (t, 0) 6= 0 whenever k1 , k2 ∈ R are
not both zero;
(2) for each s ∈ T r defined on a set of the form [t1 , t2 ), if limt→t2 − (pr1 ◦s)(t) = 0,
then pr1 (s(t)) ∈ D for some t ∈ [t1 , t2 ).
Then each right dead-end path in Σ(x∗0 ) is f1+ -escapable, where f1+ (x, y) = 2y −x
is a right extensibility measure.
Proof. Let M ′ = 1 + sup{kfi (t′ , x′ )k |(t′ , x′ ) ∈ T × Rn , i ∈ I}. Then 0 < M ′ <
+∞, because f is bounded.
Let s : [a, b) → Q be a right dead-end path and x = pr1 ◦s, σ = pr2 ◦s. Let σ ′ :
[a, +∞) → I be a function such that σ ′ (t) = σ(t), if t ∈ [a, b) and σ ′ (t) = σ(a), if
t ≥ b. Then σ = σ ′ |[a,b) , σ ′ is Lebesgue-measurable, and x(t) = x(t; a; x(a); σ ′ ) for
all t ∈ [a, b). Then there exists a limit xl = limt→b− x(t) = x(b; a; x(a); σ ′ ) ∈ Rn .
Firstly, consider the case when xl 6= 0. Then kxl k > 0. Let us choose an
arbitrary t0 ∈ (a, b) such that b − t0 < kxl k /(4M ′ ) and kx(t0 ) − xl k < kxl k /2
(this is possible, because xl = limt→b− x(t)). Let σ ′′ : [t0 , +∞) → I and x′′ :
[t0 , +∞) → Rn be functions such that σ ′′ (t) = σ(t0 ) for all t ≥ t0 and x′′ (t) =
x(t; t0 ; x(t0 ); σ ′′ ) for all t ≥ t0 . Then kx′′ (t0 )k = kx(t0 ) − xl + xl k ≥ kxl k −
kx(t0 ) − xl k > kxl k /2 > 2M ′ (b − t0 ). Then for all t ≥ t0 we have
Z t
′′ ′′
kx (t)k = x (t0 ) + fσ′′ (t) (t, x′′ (t))dt ≥
t0
Z t
≥ kx′′ (t0 )k − fσ′′ (t) (t, x′′ (t)) dt >
t0
> 2M ′ (b − t0 ) − M ′ (t − t0 ) = M ′ (2b − t0 − t).
404
Let d = 2b − t0 . Then d > t0 because t0 < b. Then x′′ (t) 6= 0 for all
t ∈ [t0 , d]. Let s∗ : [t0 , d] → Q be a function such that s∗ (t) = (x′′ (t), σ ′′ (t))
for all t ∈ [t0 , d]. It follows immediately that s∗ ∈ T r. Also, s∗ (t0 ) = s(t0 ) and
d = 2b − t0 = f1+ (t0 , b). Then s∗ is an escape from s and s is f1+ -escapable.
Now consider the case when xl = 0.
Let us choose i1 , i2 ∈ I such that v1 = fi1 (b, 0) and v2 = fi2 (b, 0) are
noncollinear (this is possible by the assumption 1 of the lemma). Then the
function h(k1 , k2 ) = kk1 v1 + k2 v2 k attains some minimal value M > 0 on
{(k1 , k2 ) ∈ R × R | |k1 | + |k2 | = 1}. Then for all k1 , k2 such that k1 6= 0 or
k2 6= 0,
h(k1 , k2 ) = (|k1 | + |k2 |)h(k1 (|k1 | + |k2 |)−1 , k2 (|k1 | + |k2 |)−1 ) ≥ M (|k1 | + |k2 |).
Let ε = M/2 > 0. Because f is continuous, there exists δ > 0 such that
for each j = 1, 2, t ∈ T , and x0 ∈ Rn such that |b − t| + kx0 k < δ we have
fij (t, x0 ) − vj = fij (t, x0 ) − fij (b, 0) < ε. Let R = δ/4, t1 = max{b − R, a},
and t2 = b + R. Then R > 0, a ≤ t1 < b < t2 and for all j = 1, 2, t ∈ [t1 , t2 ] and
x0 such that kx0 k ≤ R, fij (t, x0 ) − vj < ε.
Let us choose an arbitrary c ∈ (t1 , b) such that b − c < min{R/(2M ′ ), R/2}.
Then s|[c,b) ∈ T r by the CPR property and limt→t2 − (pr1 ◦ s|[c,b) )(t) = xl = 0,
so by the assumption 2 there exists t0 ∈ [c, b) such that pr1 (s(t0 )) = x(t0 ) ∈ D.
Let x1 : [t0 , t2 ] → Rn and x2 : [t0 , t2 ] → Rn be functions such that x1 (t) =
x(t; t0 ; x(t0 ); σ1 ) and x2 (t) = x(t; t0 ; x(t0 ); σ2 ) for all t ∈ [t0 , t2 ], where σj (t) = ij
for all t. Denote dj (t) = fij (t, xj (t)) − vj for each j = 1, 2 and t ∈ [t0 , t2 ].
Then the following two cases are possible.
a) There exists j ∈ {1, 2} such that 0 ∈ / range(xj ). Let us choose any d ∈
(max{2b − t0 , t0 }, t2 ) (this is possible, because t0 < b < t2 and 2b − t0 ≤ 2b − c <
b + R/2 < b + R = t2 ). Then let s∗ : [t0 , d] → Q be a function such that
s∗ (t0 ) = s(t0 ) = (x(t0 ), σ(t0 )) and s∗ (t) = (xj (t), ij ) for all t ∈ (t0 , d]. Because
xj (t0 ) = x(t0 ) ∈ D and xj (t) 6= 0 for all t ∈ [t0 , t2 ] ⊃ [t0 , d], we have that
s∗ ∈ T r. Besides, s∗ (t0 ) = s(t0 ) and d > 2b − t0 = f1+ (t0 , b), so s∗ is an escape
from s and s is f1+ -escapable.
b) 0 ∈ range(x1 )∩range(x2 ). Then because x1 , x2 are continuous, there exist
t′j = min{t ∈ [t0 , t2 ] | xj (t) = 0} for j = 1, 2. Moreover, t′j ∈ (t0 , t2 ] for j = 1, 2,
because x1 (t0 ) = x2 (t0 ) = x(t0 ) 6= 0.
If we suppose that kxj (t)k < R for each j = 1, 2 and t ∈ [t0 , t′j ], then
kdj (t)k = fij (t, xj (t)) − vj < ε for each j = 1, 2 and t ∈ [t0 , t′j ], whence
k0 − 0k = kx1 (t′1 ) − x2 (t′2 )k =
Z t′1 Z t′2
= x(t0 ) + fi1 (t, x1 (t))dt − x(t0 ) − fi2 (t, x2 (t))dt =
t0 t0
Z t′1 Z t′2
= v1 + d1 (t)dt − v2 + d2 (t)dt =
t0 t0
405
Z t′1 Z t′2
= v1 (t′1 − t0 ) − v2 (t′2 − t0 ) + d1 (t)dt − d2 (t)dt ≥
t0 t0
Z t′1 Z t′2
≥ kv1 (t′1 − t0 ) − v2 (t′2 − t0 )k − kd1 (t)k dt − kd2 (t)k dt ≥
t0 t0
M ′
≥ M (|t′1 − t0 | + |t′2 − t0 |) − ε(t′1 − t0 ) − ε(t′2 − t0 ) = (t − t0 + t′2 − t0 ) > 0.
2 1
We have a contradiction, so there exists j ∈ {1, 2} and t′′ ∈ [t0 , t′j ] such that
kxj (t′′ )k ≥ R. This implies that
Z t′j
R ≤ kxj (t′′ )k = xj (t′j ) − xj (t′′ ) = fij (t, xj (t))dt ≤ M ′ (t′j − t′′ ).
t′′
Then t′j − t0 ≥ t′j − t′′ ≥ R/M ′ > 2(b − c) ≥ 2(b − t0 ), so t′j > 2b − t0 . Let us
choose any d ∈ (max{2b − t0 , t0 }, t′j ). Let s∗ : [t0 , d] → Q be a function such that
s∗ (t0 ) = s(t0 ) = (x(t0 ), σ(t0 )) and s∗ (t) = (xj (t), ij ) for all t ∈ (t0 , d]. Because
xj (t0 ) = x(t0 ) ∈ D and xj (t) 6= 0 for all t ∈ [t0 , t′j ) ⊃ [t0 , d], we have s∗ ∈ T r.
Besides, s∗ (t0 ) = s(t0 ) and d > 2b − t0 = f1+ (t0 , b), so s∗ is an escape from s and
s is f1+ -escapable. ⊔
⊓
Lemma 4. Assume that:
(1) for each t ∈ T there exist i1 , i2 ∈ I such that fi1 (t, 0) and fi2 (t, 0) are
noncollinear;
(2) {0} is a path-component of {0} ∪ Y .
Then Σ(x∗0 ) has a global trajectory.
Proof. Let us show that the assumption 2 of Lemma 3 holds. Let s ∈ T r,
dom(s) = [t1 , t2 ) (t1 < t2 ), limt→t2 − (pr1 ◦ s)(t) = 0. Denote x = pr1 ◦ s. Suppose
that x(t) ∈/ D for all t ∈ [t1 , t2 ). Let γ : [0, 1] → {0} ∪ (Rn \D) be a function such
that γ(ε) = x(t1 + ε(t2 − t1 )), if ε ∈ [0, 1) and γ(1) = 0. Then γ is continuous, so
there is a path from γ(0) = x(t1 ) 6= 0 to 0 in {0}∪(Rn \D) = {0}∪Y (considered
as a topological subspace of Rn ). This contradicts the assumption that {0} is a
path-component of {0} ∪ Y . Thus x(t) ∈ D for some t ∈ [t1 , t2 ).
The assumption 1 of Lemma 3 also holds, so by Lemma 2, Lemma 3, Lemma
1, Theorem 2, Σ satisfies GFE. Besides, by Lemma 2 there exists s ∈ T r with
dom(s) = [0, ε] for some ε > 0, so by the GFE property, Σ has a global trajectory.
⊔
⊓
Proof (of Theorem 4). Follows straightforwardly from Lemma 4, because the
statement of Lemma 4 holds for any x∗0 ∈ X.
406
4 Conclusion
We have proposed the notion of an Y -strongly viable set X for nonlinear switched
systems. This notion follows naturally from interpretation of viable sets as safety
regions. We have considered the case when X is the complement of the origin
(i.e. the origin may be interpreted as a safety hazard) and proposed a convenient
sufficient condition which can be used to verify that for a given system, X, and
Y , X is Y -strongly viable. In the forthcoming papers we plan to investigate other
cases give the corresponding conditions.
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408
Natural Computing Modelling of the
Polynomial Space Turing Machines
Bogdan Aman and Gabriel Ciobanu
Romanian Academy, Institute of Computer Science
Blvd. Carol I no.11, 700506 Iaşi, Romania
baman@iit.tuiasi.ro, gabriel@info.uaic.ro
Abstract. In this paper we consider a bio-inspired description of the
polynomial space Turing machines. For this purpose we use membrane
computing, a formalism inspired by the way living cells are working.
We define and use logarithmic space systems with active membranes,
employing a binary representation in order to encode the positions on
the Turing machine tape.
Keywords. Natural computing, membrane computing, Turing machines.
Key Terms. MathematicalModel, Research.
1 Introduction
Membrane computing is a branch of the natural computing inspired by the archi-
tecture and behaviour of living cells. Various classes of membrane systems (also
called P systems) have been defined in [12], together with their connections to
other computational models. Membrane systems are characterized by three fea-
tures: (i) a membrane structure consisting of a hierarchy of membranes (which
are either disjoint or nested), with an unique top membrane called the skin; (ii)
multisets of objects associated with membranes; (iii) rules for processing the
objects and membranes. When membrane systems are seen as computing de-
vices, two main research directions are usually considered: computational power
in comparison with the classical notion of Turing computability (e.g., [2]), and
efficiency in algorithmically solving NP-complete problems in polynomial time
(e.g., [3]). Such efficient algorithms are obtained by trading space for time, with
the space grown exponentially in a linear time by means of bio-inspired op-
erations (e.g., membrane division). Thus, membrane systems define classes of
computing devices which are both powerful and efficient.
Related to the investigations of these research directions, there have been
studied several applications of these systems; among them, modelling of vari-
ous biological phenomena and the complexity and emergent properties of such
systems presented in [7]. In [4] it is presented the detailed functioning of the
sodium-potassium pump, while in [1] it is described and analyzed the immune
system in the formal framework of P systems.
409
In this paper we consider P systems with active membranes [11], and show
that they provide an interesting simulation of polynomial space Turing machines
by using only logarithmic space and a polynomial number of read-only input
objects.
2 Preliminaries
We consider P systems with active membranes extended with an input alphabet,
and such that the input objects cannot be created during the evolution [14]. The
original definition also includes dissolution and division rules, rules that are not
needed here. The version used in this paper is similar to evolution-communication
P systems used in [6] with additional read-only input objects and polarities.
Definition 1. A P system with active membranes and input objects is a tuple
Π = (Γ, ∆, Λ, µ; w1 , . . . , wd , R), where:
• d ≥ 1 is the initial degree;
• Γ is a finite non-empty alphabet of objects;
• ∆ is an input alphabet of objects such that ∆ ∩ Γ = ∅;
• Λ is a finite set of labels for membranes;
• µ is a membrane structure (i.e., a rooted unordered tree, usually represented
by nested brackets) in which each membrane is labelled by an element of Λ in
a one-to-one way, and possesses an attribute called electrical charge, which
can be either neutral (0), positive (+) or negative (-);
• w1 , . . . , wd are strings over Γ , describing the initial multisets of objects placed
in a number of d membranes of µ; notice that wi is assigned to membrane i;
• R is a finite set of rules over Γ ∪ ∆:
1. [a → w]α h object evolution rules
An object a ∈ Γ is rewritten into the multiset w, if a is placed inside
a membrane labelled by h with charge α. An object a can be deleted by
considering w the empty multiset ∅. Notice that these rules allow only to
rewritten objects from Γ , but not from ∆.
2. a[ ]α h → [b]h
β
send-in communication rules
An object a is sent into a membrane labelled by h and with charge α,
becoming b; also, the charge of h is changed to β. If b ∈ ∆, then a = b
must hold.
3. [a]α h → b[ ]h
β
send-out communication rules
An object a, placed into a membrane labelled by h and having charge α,
is sent out of membrane h and becomes b; simultaneously, the charge of
h is changed to β. If b ∈ ∆, then a = b must hold.
Each configuration Ci of a P system with active membranes and input objects is
described by the current membrane structure, including the electrical charges,
together with the multisets of objects located in the corresponding membranes.
The initial configuration of such a system is denoted by C0 . An evolution step
from the current configuration Ci to a new configuration Ci+1 , denoted by Ci ⇒
Ci+1 , is done according to the principles:
410
• Each object and membrane is involved in at most one communication rule
per step.
• Each membrane could be involved in several object evolution rules that can
be applied in parallel inside it.
• The application of rules is maximally parallel: the only objects and mem-
branes that do not evolve are those associated with no rule, or only to rules
that are not applicable due to the electrical charges.
• When several conflicting rules could be applied at the same time, a nonde-
terministic choice is performed; this implies that multiple configurations can
be reached as the result of an evolution step.
• In each computation step, all the chosen rules are applied simultaneously.
• Any object sent out from the skin membrane cannot re-enter it.
A halting evolution of such a system Π is a finite sequence of configurations
−
→
C = (C0 , . . . , Ck ), such that C0 ⇒ C1 ⇒ . . . ⇒ Ck , and no rules can be applied
→
−
any more in Ck . A non-halting evolution C = (Ci | i ∈ N) consists of an infinite
evolution C0 ⇒ C1 ⇒ . . ., where the applicable rules are never exhausted.
Example 1. Addition is trivial; we consider n objects a and m objects b placed
in a membrane 0 with charge +. The rule [b → a]+ says that an object b is
transformed in one object a. Such a rule is applied in parallel as many times
as possible. Consequently, all objects b are erased. The remaining number of
objects a represents the addition n + m. More examples can be found in [5].
In order to solve decision problems (i.e., decide languages over an alphabet
Σ), we use families of recognizer P systems Π = {Πx | x ∈ Σ ∗ } that respect
the following conditions: (1) all evolutions halt; (2) two additional objects yes
(successful evolution) and no (unsuccessful evolution) are used; (3) one of the
objects yes and no appears in the halting configuration [13]. Each input x is
associated with a P system Πx that decides the membership of x in the language
L ⊆ Σ ∗ by accepting or rejecting it. The mapping x ⊢ Πx must be efficiently
computable for each input length [10].
In this paper we use a logarithmic space uniformity condition [14].
Definition 2. A family of P systems Π = {Πx | x ∈ Σ ∗ } is said to be (L, L)-
uniform if the mapping x ⊢ Πx can be computed by two deterministic logarithmic
space Turing machines F (for “family”) and E (for “encoding”) as follows:
• F computes the mapping 1n ⊢ Πn , where Πn represents the membrane struc-
ture with some initial multisets and a specific input membrane, while n is
the length of the input x.
• E computes the mapping x ⊢ wx , where wx is a multiset encoding the specific
input x.
• Finally, Πx is Πn with wx added to the multiset placed inside its input mem-
brane.
411
In the following definition of space complexity adapted from [14], the input
objects do not contribute to the size of the configuration of a P system. In this
way, only the actual working space of the P system is measured, and P systems
working in sublinear space may be analyzed.
Definition 3. Given a configuration C, the space size |C| is defined as the sum
of the number of membranes in µ and the number of objects in Γ it contains.
→
− →
−
If C is a halting evolution of Π, then | C | = max{|C0 |, . . . , |Ck |} or, in the case
→
− → −
of a non-halting evolution C , | C | = sup{|Ci | | i ∈ N}. The space required by Π
→
− → −
itself is then |Π| = sup{| C | | C is an evolution of Π}.
Notice that |Π| = ∞ if Π has an evolution requiring infinite space or an infinite
number of halting evolutions that can occur such that for each k ∈ N there exists
at least one evolution requiring most than k steps..
3 A Membrane Structure for Simulation
Let M be a single-tape deterministic Turing machine working in polynomial
space s(n). Let Q be the set of states of M , including the initial state s; we denote
by Σ ′ = Σ ∪ {⊔} the tape alphabet which includes the blank symbol ⊔ 6∈ Σ.
A computation step is performed by using δ : Q × Σ ′ → Q × Σ ′ × {−1, 0, 1},
a (partial) transition function of M which we assume to be undefined on (q, σ)
if and only if q is a final state. We describe a uniform family of P systems
Π = {Πx | x ∈ Σ ∗ } simulating M in logarithmic space.
Let x ∈ Σ n be an input string, and let m = ⌈log s(n)⌉ be the minimum num-
ber of bits needed in order to write the tape cell indices 0, . . . , s(n)-1 in binary
notation. The P system Πn associated with the input length n and computed
as F (1n ) has a membrane structure consisting of |Σ ′ | · (m + 1) + 2 membranes.
The membrane structure contains:
– a skin membrane h;
– an inner membrane c (the input membrane) used to identify the symbol
needed to compute the δ function;
– for each symbol σ ∈ Σ ′ of M , the following set of membranes, linearly nested
inside c and listed inward:
• a membrane σ for each symbol σ of the tape alphabet Σ ′ of M ;
• for each j ∈ {0, . . . , (m − 1)}, a membrane labelled by j.
This labelling is used in order to simplify the notations. To respect the one-to-
one labelling from Definition 1, the membrane j can be labelled jσ . Thus in all
rules using membranes j, the σ symbol is implicitly considered. Furthermore,
the object z0 is located inside the skin membrane h.
The encoding of x, computed as E(x), consists of a set of objects describ-
ing the tape of M in its initial configuration on input x. These objects are the
symbols of x subscripted by their position bin(0), . . . , bin(n − 1) (where bin(i) is
the binary representation of i on m positions) in x, together with the s(n) − n
412
blank objects subscripted by their position bin(n), . . . , bin(s(n) − 1). The binary
representation, together with the polarities of the membranes, is essential when
the membrane system has to identify the symbol needed to simulate the δ func-
tion (e.g., rule (13)). The multiset E(x) is placed inside the input membrane c.
Figure 1 depicts an example.
0
0
0 0 0
0 0 0
0 0 0
1 1 1
0 0 0
a b ⊔
a00 b01 b10 ⊔11 z0
c
h
′
Fig. 1. Initial configuration of the P system Π3 with tape alphabet Σ = {a, b, ⊔},
working in space s(n) = n + 1 = 4 on the input abb.
During the first evolution steps of Πx , each input object σi is moved from
the input membrane c to the innermost membrane (m − 1) of the corresponding
membrane σ by means of the following communication rules:
σi [ ]0σ → [σi ]0σ for σ ∈ Σ ′ , bin(0) ≤ i < bin(s(n)) (1)
σi [ ]0j → [σi ]0j for σ ∈ Σ ′ , bin(0) ≤ i < bin(s(n)), 0 ≤ j < m (2)
Since only one communication rule per membrane can be applied during
each evolution step of Πx , all s(n) input objects pass through m membranes,
in order to reach the innermost membranes (m − 1), in at most l = s(n) + m
evolution steps. In the meantime, the subscript of object z0 is incremented up
to max{0, l − 3} before object zl−3 exits and enters membrane c changing the
membrane charge from 0 to +:
[zt → zt+1 ]0c for 0 ≤ t < l − 3 (3)
[zl−3 ]0c → zl−3 [ ]0c (4)
zl−3 [ ]0c → [zl−3 ]+
c (5)
The object zl−3 is rewritten to a multiset of objects containing an object z ′ (used
in rule (9)) and |Σ ′ | objects z+ (used in rules (7)
[zl−3 → z ′ z+ · · · z+ ]+
| {z } c (6)
|Σ ′ | copies
413
The objects z+ are used to change the charges from 0 to + for all membranes
σ ∈ Σ ′ using parallel communication rules, and then are deleted:
z+ [ ]0σ → [#]+
σ for σ ∈ Σ ′ (7)
[# → ∅]+
σ for σ ∈ Σ ′ (8)
In the meantime, the object z ′ is rewritten into z ′′ (in parallel with rule (7)),
and then, in parallel with rule (8), into s00 (where s is the initial state of M ):
[z ′ → z ′′ ]+
c (9)
[z ′′ → s00 ]+
c (10)
The configuration reached by Πx encodes the initial configuration of M :
0
+
+ + +
0 0 0
0 0 0
a00 b01 ⊔11
b10
1 1 1
0 0 0
a b ⊔
s00
c
h
Fig. 2. Configuration of Πx (from Figure 1) encoding the initial configuration of M on
input x = abb and using s(|x|) = 4 tape cells.
An arbitrary configuration of M on input x is encoded by a configuration
of Πx as it is described in Figure 3:
• membrane c contains the state-object qi , where q is the current state of M
and i ∈ {bin(0), . . . , bin(s(n) − 1)} is the current position of the tape head;
• membranes (m − 1) contain all input objects;
• all other membranes are empty;
• all membranes are neutrally charged, except those labelled by σ ∈ Σ ′ and
by c which all are positively charged.
We employ this encoding because the input objects must be all located in the
input membrane in the initial configuration of Πx (hence they must encode both
symbol and position on the tape), and they can never be rewritten.
414
0
+
+ + +
0 0 0
0 0 0
a00 b10 ⊔11
b01
1 1 1
q1 0 0 0
a b ⊔
q01
a a b c
0 1 2 3 h
Fig. 3. A configuration of M (from Figure 1) and the corresponding configuration of
Πx simulating it. The presence of b01 inside membrane 1 of a indicates that tape cell
1 of M contains the symbol a.
4 Simulating Polynomial Space Turing Machines
Starting from a configuration of the single-tape deterministic Turing machine
M , the simulation of a computation step of M by the membrane system Πx is
directed by the state-object qi . As stated above, qi encodes the current state
of M and the position of the head on the tape (in binary format). To simulate
the transition function δ of the Turing machine M in state q, it is necessary to
identify the actual symbol occurring at tape position i. In order to identify this
σi object from one of the (m − 1) membranes, the object qi is rewritten into |Σ ′ |
copies of qi′ , one for each membrane σ ∈ Σ ′ :
[qi → qi′ · · · qi′ ]+ q ∈ Q, bin(0) ≤ i < bin(s(n))
| {z } c (11)
|Σ ′ | copies
The objects qi′ first enter the symbol-membranes in parallel, without changing
the charges:
qi′ [ ]+ ′ +
σ → [qi ]σ for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (12)
The object qi′ traverses the membranes 0, . . . , (m − 1) while changing their
charges such that they represent the bits of i from the least to the most significant
one, where a positive charge is interpreted as 1 and a negative charge as 0.
− +
For instance, the charges of [[[ ]−
2 ]1 ]0 encode the binary number 001 (that is,
decimal 1). By the j-th bit of a binary number is understood the bit from the
j-th position when the number is read from right to left (e.g, the 0-th bit of the
binary number 001 is 1). The changes of charges are accomplished by the rules:
qi′ [ ]0j → [qi′ ]α
j for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)), 0 ≤ j < m, (13)
where α is − if the j-th bit of i is 0, and α is + if the j-th bit of i is 1.
The membranes j, where 0 ≤ j < m, behave now as “filters” for the input
objects σk occurring in membrane (m − 1): these objects are sent out from each
membrane j if and only if the j-th bit of k corresponds to the charge of j.
j → [ ]j σk
[σk ]α α
for σ ∈ Σ ′ , bin(0) ≤ k < bin(s(n)), 0 < j < m, (14)
415
where α is − if the j-th bit of k is 0, and α is + if j-th bit of k is 1.
If an object σk reaches membrane 0, it is sent outside if the 0-th bit of k
corresponds to the charge of membrane 0. In order to signal that it is the symbol
occurring at location i of the tape, the charge of the corresponding membrane 0
is changed (either from + to − or from − to +). By applying the rules (15) to
(17), exactly one object σk , with k = i, will exit through membrane c:
[σk ]+ −
0 → [ ]0 σk for σ ∈ Σ ′ , bin(0) ≤ k < bin(s(n)),
(15)
[σk ]0 → [ ]+
−
0 σk for σ ∈ Σ ′ , bin(0) ≤ k < bin(s(n)),
where α is − if the j-th bit of k is 0, and α is + if the j-th bit of k is 1;
[σk ]+ −
τ → σk [ ]τ for σ, τ ∈ Σ ′ , bin(0) ≤ k < bin(s(n)). (16)
After an σi exits from membrane c it gets blocked inside membrane h, by the
new charge of membrane c, until it is allowed to move to its new location accord-
ing to function δ of the Turing machine M . Thus, if another object τj reached
membrane σ due to the new charge of membrane 0 established by rule (15), τj is
contained in membrane σ until reintroduced in a membrane (m-1) using rule (2).
[σk ]+ −
c → σk [ ]c for σ ∈ Σ ′ , bin(0) ≤ k < bin(s(n)) (17)
Since there are s(n) input objects, and each of them must traverse at most
(m + 1) membranes, the object σi reaches the skin membrane h after at most
l + 1 steps, where l is as defined in Section 3 before rule (3). While the input
objects are “filtered out”, the state-object qi′ “waits” for l steps using the rules:
[qi′ → qi,1
′′ α
]m−1 for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)), α ∈ {−, +} (18)
′′ ′′
[qi,t → qi,t+1 ]α for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)),
m−1
(19)
α ∈ {−, +}, 1 ≤ t ≤ l
′′
[qi,l+1 → qi′′ ]α for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)), α ∈ {−, +}
m−1
(20)
′′
In order to reach membrane c, the objects qi are sent out through membranes
j (0 < j ≤ m − 1) using rule (21), through membrane 0 by rules (22) and (24),
and through membranes σ ∈ Σ ′ by rule (23). While passing through all these
membranes, the charges are changed to neutral. This allows the input objects to
move back to the innermost membrane (m − 1) by using rules of type (2).
0 ′′
[qi′′ ]α
j → [ ]j qi for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n))
(21)
0 < j ≤ m − 1, α ∈ {−, +}
When qi′′ reaches the membranes 0, only one has the charge different from the
0-th bit of i, thus allowing qi′′ to identify the symbol in tape location i of M :
0 ′′′
[qi′′ ]α
0 → [ ]0 qi for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)), (22)
416
where α is − if the 0-th bit of i is 1, and α is + if the 0-th bit of i is 0.
0
[qi′′′ ]−
σ → [ ]σ qi,σ,1 for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (23)
The other copies of qi′′ are sent out as objects # through membrane 0, and then
deleted by rules of type (8):
0
[qi′′ ]α ′
0 → [ ]0 # for σ ∈ Σ , q ∈ Q, bin(0) ≤ i < bin(s(n)), (24)
where α is − if the 0-th bit of i is 0, and α is + if the 0-th bit of i is 1.
The state-object qi,σ,1 waits in membrane c for l steps, l representing an
upper bound of the number of steps needed for all the input objects to reach the
innermost membranes:
[qi,σ,t → qi,σ,t+1 ]−
c for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)), 1 ≤ t < l (25)
qi,σ,l [ ]0σ → [qi,σ,l ]+
σ for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (26)
+ +
[qi,σ,l ]σ → qi,σ [ ]σ for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n))
′
(27)
′
The state-object qi,σ now contains all the information needed to compute the
transition function δ of the Turing machine M . Suppose δ(q, σ) = (r, v, d) for
′
some d ∈ {−1, 0, +1}. Then qi,σ sets the charge of membrane v to − and waits
for m + 1 steps, thus allowing σi to move to membrane (m − 1) of v by using
the rules (31), (32) and (2):
′
qi,σ [ ]+ ′ +
v → [qi,σ ]v for σ, v ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (28)
′
[qi,σ ]+ ′ −
v → qi,σ,1 [ ]v
′
for σ ∈ Σ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (29)
′ 0
[qi,σ,1 ]− ′
c → qi,σ,1 [ ]c for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (30)
σi [ ]0c → [σi ]0c for σ ∈ Σ ′ , bin(0) ≤ i < bin(s(n)) (31)
σi [ ]v → [σi ]v for σ, v ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n))
− −
(32)
′
[qi,σ,t ′
→ qi,σ,t+1 ]0h for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n))
(33)
1≤t≤m
′
The object qi,σ,m+1 is used to change the charges of membranes c and v to +,
thus preparing the system for the next step of the simulation:
′
qi,σ,m+1 [ ]0c → [qi,σ,m+1
′
]+
c for σ ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (34)
′
qi,σ,m+1 [ ]− ′ −
v → [qi,σ,m+1 ]v for σ, v ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (35)
′ +
[qi,σ,m+1 ]− ′′
v → qi,σ [ ]v for σ, v ∈ Σ ′ , q ∈ Q, bin(0) ≤ i < bin(s(n)) (36)
′′
Finally, the state-object qi,σ is rewritten to reflect the change of state and head
position, thus producing a configuration of Πx corresponding to the new config-
uration of M , as described in Section 3:
′′
[qi,σ → ri+d ]+
c for bin(0) ≤ i < bin(s(n)) (37)
417
The P system Πx is now ready to simulate the next step of M . If q ∈ Q is a final
state of M , we assume that δ(q, σ) is undefined for all σ ∈ Σ ′ ; thus we introduce
the following rules which halt the P system with the same result (acceptance or
rejection) as M :
[qi ]+ +
c → [ ]c yes for bin(0) ≤ i < bin(s(n)), if q is an accepting state (38)
[yes]0h → [ ]0h yes for bin(0) ≤ i < bin(s(n)), if q is an accepting state (39)
[qi ]+ +
c → [ ]c no for bin(0) ≤ i < bin(s(n)), if q is a rejecting state (40)
[no]0h → [ ]0h no for bin(0) ≤ i < bin(s(n)), if q is a rejecting state (41)
The simulation directly leads to the following result.
Theorem 1. Let M be a single-tape deterministic Turing machine working in
polynomial space s(n) and time t(n). Then there exists an (L, L)-uniform family
Π of P systems Πx with active membranes using object evolution and commu-
nication rules that simulates M in space O(log n) and time O(t(n)s(n)).
Proof. For each x ∈ Σ n , the P system Πx can be built from 1n and x in logarith-
mic space as it is described in Definition 2; thus, the family Π is (L, L)-uniform.
Each P system Πx uses only a logarithmic number of membranes and a constant
number of objects per configuration; thus, Πx works in space O(log n). Simu-
lating one of the t(n) steps of M requires O(s(n)) time, an upper bound to the
subscripts of objects used to introduce delays during the simulation; thus, the
total time is O(t(n)s(n)).
5 Conclusion
In this paper we provided a simulation of the polynomial space Turing ma-
chines by using logarithmic space P systems with active membranes and binary
representations for the positions on the tape. A similar approach is presented
in [9]. There are important differences in terms of technical details and effi-
cient representation; in comparison to [9], we improve the simulation by re-
ducing the number of membranes (by |Σ ′ | − 1) and the number of rules (by
|Σ ′ |·|Q|·s(n)·(5−|Σ ′ |)+|Σ ′ |·|Σ ′ |s(n)·(2·m+1)+|Q|·s(n)−|Σ ′ |·s(n)·(m+3)). In
particular, for the running example, the number of rules is reduced by 14·|Q|+84.
A different approach is presented in [8] where it is claimed that a constant space
is sufficient. However, in order to obtain the constant space space, input objects
(from ∆) are allowed to create other objects (from Γ ) leading to a different and
more powerful formalism than the one used by us in this paper, and making
such an approach not so interesting because of these unrealistic (powerful) input
objects.
418
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419
Discrete and Continuous Time High-Order Markov
Models for Software Reliability Assessment
Vitaliy Yakovyna and Oksana Nytrebych
Software Department, Lviv Polytechnic National University, Lviv, Ukraine
vitaliy.s.yakovyna@lpnu.ua, ksenija.volynj@gmail.com
Abstract. Due to the critical challenges and complexity of modern software
systems developed over the last decade, there has arisen an ever increasing at-
tention to look for products with high reliability at reasonable costs. Software
development process moves toward component-based design, and architecture
based approach in software reliability modeling is widely used. However, in
lots of models for software reliability assessment the assumption of independent
software runs is a simplification of real software behaviour. This paper de-
scribes two software reliability models that use high-order Markov chains thus
taking into account dependencies among software component runs for more ac-
curate software reliability assessment. The efficiency and accuracy of devel-
oped models is investigated by the example of several software products. It is
shown that using the software reliability models based on the high-order Mar-
kov chains results in the software reliability assessment accuracy up to 10–20%.
Keywords. Software reliability, architecture-based model, high-order Markov
chains.
Key Terms. SoftwareComponent, SoftwareSystem, MathematicalModel.
1 Introduction
Computer systems are widely used in modern industry for control and automation
purposes. All of these systems are controlled by software. Thus, software is used in
air traffic control, nuclear power plants, automated patients monitoring etc. Therefore
high requirements for software reliability are demanded because failures of such sys-
tems can lead not only to significant financial losses, but also threaten human life and
health. Although techniques that allow assessing and ensuring the specified hardware
reliability requirements have been developed, there are no common approaches for
software systems assessment.
According to STD-729, software reliability is defined as the probability of failure-
free software operation for a specified period of time in a specified environment [1,
2]. Although Software Reliability is defined as a probabilistic function, and comes
with the notion of time, it should be noted that, contrast to traditional hardware relia-
420
bility, software reliability is not a direct function of time [1]. Electronic and mechani-
cal parts may become "old" and wear out with time and usage, but software will not
rust or wear-out during its life cycle. Software will not change over time unless inten-
tionally changed or upgraded.
The history of software reliability assessment methods and tools began in the 60s
of last century. A number of researchers [3-7] worked on issues of development and
research of software reliability analysis and assessment models and methods that
would allow reducing the costs required for software testing stage. New software
reliability assessment models that reflect the internal structure of the application and
interaction of its components [6], called architectural-based models, are being devel-
oped because of increasing complexity of software systems and the result of expand-
ing their functional purpose.
In known models based on architectural approach [6, 7] the theory of first order
Markov chains is used with the assumption that the software components runs are
independent. This assumption is not always true due to the complexity of modern
software architecture and huge set of usage scenarios this assumption [8, 9]. There-
fore, for the development of adequate software reliability assessment models, which
will improve the testing process (e.g. allow to reduce the needed resources), one
should consider the high-order Markov chains, which allow to take into account the
interdependence of components runs [10].
This paper describes the software reliability assessment models based on architec-
tural approach, which use discrete and continuous time high-order Markov chains and
their comparison based on real world data. Nowadays architecture-based software
reliability models have been well studied in theory, but there is lack of papers describ-
ing their practical applications. Developing of high-order models for software reliabil-
ity assessment is not described enough in literature as well. Thus, the development of
new architecture-based software reliability assessment models that take into account
the dependencies among software component runs along with their application to real
world data is still a problem waiting for solution.
2 Software Reliability Model with Discrete Time High-Order
Markov Chain
This model considers absorbing Markov process that implies the existence of one
or more absorbing states, i.e. states that, once entered, cannot be left.
The developed software reliability assessment model [10] is hierarchical, that is in-
itially software architecture parameters are calculated based on software usage model
[11] using the theory of Markov processes, and then the behaviour of each component
failures is taken into account.
The discrete time HOMC software reliability model can be described using the fol-
lowing components – Ci is the graph with vertices corresponding to software
components, while edges indicates the program control flow ( i 1, N , where N is
the number of program components); P pij..kl is the high-order transition proba-
421
bility matrix ( pij..kl – transition probability from component і to component l de-
pending on being in previous K components); Q qij..kl is the initial probability
vector; i t is the failure rate of i -th software component.
According to this model the reliability of the whole system is calculated as
N
R Rl (1)
l 1
.
In turn, the reliabilities of each component ( Rl ) using high-order Markov chains
are calculated by
Vij ... kl tij ... kl
ij .. k
Rl exp( l (t )dt ) (2)
0 .
To calculate Vij ..kl – the expected number of visits a component l depending on be-
ing in previous K components – one has to solve the following system of linear equa-
tions:
N 1
V j..kl qij..k Vij..k pij..kl (3)
i 1 ,
here tij ..kl denotes the time spent at the component l depending on being in previous
K components.
3 Software Reliability Model with Continuous Time High-
Order Markov Chain
Using discrete-time model has a number of significant simplifications and re-
strictions. Thus, this model takes into account only the number of visits to i -th com-
ponent without taking into account of the distribution function of this random variable
(while taking it into account the expected value should be used). In addition, it is clear
that at any given time t the software failure is generally caused by the failure of the
software component, which is executed at a given time (in case of sequential connec-
tion of software components in Reliability Block Diagram). Thus, to increase the
degree of adequacy of the software reliability architectural model the continuous time
Markov chains should be used.
The continuous time HOMC software reliability model can be described using the
following components – Ci is the graph with vertices corresponding to software
components, while edges indicates the program control flow ( i 1, N , where N is
the number of program components); A aij is the high-order transition probabil-
422
ity matrix i, j 1, N (the values of matrix elements aij depends on the way of get-
ting into the state i ); P pi t is the probability vector, where pi t is the prob-
ability being in state C i at time t ; i t is the failure rate of i -th software compo-
nent.
In this case, the failure rate of a software system consisting of N components can
be written as [12]
N
t pi t i t (4)
i 1 ,
here i t is the failure rate of i -th component, pi t is the probability of i -th
component execution at time t .
Components failure rates i t can be obtained from the results of unit testing us-
ing known software reliability models, for example ones based on an inhomogeneous
Poisson process [13].
If the flow control between the components of the software is presented as a Mar-
kov process with continuous time, assuming that the i -th state of the process is the
execution of i -th component, the time dependences of the probabilities being in i -th
state ( pi t ) can be obtained by solving the system of equations of the Kolmogorov–
Chapman [14] for this process:
dpi t
ij (t ) p j (t ) ji (t ) p j (t ), i S (5)
dt jS jS
,
here ij (t ) is the transition intensity from component і to component j at time t, and
S denotes the set of all system states. In general the transition intensities ij (t ) de-
pends on the transition probabilities aij and could be calculated from latter.
To take into account the interdependence of execution of software component (and
consequently changes of transition probability from i -th state) depending on the way
of getting to the current state, the high-order Markov chain should be used (the order
K of the model determines the accounted length of the path). In a case of high-order
Markov chains the actual problem is to calculate the transition probabilities depending
on the program control flow background.
It is well known that a high order Markov chain can be represented as a first order
chain by appropriate redefining the state space [15]. For software implementation of
models that use high-order chains, it is necessary to have the formalized algorithm for
this representation. Using the analogy with the known Erlang phase method [16] a
high-order Markov process can be represented as an equivalent first-order process
with additional virtual states. Each state of the original graph Ci (geometric dia-
423
gram, showing the possible states of the system and the possible transitions of the
system from one state to another) is split into such number of virtual states as many
different paths of length K to this state exist. Thus the problem solution essentially is
K
reduced to using of graph theory. Therefore, to calculate the number mij of chains of
K-th order from state i to state j the following expression based on the Floyd method
can be used:
S
mijK mil K 1 eil mlj1 (6)
j 1 ,
here eij are the elements of the identity matrix.
Using (6) one can build an equivalent graph Ci which is a representation of the
initial graph Ci , taking into account all K -th order paths to i -th state. This allows
to avoid the dependencies of the transition intensities ij (t ) on the program control
flow background. Then the time dependence of the software component execution
probability is obtained by solving the system of Kolmogorov–Chapman equations (5)
for the equivalent first order Markov process. Using this dependence in (4) together
with the component failure rate, the failure rate of the whole software system can be
calculated.
For calculation of software reliability measures, based on the obtained relationship
(4), one can use the following relations [14]:
- reliability function P(t) – the probability that no failure will occur within the
time interval [0, t] – can be calculated as
t
P(t ) exp( ( )d ) (7)
0
- mean operating time to failure Tl
T1 P( )d (8)
0
4 Determination of the Markov Chain Order for Software
Reliability Assessment
In this paper it is proposed to use AIC and BIC criteria [17] since they are not a
hypothesis test and thОy Нon’t usО thО significancО lОvОl. Although these criteria give
consistent results and don’t depend on the estimated model order. They are efficiently
424
used for weather forecasting and selection of adequate environmental model [18]. But
the usage of these criteria in software reliability modeling still remains unexamined.
In general AIC criterion [19] is calculated by the following expression:
AIC 2k 2 ln(L) , (9)
here k is the number of independent parameters in the model, and L is the moНОl’s
maximum likelihood function.
If the value of this software moНОl’s maximum likОlihooН function is substituted in
the expression (9), and instead of parameter k one substitute the number of the K-th
order model parameters, which contain N components ( k N K ( N 1) ), then the
following expression can be obtained [20]
AIC ( K ) 2 N K ( N 1) 2 ln( pij..kl nij..kl ) , (10)
i, j ,.., k ,l
here nij ..kl is the number of transitions from component і to component l depending
on being in previous components ( i j ... k l ) in observed sequence
and pij ..kl is the transition probability in this sequence.
As it can be seen from (10), this criterion is independent of sample size. Therefore,
AIC criterion is used in the case of a large sample size (observable sequence) when
the software is tested many times and the sequence of software component runs is
logged.
An alternative to AIC criterion is ВІС [21], which takes into account the number of
elements in observable sequence and expressed as
BIC ( K ) 2 ln(L) ln(n)k. (11)
In the case of using the BIC criterion for the Markov chain optimal order determi-
nation in the case of software reliability modeling, the expression similar to AIC crite-
rion (10) is obtained:
BIC ( K ) 2 N K ( N 1) ln(n) 2 nij..kl ln pij..kl . (12)
i, j ,.., k ,l
It is worth noted that the BIC criterion should be used at the small sample size of
empirical data concerning the software usage, because it imposes stronger penalties
even when the sample size n>8.
Thus, after determining the order of Markov chain, the well-known classical Mar-
kov tools can be used for software reliability assessment as it was described above.
425
5 Verification of the Models
To study the efficiency of the developed software reliability assessment model
that uses the discrete time high-order Markov chains, the reliabilities of the five soft-
ware systems, developed by one of the authors, were calculated using the first and the
high order Markov chain models. The average amount of software components in
tested software systems is 10. The results of reliability calculations using the first and
the high-order models are shown in Fig. 1 along with the reliability obtained from unit
testing data.
0,90
First-order model
Second-order model
Testing data
0,85
Reliability, R
0,80
0,75
0,70
1 2 3 4 5
Software
Fig.1. The comparison diagram of the software reliability assessment accuracy using first and
high order discrete time models.
As shown in fig. 1, the usage of software reliability assessment model based on
discrete time high-order Markov chains makes it possible to increase the software
reliability accuracy to 6% even for software systems with a small number of compo-
nents.
To illustrate the efficiency of continuous time software reliability model, the relia-
bility of the authors' developed program with four components (in this case, each
component refers to one of the following program classes – Input, Calculation, Out-
put, Exit) was analyzed. The values of each component failures rates are presented in
Table 1.
Table 1. Failure detection frequency for each component
Component Failures detection frequency
Input 0.11
Calculation 0.18
Output 0.09
Exit 0.01
426
The probability transition matrix and the initial probability vector of the Markov
chain were calculated and are summarized in Table 2 and Table 3 correspondingly.
Table 2. The first order probability transition matrix
Component Input Calculation Output Exit
Input 0.2987 0.66233 0 0.03897
Calculation 0.2666 0.05 0.6333 0.0501
Output 0.5 0 0.3148 0.1852
Exit 0 0 0 1
Table 3. The first order initial probability vector
Components Input Calculation Output Exit
Probability 1 0 0 0
The AIC criterion was used for optimal Markov chain order determination (the
sample set contains 188 entries). The AIC values are listed in Table 4.
Table 4. The values of АІС for different chain orders
The process order AIC value
1 223.7
2 203.5
3 352.7
4 1082.8
The initial graph Ci indicating the program components and control flow, as
well as graph Ci of the equivalent second order (see Table 4) Markov process are
shown in Fig. 2 and 3 correspondingly. The notations in these figures are as follows: I
correspond to Input state, C – to Calculation, O – to Output, and E to Exit state (see
Table 2); indexes indicates the previous state in control flow history (thus state OC
means that the current state Output has been reached from previous state Calculation).
427
I
C E
O
Fig.2. Initial graph, representing the components and control flows of the software used for
continuous time reliability model verification.
E
Io Ic Ii
Ci
Oc Cc
Oo
Fig.3. Graph representing an equivalent to the second order Markov chain process for software
shown in Fig. 2.
Fig. 4 shows the time dependency of failure rate on tested software system (Fig. 2)
obtained from continuous time first- and second-order Markov chains. It’s worth not-
ing that for continuous time model simulations time was counted as arbitrary time
units (a.u).
As it is seen from this figure the first order model gives slightly (1–5%) reduced
failure rate value for small values of time, while it gives significantly (20%) overes-
timated failure rate value for middle time values range, and when the value of t in-
creases by more than 60 a.u. the difference between values of t obtained from
428
both models almost tends to be negligible. Reducing the difference of t values,
obtained from the first and the second-order models, to zero at high times can be ex-
plained by decreasing of the t value itself and by the absence of differences in
the software behaviour description by two models in this case. In the case of t
both models suggest that system is in thО “Exit” state (see Fig. 2, 3) and, accordingly,
its failure rate is limited by this component failure rate. Differences of t behav-
iour on the initial evolution stages of software system can be entirely explained by
differences in the software system behaviour description by different models, where
the first-order model ignores the interdependence of software component runs, and
therefore the probabilities of components executing are different at given time t for
both models. Thus, it could be argued that software reliability model based on the
high order Markov chain describes the software system behaviour more adequately
and determines its reliability measures more accurately.
0,15
1 - first order model
2 - second order model
0,10
(t)
1
0,05
2
0,00
0 10 20 30 40 90 100
t, a.u.
Fig.4. Time dependence of the tested software failure rate, obtained from the first (1) and sec-
ond-order (2) models.
This conclusion is confirmed by the analysis of software system reliability function
time dependence obtained using equation (7) as shown in Fig. 5. Note that the relia-
bility function is calculated using Ukrainian national standards [22] and, as it was
indicated in (7), represents the probability of failure free operation during the time
interval 0, t , but not exactly at the time t . So, it is evidently that the reliability
function is time-decreasing one. As it can be seen from Fig. 5, the difference in the
values Pt increases up to 20% with time value increasing. This behavior is easily
429
understood if taking into account the interval estimation of reliability for the range
0, t [15], and its deviation evidently increases with interval length increasing.
So, we can conclude that ignoring the interdependence of software components
runs could results in increasing inaccuracy of software reliability measures estimation
up to 20%.
Another measure of reliability, which was used to determine the developed high-
order model effectiveness and adequacy, is the mean operating time to failure T1 . The
value of mean operating time to failure calculated by the expression (8) is 20.9 time
units for first-order model, while the value obtained from the second-order model is
23.3 time units. Obviously the difference between the first and the second-order mod-
els is 11.5%, which can be crucial in the reliability analysis of the complex technical
systems.
1,0 1 - first order model
2 - second order model
0,8
0,6
P(t)
0,4
0,2 2
1
0 10 20 30 40 50 60 70 80 90 100
t, a.u.
Fig.5. The time dependence of the tested software reliability function, obtained from the first
(1) and second-order (2) models.
Therefore, the usage of software reliability models based on the high-order Markov
chains even with a small components number (in this case there was 4 component
software, see Fig. 2) and complexity (in this case the optimal model order is 2, see
Table 4) results in the increase of model adequacy and the software reliability assess-
ment accuracy on 10–20%. The value of such growth of reliability estimation accura-
cy is especially important in the case of complex hardware and software systems in
which the mistake of software component reliability estimation can repeatedly affect
the accuracy of whole system reliability assessment. Using the high-order models for
more complex software systems could results in more significant improvements of
reliability assessment.
430
6 Conclusions
In this paper the software reliability models using discrete and continuous time
high-order Markov chains, which enable consideration the dependencies among soft-
ware components runs, have been developed. Software reliability assessment based
on the high-order discrete time Markov chains allows to increase the software reliabil-
ity measures accuracy up to 6 %, and high-order continuous time Markov chain – up
to 10–20%. The advantage of high-order discrete time Markov chains model for soft-
ware reliability analysis is small computing resources needed even for software with a
lot of components, while the advantages of high-order continuous time Markov chains
model are independence from the sampling step (in the case of discrete time model it
may cause inaccurate transition probabilities calculation), and also automatic consid-
eration of transitions pii that avoids unnecessary computations. Practical aspects of
estimating input parameters for the models as well as studying the dependence of the
software reliability on its characteristics (components number, the average number of
variables in the component, components cohesion etc.) will be described elsewhere.
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432
Evolution of Software Quality Models: Green and
Reliability Issues
Oleksandr Gordieiev1, Vyacheslav Kharchenko2 and Mario Fusani3
1
University of Banking of the National Bank of Ukraine, 1 Andriivska Street, Kyiv, Ukraine
alex.gordeyev@gmail.com
2
National Aerospace University «KhAI», 17 Chkalova Street, Kharkiv, Ukraine
V.Kharchenko@khai.edu
3
ISTI-CNR, System and Software Evaluation Center, Via Moruzzi, 1 56124 Pisa, Italy
mario.fusani@isti.cnr.it
Abstract. The group of attributes (characteristics, requirements) related to
green software is essential part of software quality model. It consists of the two
main attributes as a resources (energy) saving and sustainability. Evolution of
software quality models is analyzed in context of green and reliability. In
particular, well known software quality models beginning from on the first
McCall’s model (1977) to models described in standards ISO/IEC9126 (2001)
and ISO/IEC25010 (2010) are analyzed according with green and reliability
issues. Comparing of the software quality models are carried out using a special
metrics of complexity and technique considering the number of levels and
attributes and their semantics. Prediction of complexity for the next software
quality model (2020) is fulfilled and variants of green software attributes
inclusion in model are proposed.
Keywords. software quality model, green software, software reliability,
evolution analysis, metrics, ISO/IEC9126, ISO/IEC25010, structure-semantic
analysis.
Key Terms. Model, Reliability, Requirement, SoftwareSystem.
1 Introduction
1.1 Motivation and Work Related Analysis
A set of Software Quality Models (SWQM) has been introduced during evolution
of software engineering [1]. Software quality is a degree to which a software product
satisfies stated and implied needs when used under specified conditions [2]. Software
Quality Model (SWQM) is usually defined as a set of characteristics and relationships
between them which actually provide the basis for specifying the requirements of
quality, evaluating quality and comparing of SWQMs [3-9]. There are a lot of the
models suggested during «software engineering era» [10]. Some of SWQM, described
in IEEE, ISO, IEC standards, became well-known and can be called basic. New
433
significant SWQM appear just about once in 10 years. The characteristics and
subcharacteristics set and structure (graph-based hierarchy and semantic content) of
such SWQMs are changed [11-14]. Generally, these sets are extended and the next
SWQM becomes more and more complicated. Changing’s of SWQMs are caused by
evolution of technologies, new challenges in software engineering and so on.
One of the challenges is development of energy-saving (green) information
technologies. It has been caused by appearance of a concept «green software» [15].
Gist of «green software» (GSW) in a broad sense is described by the following words:
«decrease» (energy or other resources consumption), «don't do much harm and
preserve» (energy, resources, environment) and «improve» (make environment more
comfortable and safe). More wide aspects and directions of green and safe/reliable
computing are discussed in [16,17].
«Green» characteristics for software are resources saving and sustainability, which
were not explicitly defined in well known SWQMs described by standards
ISO/IEC9126 [18], ISO/IEC25010 [2]. Analysis of [3,4,6-8] allowing to conclude that
SWQMs do not include such characteristics in explicit form.
Taking into consideration the prerequisites for emergence of green characteristics
in future SWQMs in direct form we analyze the evolution of the characteristics
associated with GSW for existing quality models and try to predict their changing.
The analysis will allow defining tendencies of green characteristics and suggesting
variants of including some in future SWQMs.
1.2 Goal and Approach
A goal of the paper is carrying out of analysis of known software quality models
and their development in context of GSW and software reliability. We aim to
investigating SWQMs using metric-based approach to assess “weights” of different
software quality attributes, first of all, green and reliability characteristics, changing
of the weights during evolution of the models and to predict their changing in future.
Stages of the research are the following:
1. Determination of occurrence rates for different SWQM attributes
(characteristics at the first level of hierarchy and subcharacteristics at the second one)
in different quality models;
2. Selection and analysis of SWQM characteristics which are implicitly
associated with green software;
3. Analysis of SWQMs in context green software and reliability by use of
complexity metrics and calculation of corresponding weights for attributes;
4. Research of relationship/dependency between metric values for green
software, reliability and the years of emergence for known basic SWQMs;
5. Calculation of complexity metric for using results of SWQMs
relationship/dependency comparison, described in [11];
6. Calculation of complexity metric for green and reliability attributes of new
SWQMs using function describing of dependency between metric values and years of
SWQMs emergence;
7. Analysis of SWQM in use in context of green software and definition of
possible variants of inclusion of green attributes in new models.
434
2 SWQM Analysis in Context of Green Software and Reliability
2.1 Analyzed Models
Let’s select and analyse SWQM characteristics which can be implicitly associated
with green software and reliability. The results of analysis are shown in Table 1 and
Table 2 for green characteristics and reliability characteristics correspondingly.
Numeration of the characteristics corresponds with their “places” in hierarchy of
SWQMs.
Table 1. SWQM characteristics associated with Table 2. Reliability characteristics of
GSW. SWQM.
SWQMs GSW SWQMs Reliability
№ №
(years) characteristics (years) characteristics
4. Efficiency 2. Reliability
McCall
1. 4.1 Execution efficiency McCall 2.1 Accuracy
(1977) 1.
4.2 Storage efficiency (1977) 2.2 Error tolerance
2.2 Efficiency 2.3 Consistency
Boehm
2. 2.2.1 Accountability 2.1 Reliability
(1978)
2.2.2 Accessibility 2.2.1 Self
Boehm
2. contentedness
(1978)
Carlo 2.2.2 Integrity
3. Ghezzi – 2.2.3 Accuracy
(1991) CarloGhe 3. Reliability
3.
zzi (1991)
4 Performance 3. Reliability
4.1 Velocity 3.1 Frequency and
4.2 Efficiency FURPS servity of failures
4.
FURPS 4.3 Availability (1992) 3.2 Recoverability
4.
(1992) 4.4 Time of answer 3.3 Time among
4.5 Time of recovery failures
4.6 Utilization of resources 2. Reliability
1.2 Capacity IEEE 2.1 Non deficiency
5.
1 Efficiency (1993) 2.1 Error tolerance
IEEE
5. 1.1 Temporal efficiency 1.3 Availability
(1993)
1.2 Resource efficiency Dromey 1.2 Reliability
6.
Dromey 2.2 Efficiency (1995)
6.
(1995) 2. Reliability
ISO
4 Efficiency 2.1 Maturity
ISO 9126- 7. 9126-1
7. 4.1 Time behavior 2.2 Fault tolerance
1 (2001) (2001)
4.2 Resource utilization 2.3 Recoverability
QMOOD 6 Effectiveness QMOOD -
8.
8. (2002) (2002)
5. Reliability
2 Performance efficiency ISO 5.1 Maturity
ISO
2.1 Time behavior 9. 25010 5.2 Availability
9. 25010
2.2 Resource utilization (2010) 5.3 Fault tolerance
(2010)
2.3 Capacity 5.4 Recoverability
435
To assess “weights” of green characteristics the technique of SWQM structure-
semantic analysis (SSA-technique) can be applied [11]. The technique describes
quality models as a facet-hierarchy structure (graph). Nodes corresponds quality
attributes and links take into account hierarchy dependencies. To briefly characterize
the proposed analysis technique, let us introduce some initial terms:
conceptual model is a model which a model under study is compared with;
model under study is a model which is compared with a conceptual model;
characteristic under study is a conceptual model characteristic which is
compared with model under study characteristics.
2.2 Metrics
SSA-technique is based on comparing a model under study with the conceptual
model, i.e. every SW Quality Model is compared with the conceptual model. So, the
analysis is equivalent to semantic comparing characteristics and subcharacteristics of
a model under study and the conceptual model with regard to their structures.
Selecting a reference model is usually performed by an expert who has relevant
experience and qualifications.
At the following stage comparison of models among themselves should be
performed. The simplest and most obvious metrics are offered. Hierarchy of these
metrics is presented in Fig. 1. The metrics are used to compare models with reference
model bottom up, i.e. first at the level of subcharacteristics (subcharacteristics
matching metric SMM, cumulative subcharacteristics comparison metric CSCM,
characteristics matching metric CMM), then at the level of characteristics (cumulative
matching characteristics metric CMCM) and finally at the level of models as a whole
(cumulative software quality models comparison metric CSQMCM).
CSQMCM
CMCMi CMCMi+1 ...
CMMi CSCMi ...
SMMj SMMj+1 ... SMMm
Fig. 1. Metrics hierarchy.
Features of the metrics are the following:
– subcharacteristic matching metric (SMMj). Every subcharacteristic match value
is identified as SMMj = 0,5 / number of reference (conceptual) model elements
subcharacteristics of the characteristic under study. Weights of characteristics are not
considered when calculating metrics;
– cumulative subcharacteristics comparison metric (CSCM) is evaluated as a sum
of SMM:
CSCM i = ∑kj=1SMM j ; (1)
436
– characteristics matching metric (CMM) takes the value of 0.5 in case of
matching or 0 if the characteristics are different;
– cumulative matching characteristics metric (CMCM) is calculated as a sum of
j1CSCM j :
k
CMM metric and
CMCM i = CMM i + ∑kj=1 CSCM j ; (2)
– cumulative software quality models comparison metric (CSQMCM) is
calculated according to the formula:
CSQMCM i = ∑nj=1 CMCM j (3)
2.3 Results of SWQM Analysis in Context of Green Software and Reliability
Characteristics
Let us conduct SW QM analysis and first of all, define the reference (conceptual)
model. SW Quality Model ISO/IEC 25010 will be considered as uppermost and
etalon regarding to all other models. It is the newest introduced model and takes into
account main modern software peculiarities in point of view quality evaluation. This
model is described by international standard of top level.
According with results of analysis CMCM is calculated for set of characteristics
presented in Table 1. The results of calculation are shown in Table 3 (Сhs –
characteristics, SChs – subcharacteristics) for GSW characteristics and Table 4 for
reliability characteristics.
The histogram of CMCM values for software quality models is presented on Fig. 2.
An abscissa axis corresponds to years of SWQM emergence. Initial point (year) is
1970 (as a first year after 1968 which is multiple of a ten years).
CMCM values will be further represented and analysed only for so-called basic
SWQMs [18]. Basic models were selected considering their support by standards, the
international reputation and application. The models of McCall and Boehm are
similar, hence first one was selected. Hence, the models of Boehm, Ghezzi, FURPS,
Dromey, QMOOD were excluded (Fig. 3).
The analytical dependency between SWQM appearance year (X axis) and CMCM
value (Y axis) for characteristics associated with GSW may be represented by
regressive liner function:
y = ax+b, (4)
where x – variable, a and b - regression coefficients. For 1970 year variable (x) has
value 0, for 1980 year x=10, for 1990 year x=20, for 2000 year x=30 and for 2010
year x=40.
Linear subjection was chosen by graphic data analysis (Fig. 3). Satisfiability of
applying linear subjection is confirmed by coefficient of determination (R2) which
equals 0,94.
437
Table 3. Results of GSW characteristics comparison and CMCM calculation.
Conceptual
model McCall model Boehm model Ghezzi model
(ISO 25010)
Chs SChs Chs SChs CMM SMM Chs SChs CMM SMM Chs SChs CMM SMM
2 4 0,5 0 - 2.2 0 0,5 - - 0 0
2.1 - - 0 0 - - 0 0 - - 0 0
2.2 - - 0 0 - - 0 0 - - 0 0
2.3 - - 0 0 - - 0 0 - - 0 0
CMCM=0,5 CMCM=0,5 CMCM=0
Conceptual
model FURPS Model IEEE Model Dromey model
(ISO 25010)
Chs SChs Chs SChs CMM SMM Chs SChs CMM SMM Chs SChs CMM SMM
2 - 4.2 0 0,5 1 - 0,5 0 - 2.2 0 0.5
2.1 - - 0 0 - - 0 0 - - 0 0
2.2 - 4.6 0 0,17 - 1.2 0 0,17 - - 0 0
2.3 - 1.2 0 0,17 - - 0 0 - - 0 0
CMCM =0,84 CMCM =0,67 CMCM =0,5
Conceptual
model ISO 9126 model QMOOD model
(ISO 25010)
Chs SChs Chs SChs CMM SMM Chs SChs CMM SMM
2 4 - 0,5 0 2 - 0,5 0
2.1 - 4.1 0 0,17 - - 0 0
2.2 - 4.2 0 0,17 - - 0
2.3 - - 0 0 - - 0 0
CMCM=0,84 CMCM=0,5
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
Ghe zzi (1991)
Dromey (1995)
ISO/IEC 9126 (2001)
McC all (1977)
F URP S (1992)
Boehm (1978)
IEEE (1993)
ISO/IEC 25010 (2010)
QMOOD (2002)
GWS characteristics reliability characteristics
Fig. 2. CMCM values for GSW and reliability characteristics of SWQMs.
438
Table 4. Results of reliability characteristics comparison and CMCM calculation.
Conceptual
model McCall model Boehm model Ghezzi model
(ISO 25010)
Chs SChs Chs SChs CMM SMM Chs SChs CMM SMM Chs SChs CMM SMM
5 2. - 0,5 0 - 2.1 0 0,5 3 - 0,5 0
5.1 - - 0 0 - - 0 0 - - 0 0
5.2 - - 0 0 - - 0 0 - - 0 0
5.3 - 2.2 0 0,125 - - 0 0 - - 0 0
5.4 - - 0 0 - - 0 0 - - 0 0
CMCM=0,625 CMCM=0,5 CMCM=0,5
Conceptual
model FURPS Model IEEE Model Dromey model
(ISO 25010)
Chs SChs Chs SChs CMM SMM Chs SChs CMM SMM Chs SChs CMM SMM
5 3. - 0,5 2 0,5 0 1.2,2.3, 0 0,5
3.4,4.4
5.1 5.1 - - 0 - - 0 0 - - 0 0
5.2 5.2 - 4.3 0 - 2.3 0 0,125 - - 0 0
5.3 5.3 - - 0 - 2.2 0 0,125 - - 0 0
5.4 5.4 - 3.2 0 - - 0 0 - - 0 0
CMCM =0,75 CMCM =0,75 CMCM =0,5
Conceptual
model ISO 9126 model QMOOD model
(ISO 25010)
Chs SChs Chs SChs CMM SMM Chs SChs CMM SMM
5 2 - 0,5 0 - - 0 0
5.1 - 2.1 0 0,125 - - 0 0
5.2 - - 0 0 - - 0 0
5.3 - 2.2 0 0,125 - - 0 0
5.4 - 2.3 0 0,125 - - 0 0
CMCM=0,87 CMCM=0
Fig. 3. CMCM values for GSW and reliability characteristics of basic SWQMs.
439
The values of parameters a and b can be calculated using Least Square Method:
n n n
n ∑x i yi ∑x i ∑yi
a = i = 0n i =1 i =1
n , (5)
∑
n x 2 ( xi )2 ∑
i =1 i =1
n n
∑ yi a ∑xi
i =1 i =1
b= . (6)
n
As a result а = 0.0146, b = 0.4108 and function:
y = 0.0146x+0.4108. (7)
The obtained function may be called a law of increasing of characteristics
associated with GSW for SWQM.
The similar dependency can be obtained for reliability characteristics. In this case а
= 0.011, b = 0.5 and function:
y = 0.011x+0.5. (8)
Formulas 7 and 8 illustrate a tendency of SWQMs characteristics/
subcharacteristics changes. Analysis of dependencies (Fig.3) allows concluding that
weights of green and reliability characteristics became equal in 2010 (the standard
ISO/IEC 25010). Hence, since first SWQMs the characteristics/ subcharacteristics
related to green attributes have faster dynamics of increasing.
3 Development of SWQM in Context of Green Software
We can assume that the next general SWQM will include GSW characteristics in
an explicit form. Let’s analyse SWQM evolution tendency in context GSW as a
whole. CSQMCM for SWQM may be calculated as shown in formula (3). It may be
appeared for future model (2020 year). In compliance with [11] and basing on the
analytical relationship between SWQM appearance year (X axis) and CSQMCM
value (Y axis) the following formula may be obtained:
y=0,153x+1,363. (9)
Besides, considering that each new SWQM approved as a standard is received
about once per 10 years, and that the last model was introduced by the standard
ISO/IEC 25010 appeared in 2010 the prediction of the CSQMCM value can be done.
With this in mind:
CSQMCM = 0,153*50 + 1,363= 9,013. (10)
440
CSQMCM values change is illustrated in Fig. 4 as a histogram for the well known
base SWQM as columns of gray and subsequent SWQM 2020 as a column of light
gray column.
Fig. 4. CSQMCM values for known and predictable SWQMs.
According to the obtained dependence (4) CMCM for green software
characteristics is calculated for predictable SWQM 2020 (Fig. 5).
y=0,0146*50+0,4108=1,1408. (11)
And CMCM for reliability characteristics is calculated for predictable SWQM
2020 (Fig. 5).
y = 0,011*50+0,5=1,05. (12)
Fig. 5. CMCM values for reliability characteristics and green characteristics for basic SWQMs.
CMCM values of SWQM 2020 for characteristics associated with «green»
software exceed the value of the same metric for SWQM ISO/IEC 25010 by 0.1408.
CMCM values of SWQM 2020 for reliability characteristics exceed the value of
the same metric for SWQM ISO/IEC 25010 by 0.05.
441
Analysis of dependencies (Fig.5) allows predicting that green characteristics
number will increase faster comparing with other more conservative characteristics.
4 GSW Oriented ON Extending of SWQMs
Taking into account predictable changing of SWQMs let’s analyse how content of
such models may be added including software quality models in use.
4.1 Variants of GSW Characteristics Inclusion in SWQM
In the following, possible variants are shown of inclusion of GSW characteristics
and its components in a SWQM.
1. GSW characteristic can be introduced in SWQM as a separated characteristic
with subcharacteristics resources saving and sustainability. It should be noted that
usually resources saving excludes resource utilization from performance efficiency
characteristic (Fig. 6).
Software quality
Performance
Green software ... efficiency
Resource
Resources saving Sustainability
utilisation
Fig. 6. Green software characteristics in SWQM at the level of characteristics (1).
2. Green software characteristics are not included in SWQM explicitly, but
subcharacteristics can go in to SWQM (Fig. 7). Resources saving goes in to SWQM
as the subcharacteristic in place of resource utilization. Subcharacteristic
sustainability goes in to SWQM as separated characteristic.
442
Software quality
Performance Sustainability
efficiency ...
Resource
Resources saving
utilisation
Fig. 7. «Green» software characteristics in SWQM at the level of characteristics and
subcharacteristics (2).
3. GSW characteristic cannot be explicitly included in SWQM, but
subcharacteristics can be explicitly included (Fig. 8). Resources saving is included in
SWQM as subcharacteristic in place of resource utilization. Sustainability is included
in SWQM as subcharacteristic to characteristic security.
Software quality
Performance
Security
efficiency ...
Resource
Resources saving Sustainability
utilisation
Fig. 8. Green software characteristics in SWQM at the level of subcharacteristics (3).
4.2 SWQM in Use. Analysis in Context of GSW
The standards ISO/IEC9126 and 25010 describe a separate type of models -
software quality models in use (SWQM-U). SWQM-U is a capability of the software
product to enable specified users to achieve specified goals with effectiveness,
productivity, safety and satisfaction in specified contexts of use [18]. The SWQM-Us
include characteristics, which can be associated with GSW subcharacteristics, in
particular resources saving and sustainability:
for SWQM-U, ISO/IEC 9126: resources saving – productivity; sustainability
– safety. Productivity is a capability of the software product to enable users to expend
appropriate amounts of resources in relation to the effectiveness achieved in a
specified context of use. Safety is a capability of the software product to achieve
acceptable levels of risk of harm to people, business, software, property or the
443
environment in a specified context of use. Risks are usually a result of deficiencies in
the functionality (including security), reliability, usability or maintainability;
for SWQM-U, ISO/IEC 25010: resources saving – efficiency; sustainability
– freedom from risk, which include 3 subcharacteristics – economic risk mitigation,
health and safety risk mitigation and environmental risk mitigation. Efficiency is a
ratio of expended resources to the accuracy and completeness with which users
achieve goals. Freedom from risk is a degree to which a product or system mitigates
the potential risk to economic status, human life, health, or the environment.
Correlation of SWQM-U characteristics for standards ISO/IEC 9126 and 25010,
which are implicitly associated with «green software» and among themselves is
shown in Fig. 9.
Thus, GSW related characteristics should be taken into account on development of
the next SWQM (SWQM-U) as well.
«Green software»
ISO/IEC 9126 ISO/IEC 25010
characteristics
Resources saving 2. Productivity 2. Efficiency
3. Safety 4. Freedom from risk
4.1 Economic risk mitigation
Sustainability
4.2 Health and safety risk mitigation
4.3 Environmental risk mitigation
Fig. 9. Correlation of characteristics of SWQM-Us (ISO/IEC 9126 and ISO/IEC 25010) with
GSW characteristics.
5 Conclusions
In compliance with SWQM structural and semantic analysis technique we have
analyzed SWQM of standards ISO/IEC 9126 and 25010 in context characteristics
associated with green software. Using SSA-technique, a relationship between the year
of the SWQM appearance and the value of CMCM was obtained and analyzed.
Besides, we have calculated the CMCM values for the green software characteristics
of the next SWQM, the output of which may be expected in 2020.
It was also obtained the value of metric - CSQMCM for SWQM of 2020, which
exceeds the value of this indicator for SWQM ISO/IEC 25010 (Fig. 4). It may be
explained by possible inclusion of green software characteristics in SWQM explicitly.
According with results of analysis we can conclude that:
- since first SWQMs the characteristics/ subcharacteristics related to green
attributes have faster dynamics of increasing;
444
- weights of green and reliability characteristics became equal in the standard
ISO/IEC 25010;
- it is predicted faster increasing of number green characteristics comparing with
other more conservative characteristics.
However, implementation of green characteristics in future quality models should
be harmonized with basic attributes such as reliability.
In the future we plan to investigate every SWQM characteristic separately. The
data obtained in this case will provide development of a prototype of the new SWQM.
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446
Service and Business Models with Implementation
Analysis of Distributed Cloud Solution
Olga Yanovskaya1, Maria Anna Devetzoglou2, Vyacheslav Kharchenko1,3 and
Max Yanovsky1,
1
National Aerospace University named after N.E. Zhukovsky "KhAI", Kharkiv, Ukraine
2
International Creativity Engineering Group, Athens, Greece
3
Centre for Safety Infrastructure-Oriented Research and Analysis, Kharkiv, Ukraine
1{O.Yanovskaya, M.Yanovsky}@csn.khai.edu
2M.Devetzoglou@interceg.com
1,3V.Kharchenko@khai.edu
Abstract. The service and business models of a Distributed Cloud solution
based on peer-to-peer technology are presented in this article, in order to im-
plement the proposed solution. Methods for organizing the interaction between
the participants’ nodes and nodes that are non-participants in the Distributed
Cloud are proposed. Passive replication is used to improve service reliability. A
competitive analysis of existing solutions within the scope of a decentralization
approach for content sharing is conducted. Average response time to a request
for a centralized client-server and distributed Cloud architecture is estimated.
Keywords. Distributed Cloud, Peer-to-Peer Network, Data Center, Participa-
tory Business Model, Service Reliability.
Key Terms. DataCloud, Reliability, Model, Infrastructure, Market.
1 Introduction
The IT industry constantly grows, raising the expectations of big organizations and
individuals alike, changing the way things are done nowadays; in fact, without it, it
would be impossible to conduct business and human interaction as we know it today
would be greatly different across numerous professional and social sectors. At the
same time, gradually more people and enterprises access the Internet, adding to the
increasing needs of computing and generating data through various devices, at an
accelerating rate. This data is required to be stored and handled in order to be secure
and available to be retrieved once the user requests it.
To accommodate demand, large, expensive, energy hungry data centers have been
built that only powerful company can afford to have. Additionally, they require high
costs of maintenance, personnel, power back up systems and space. Located at a
physical place, they are vulnerable to local conditions, be it weather phenomena, re-
447
gional power cuts, earthquakes etc. Furthermore, 2% of global CO2 emissions are
attributed to the ICT industry, a significant part of which is caused by data centers.
High investment costs for data centers prevent smaller companies from entering the
market, making it necessary to improve service reliability, energy and cost efficiency
of Cloud computing infrastructure.
Currently, the concept of P2P technology is not new but its application to cloud
computing is at its early stages. However, it is gradually growing as more new com-
panies begin to join the race to provide smarter and cheaper solutions. More specifi-
cally, the majority of the companies that are active in P2P cloud technology are
strongly focusing on storage and sharing of documents, in order to facilitate storing
options and to assist teams or groups to virtually interact through their documents.
Additionally, they enhance user experience due to optimized infrastructure, collabora-
tion and sync. BitTorrent goes a step further, by offering information sharing from
device to device, skipping the use of cloud [1]. Within this suggestion, we propose a
method for Cloud data center architecture modernization [2]. The method assumes
implementation of distributional technologies such as peer-to-peer (P2P) networks to
Cloud architecture. Distributed Cloud computing, being part of cloud computing,
supports customers’ needs and provides main cloud benefits. However, it differenti-
ates itself from the existing Cloud Computing in a unique way: it is anthropocentric,
revolving around people and their activities, making them sources and consumers at
the same time. In addition to its human-centered function, P2P Cloud Computing is a
new application of previous technologies, one that can provide both, value and results.
2 State of the Art
According to a Cisco study [3], it is estimated that data traffic will reach 7.7 ZB by
2017 and the need for more websites constantly and steadily rises. This need does not
only apply to professionals and big companies that either have the money to allocate
the task to a skilled person or have the skills themselves. It also corresponds to a wide
number of individuals and companies that, although experienced in a number of sec-
tors, may not have the skills or financial resources to create their content.
Currently, customers deal with scalability issues by using the services of Cloud
providers. Studying the pricing of these services [4], it is found that customers may
very well enjoy the benefits of the Cloud but at a rather significant cost. Many Cloud
providers have joined the sector and provide solutions to customers. For companies
that aim to scale up and grow, this can have a heavy toll on their budget and, in more
than one cases, budget limitations may actually delay or even prohibit growth. Ac-
cording to the IDC, the cloud software market is forecast to surpass $75 B by 2017,
while at the same time, the percentage of IT budget expected to be spent on cloud-
based applications and platforms by current organizations within the next 2 years
reaches 53.7%. Regarding storage as a service model, several solutions within the use
of the decentralization approach were developed for content sharing. The following
table depicts competitive products, their key features, their advantages and disad-
vantages.
448
Table 1. Competitive analysis of existing solutions within the use of decentralization approach
for content sharing
Name Key features Advantages Disadvantages
Storage solution Expensive device
based on P2P tech- ($795). Annual
SpaceMonkey
nology that saves payment $49. Can
users’ data both lo- A cross-platform applica- only be used as
cally and remotely in tion. Cloud storage and
a separate, remote 1 Free for the first year. doesn’t support
TB hard drive with 2 other types of
TB space using as Cloud services.
P2P sync [5].
Web browser based
Can only be ap-
Maelstrom
on the Chromium
plied for static web
Project
Project that allows No limits to file size and
pages without
access to static web transfer speeds.
server part (data-
pages using torrent
base, cgi, etc.).
protocol [6].
Components are secure No free subscrip-
Secure Cloud storage, against cryptanalysis (AES- tion. Can only be
Wuala
a haven in the Cloud 256 for encryption, RSA used as Cloud
to store customers’ 2048, SHA-256). storage and doesn’t
files [7]. System has redundant stor- support other types
age in different locations. of Cloud services.
Robust reporting. Simple
access to management con-
trols. Build-in auditing tools. Can only be used
Sharing large files
Does not distribute copies of as Cloud storage
Sherly
(>20Gb) with secure
users’ data but grants access and does not sup-
access control [8].
to it instead. Can be used in port other types of
both ways with either hard- Cloud services.
ware (Sherlybox) or soft-
ware.
Can only be used
Symform
Customers get 1GB A cross-platform applica- as Cloud storage
free for every 2GB tion. Free and paid subscrip- and does not sup-
contributed [9]. tions. port other types of
Cloud services.
Uses the idle time on Software is for
users’ computer volunteers within
BOINC
(Windows, Mac, the academic soci-
Free.
Linux, or Android) to ety. Does not pro-
perform scientific vide profits to
computing [10]. users.
449
As seen by the table above, almost all of the presented solutions provide users with
only one type of Cloud services – storage as a service, meaning they are unsuitable
for deploying applications and service delivery. Moreover, the expenses issue remains
unsolved.
The aim of this paper is to present the concept of a decentralized cloud architecture
based on P2P technology, estimate its availability and to highlight the changes it may
bring to business models within the sector. The paper is structured in the following
way: section 2 presents the current status of the technology and benefits of Cloud
usage. Section 3 describes the proposed solution. In section 4, the service model of
the distributed cloud is presented. Sections 5 and 6 examine the response time to a
request and the service availability respectively, while section 7 contemplates the
business model that may be formed around the proposed idea. Finally, section 8 pro-
vides a case study for the implementation of the solution while the conclusion is pre-
sented in section 9.
3 Description of the proposed solution
When a company or individual wants to create a website about their activities or
themselves, they usually have two options to select from, in order to successfully
complete the task.
1. Hire professionals who will handle all the necessary steps, from ensuring a
domain name to publishing the website. This solution is time efficient for the custom-
er, as they do not allocate internal resources to such tasks and receive a ready-to-use
product.
2. Use internal skills and set up the website on their own. This implies that
members of the team have the skill and experience to create the website. The team has
to allocate responsibilities, select and ensure a domain name, find and pay for a relia-
ble host, use a template or create their own (based on their level of skills), insert and
organize all content and then manage it.
Both solutions require a significant amount of money and, if the second option is
selected, time and skills while at the same time, they completely depend upon the
server and the data center that hosts them. In addition, there are fixed costs that need
to be paid on an annual basis for maintaining it. Businesses may end up paying more
than they actually use, limiting collaboration within the business teams due to teams
operating in silos, easily maxing out their budget and facing scalability problems,
which is one the biggest issues for companies when they plan for growth.
Cloud computing has been introduced as a new approach to satisfy customers’
needs and is expected to continue its impressive growth. Cloud technologies facilitate
data storage, data exchange and organization amongst businesses and individuals,
provide flexibility, vastly reduce infrastructure costs and allow the workforce to better
concentrate on their work, leading to increased productivity and efficiency.
However, the relationship between Cloud providers and companies/individuals is
no different to any other model of service: supplier – buyer. This one-way model
450
allows customers to store, manage and share data privately or publicly, using the
Cloud service that the supplier provides.
The business model Cloud computing is founded on is a very intriguing and value
centered model as it enables users to pay per use instead of paying on a time-set basis,
regardless of the use they make. Distributed Cloud technology introduces a new type
of Cloud services based on peer-to-peer technology that aims to facilitate and enhance
content creation and resource sharing. The idea of distributed Cloud computing is to
combine the Grid and Cloud concepts. For a distributed Cloud, users’ workstations
provide their own computing recourses (storage and computing power) to Cloud par-
ticipants. The network architecture is based on the principle of equal interaction be-
tween nodes. The number of users who may share the resource increases as a function
of the resource's popularity. This means that the more popular a resource is, the more
the users that can access it and share it. Apart from the above advantages, the unique
point of differentiation lies within scalability. Peer-to-peer technology enables users
to scale their content for free, regardless of the scalability level.
As a result, both, small and big companies can use the same technological basis to
scale their content and grow to new levels.
4 Distributed P2P Based Cloud Service Model
The focus of the study is to improve the process of allocating resources between
user nodes in a Cloud with a distributed architecture [2] and to reduce the response
time for such a Cloud. Fig. 1 illustrates an implementation of the proposed approach.
Access to
Resource Using
Received Address
Resource owner Nodes that are non-participants
of the Distributed Cloud
Participants’ Nodes in the Requesting Responding with
Distributed Cloud with Full Resource’s Address Resource’s Address
Resource
Resource Publication
Peer-to-Peer Peer-to-Peer
Protocols Protocols
DNS-Server
Participant’s Node in the
Distributed Cloud
Modified Resource Records
...
...
Peer-to-Peer
Protocols
Participant’s Node in the
Distributed Cloud
Fig. 1. Service model of the distributed Cloud
451
The solution can be found in organizing the decentralized resources between user
nodes in a Cloud by using peer-to-peer protocols. Each node acts in 3 ways: as a cli-
ent when making a request to the resource, as a server when responding to requests
providing the resources and as a resource owner who has permission for full access.
The initial stage entails the process of publishing the resource by its owner. It consists
of creating an association between the domain name and the resource by adding the
network address of the owner and the unique resource identifiers to DNS-record.
The domain name is used as a unique identifier while the resource allocation pro-
cess is coordinated through the DNS-server by modifying the resource records. After
the participant’s node processes the request of a resource, it addresses it to the DNS-
server and receives the address of the resource owner. The next stage is the resource
replication process, which is implemented by a cache of request, and the response
data on the storage of the user’s workstation node makes it possible to share the result
of the cache with other Cloud nodes. As a result, the node that responds to a request
acts as a server and its address is added to one of the resource records of the DNS-
server. It enables the node participant of the distributed Cloud to access the resource
from several addresses contained in the DNS records, due to the fact that the request-
ed resource is replicated, thus increasing the availability of the service. The more
popular the resource, the more nodes can share it.
However, server functionality requires from the participant node to share the hard-
ware resources of its workstation, such as storage space and processing power. The
participants’ nodes that interact with each other are equal and the implementation of
the distributed Cloud on the users’ side is achieved through the installation of a soft-
ware on the workstations of each participant node. Furthermore, it is possible for par-
ticipants’ nodes that are non-members to access the resources through a regular re-
quest to DNS-server and to get the network addresses of the owner’s station or the
participants’ nodes with the full resource. After receiving their addresses, they can
interact with each other. However, it is important to note that for such users, the
bandwidth is limited by the number of users that use the standard interaction mecha-
nism.
5 Response time to a request
The response time to a remote Cloud server depends on several factors, such as
customers’ geographical location in relation to the server, the available bandwidth of
communication channels and network interfaces, the number of concurrent user con-
nections to the server, the rate of requests, the hardware configuration of the server
etc. [11].
The average response time (receiving the service) for the end-user in a Cloud cli-
ent-server architecture in general form can be expressed by the following formula:
trrt_c-s = tbase_c-s + tresponse_serv + tresponse_BD, (1)
where trrt_c-s – the average time to access the resource,
tbase_c-s – the basic transmission delay on the communication channels,
452
tresponse_serv – the server response time,
tresponse_BD – the data base response time.
Consequently, the basic delay of the network transmission response is determined
by the ratio of the data transmitted to the bandwidth:
tbase_c-s = V/C, (2)
where V – the data response size,
C – the available bandwidth.
The available user goodput is limited by the following: - the network adapter, - ac-
tual Internet access speed determined by the ISP, - the server bandwidth, - communi-
cation channels [12]. Thus, all users that are concurrently connected to the server
evenly share the bandwidth. It means that the available goodput of the connection
between the client and the server is determined by the goodput of the "bottle neck" of
the route between the client and the server [13].
Therefore, to determine the value of the available goodput, the following expres-
sion can be used:
C = min (G, Gserv, Glink), (3)
where G – the available user goodput,
Gserv – the available server goodput,
Glink – the available link goodput.
In cases where nodes of the distributed Cloud interact with each other, the average
response time is defined by the sum of the basic time delay of the network component
and the delay that is related to the process of finding and selecting the nodes that pro-
vide part of the resource, combining all the parts of the resource together and other
time delays.
trrt_p2p = tbase_p2p +tinteraction, (4)
where trrt_p2p – average time to access the resource,
tbase_p2p – basic transmission delay of the communication channels,
tinteraction – interaction delay between nodes that provides resource or its part.
The basic transmission delay on communication channels, as previously men-
tioned, is determined by the bandwidth of the "bottle neck" of the network. The trans-
fer of several parts of the resource may occur concurrently from multiple nodes with
sufficient bandwidth. The overall delay network component will be determined by the
slowest transmission time:
tbase_p2p = max (tb_p2p_1, tb_p2p_2, …, tb_p2p_N), (5)
where tb_p2p_i – the basic delay of the transmission communication channel from
node i,
N – the number of nodes, from where receiving the resources occur concurrently.
Given the constraints of the available bandwidth, the user network adapter and the
internet speed connection:
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Vi N
, Gi G ;
min G , Gi , G i 1
tb _ p 2 p _ i
link _ i
(6)
V , Gi G.
N
G
i 1
where G – the available user goodput,
Gi – the available goodput of i node,
Glink_i – the available link to the i node goodput,
Vi – the size of the resource V, provided by node i.
For a comparative evaluation of the average response time to a request for central-
ized client-server and distributed Cloud architectures, initial data (Table 2) is collect-
ed based on the analysis of the research [11-14].
Table 2. Initial data
Available user goodput, G 10 Mb/s
Available server goodput, Gserv 10 Gb/s
Available link goodput, Glink 8 Mb/s
Available goodput of i node, Gi 2 Mb/s
Available link to the i node goodput, Glink_i 5 Mb/s
The data response size, V 100 kB
Fig. 2 depicts the results of an estimation of the response time to a request for a
centralized client-server t_rrt_c-s and a distributed t_rrt_p2p Cloud architecture for
different numbers of concurrent users.
Fig. 2. Results of the response time estimation
Analyzing the graphical representation of the two types of architectures’ behavior
with the number of concurrent users makes it possible to conclude that the selected set
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of input data can achieve a significant reduction of response time in the case of a dis-
tributed Cloud architecture with 15 or more concurrent users that all interact with
each other.
6 Service Availability
As previously mentioned, the main advantage of a distributed cloud architecture is
the high degree of resource replication. The copies of the resource are distributed
among the nodes that had previously requested it. Thus, the number, states and hard-
ware properties of the nodes will determine the Service Availability. There are differ-
ent methods for the evaluation of Service Availability [15]. Within the scope of this
study, the evaluation of Service Availability deployed on two types of cloud architec-
tures is considered: centralized and distributed. Furthermore, Service Availability
evaluation does not take into account the hardware, software and network failures. It
is assumed that service is available when there are no performance-related failures
that usually occur when incoming requests are not served due to limited capacity of
the server. If the service is implemented based on the standard cloud server, then the
probability that an arriving request is lost due to buffer overflow is described by the
formula [15]:
b 1 , 1;
1
b 1
Pb , (7)
1 , 1.
b 1
where – the server load,
b – the server input buffer size.
The server’s behavior can be modeled by a M/M/1/b queue. Then, when the steady
state probability of the up state corresponds to the system’s steady-state availability
and when it is equal to 1, then the availability of the service is:
A(WS) = (1 - Pb). (8)
In the case of applying the distributed approach, the service is successfully provid-
ed as long as at least one of the replication nodes is available. The model of the sys-
tem’s behavior is described as M/M/c/b queue, where c - the number of available
nodes that function as a replication, b – the node input buffer size. The probability of
requests being lost due to buffer overflow is given by [15]:
455
1
n bn c 1 n j b
nb
bc j c , bn c;
c c ! j 0 j ! j c c c !
Lb ( c ) 1
(9)
n bn bn n j
, bn c.
bn ! j 0 j !
where c – the number of replication nodes,
n – the node load,
bn – the node input buffer size.
Similarly (2), the availability of the service is:
A(NS) = (1 – Lb(c)). (10)
The initial data that is used for the evaluation of Service Availability is taken from
[14]. The input data and evaluation results are summarized in tabl. 3:
Table 3. Input data and estimation results
b c n bn A(WS) A(NS)
1 3000 100 1 7 0.99966 0.999927
As seen from the table, for the given set of input parameters, Service Availability is
implemented through passive replication based on the above properties of the distrib-
uted cloud. Service Availability increases significantly with the number of replication
nodes is increased and is, therefore, dependent on the popularity of the resource.
However, in cases where the service is insufficiently popular and has a low degree of
replication nodes, it would be more appropriate for the implementation to be based on
a centralized cloud architecture, where the replication of existing nodes can reduce the
load on the server. In order to implement an autonomous and stable operation of the
service-based distributed cloud infrastructure without a server, it is important to de-
termine the number of nodes’ replication as sufficient enough. This is a crucial area
for further research. Furthermore, it is necessary to consider a new business model for
such an approach.
7 Moulding a new business model
Customers of distributed Cloud vary from individuals who plan to make a website
for personal reasons, to freelancers or professionals who need a reliable service at a
smart price, all the way to small and large corporations who seek to be innovative but
without compromising their financial resources.
The use of websites is global but the needs are very different, depending on the
quality, quantity, target group and nature of the information of it. Studying the market
and creating a list of questions to guide the team throughout the process of identifying
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each customer group, the following segments have been determined and are presented
in table below.
Table 4. Customer segments and needs
Segment Needs
- Interested in a small number of websites
Private individuals, blogs, - Personal use mainly
small societies - Not significantly big amounts of data
- Seek low prices and easy-to-use solutions
- Minimize IT costs
Professionals, freelancers, - Flexibility & reliability
businesses - Scalability “Value for money”
- Security
- Low costs to create their web identity
- Accessibility
Startup companies and spe-
cial organizations - Scalability
- Use of innovative tools
- Promotional tools
Emerging markets and technologies consist of a number of risks that should be
taken into consideration before venturing. Distributed Cloud computing, slightly lag-
ging Cloud computing, is at the beginning of its Life Cycle, where the early majority
has already started adopting the technology for a number of daily applications. For a
startup company, this point is a good one to enter the market, provided it can offer a
unique differentiation and a well perceived value to its customers.
Various technologies have not only introduced new benefits and solutions to exist-
ing and new needs, but have also encouraged business models and strategies to
change accordingly, in order to accommodate new trends and expectations. Cloud
computing consists one of the most revolutionary technologies, mainly due to the fact
that it shapes a different future. Through a shift in business conduct, it further em-
powers existing and new parties allowing more versatility, flexibility and innovation
to grow.
However, technology does not create value on its own. It is the design and applica-
tion of a sustainable and evolving business model that enables technology to create
value for its users. A successful and well-developed business plan may result in cost
reduction, strategic flexibility or even reduction in risk, amongst other benefits.
Existing business models have a distinct separation in roles. As depicted in
Ostewalder’s business model canvas, the company works with key partners and sup-
pliers in order to create value for its customers and maintain a good and profitable
relationship that will ensure a stable and increasing revenue stream. So far, usual
business models may be characterized as “non-interactive” models, as the end-target
(the customer) does not participate. Distributed Cloud enables business models to
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change and include their customers in the value creation process. Fig. 3 depicts the
distinct roles and interactions between participating sides within distributed Cloud, as
structured in the business model canvas.
Production Side (PS) Consumption Side (CS)
Key Partners Key Activities Value Customer Customer
Proposition Relations Segments
Value Creation
Key Resources Channels
The customers become an The customers enjoy the benefits
invaluable part of the resources of the product and affect the
that enable the company to provide company’s collaboration with the
the value and the product suppliers by driving demand
Cost Structure Revenue Structure
Customers – receivers become suppliers – sources at the same time by
sharing resources through P2P technology, as delivered by the company
Fig. 3. Business model canvas
The Production Side (PS) refers to the cluster of parties that work together to create
and deliver the value to the customers. Based on the customers’ needs and demand,
the PS organizes itself to ensure cost reduction, trusted relationships and quality part-
nerships that will lead to the product. The Consumption Side (CS) consists of the
market cluster – the customers who are using the product and enjoy the benefits and
the value it creates. Their needs and their demand is the major factor based on which
the PS makes alterations and adjustments. For this reason, market and business intel-
ligence is extremely critical, as the data provides companies with sufficient intel to
allow trends predictions and needs insights. The capabilities of distributed Cloud
technology set new foundations for business models to evolve and grow in order to
better facilitate all interested parties. Distributed Cloud technology is a technology
that interacts with users, depends on user popularity and constantly moves to adapt to
its users. By natural consequence, business models that correspond to P2P technology
need to interact with the user and adapt to changes in demand.
Distributed Cloud approach sets new roles and multiple sides to the business model
canvas. Companies do not simply work with suppliers to create a product and cus-
tomers and users of the technology do not simply purchase or enjoy the value of the
product. Instead, the company becomes the technology facilitator and the customers
become the suppliers as well. As a result, the business model that emerges is a model
that is “alive” and “evolving” with change and a series of “participatory business
models” is introduced, where customers obtain a double identity – that of the con-
sumer and that of the source-supplier.
458
It is essential to notice that the Production Side of the business model canvas does
not have any interaction with the Consumption Side, other than any alterations that
result from business intelligence.
The double role of the customers is the key to this new business model ecosystem,
significantly affecting the interaction between customer-user and customer-supplier,
through the technology.
It is important to note that in such business models, monitoring intellectual proper-
ty and rights is challenging and needs to be dealt with utmost care and responsibility
in order to ensure protection of all participants.
In the field of distributed Cloud for website applications, the use of such a dynamic
business model is essential, as it is the core of value creation and value delivery to
customers. Users purchase or subscribe to the service to enjoy the benefits of the dis-
tributed Cloud solution as provided by the company, in the form of a software, thus
becoming customers-consumers. In return, other customers-consumers that request
access to the content of the website through the same software service, retrieve it from
fellow customers-consumers who, having a virtual footprint of the information on
their computers, they now become sources-suppliers for the new customers-
consumers.
As a result, the group of people who share a common interest in the content they
seek, participate in a “shared cluster” of information and act as both, sources and
consumers of the content. Apart from the development of new business models, com-
panies may find it beneficial to use distributed Cloud as it offers new options in terms
of budget and scalability. Budget and scalability consist of the two main issues that
companies face. Increased demand may indeed increase revenue stream. However, in
order to meet this demand, companies need to invest in more resources. Even with
current cloud services, suppliers’ costs are high and not easy to handle.
Currently, companies increase their IT infrastructure and spend significant amounts
on adding new serves in order to accommodate their customers’ needs and the com-
pany’s workload. Without this expansion, the company cannot achieve scalability.
Churn is also important, as users may activate and deactivate their nodes, altering
the dynamic of the P2P system. However, the bigger the network of customers-
sources, the more manageable is the churn, as the system will dynamically adapt to
changes and maintain its efficiency.
Overall, distributed Cloud technology has a number of potential applications that
can benefit different companies and users. However, the technology itself produces
value when a major condition is met: the design of an appropriate, innovative and
predictive business model that ensures value is captured and transferred to users, de-
livers results and revenue for the company and adapts to the dynamic nature of the
system.
It is necessary to highlight that there is no correct business model. Different models
may work as long as they incorporate the P2P values and focus on the double role of
the customers. The term “participatory business models” is suggested to describe the
new reality that companies and entrepreneurs are expected to face. Monetization
through such a business model may be significantly more challenging compared to
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more popular business models but this may set the foundations for a new way of con-
ducting business and commercializing technologies, ideas and goods.
8 Case study
In order to implement distributed Cloud solution, a number of expenses categories
has been created:
- Operational expenses refer to the expenses that the company needs to cover
in order to operate and run smoothly. The expenses required for the running and
operation are originally limited to the renting of a small server of 50-70 accounts
and to the costs of premises and power (office rent, electricity etc.). The initial
premises costs are small due to the fact that a big part of the work completed will
be through computers and virtual desktops.
- Labour expenses refer to the amount of money the company needs to pay for
the services of its human resources. In this category, all expenses that refer to sala-
ries of regular employees or outsourced partners are included.
- Variable expenses refer to the expenses of other parameters such as market-
ing campaigns, royalties to the university, depreciation of the investment within
maximum 2 years etc. Variable expenses include marketing budget, university roy-
alties of 3% for the first year and 5% onwards and depreciation of the investment
cost within 2 years.
The proposed solution has a number of implementation stages in order to be fully
developed and be ready to use. Strategic planning before starting the development
will ensure time efficiency, productive allocation of tasks and smart use of resources.
More specifically, the development stages of the project are summarized in the table
below:
Table 5. Suggested implementation stages
Stage Description
Stage 1. Implementation of the Within the first stage, a number of steps are
PaaS (platform as a service) service included: implementation of the static website
model, based on the distribution of functionality, distribution of the website tasks
tasks, services, websites and stor- and storage between the users’ hardware, and
age between the users. finally, implementation of the general service.
Stage 2. Implementation of the Implementation of the special software lay-
IaaS (infrastructure as a service) er, which is responsible for distributing the
service model. system requests of the guest operating system
between the participants' devices, allowing the
running of a virtual machine.
Stage 3. Implementation of the The last stage assumes improvement of the
SaaS (software as a service) service software based on the specifically configured
model. virtual machine that was mentioned above.
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The distributed Cloud solution can begin its commercialization from within the ac-
ademic society. The educational sector is a potential big customer that could highly
benefit from the proposed approach, and the use of academic and EU connections can
greatly help spread the technology. The aim is to begin locally by promoting the pro-
posed solution through academic events and contacts with the respective IT admin-
istration departments in order to expand to more universities locally and international-
ly.
9 Conclusion
Cloud Computing has arrived at a very good timing to introduce a new reality
based on current needs and future aspirations. Granted, as a new technology, it re-
quires a number of years to set and to become popular, constantly raising awareness
amongst people and introducing them to its benefits. The above trends demonstrate
the high prospects of different types of Cloud Computing that is expected to grow in
the following years in many markets and to extend to a variety of applications. Com-
petition is an expected to be high and technology progress will demand constant up-
date of versions and improvement of products and solutions, in order to successfully
supply an ever growing market and a rapidly changing business and social environ-
ment.
The Distributed P2P based Cloud is a new solution that aspires to change the way
companies and organizations work with regards to creating, publishing and sharing
content. The purpose of the Distributed Cloud approach is to provide P2P Cloud ser-
vices to individuals, companies and organizations with the view to facilitating cost-
effective scalability, flexibility and efficiency and enhancing the experience of creat-
ing, organizing, publishing and sharing content. Its competitive advantage lies within
the concept of reliability and scalability at significantly lower costs, allowing custom-
ers to differently allocate their financial resources or to grow even on a budget.
In addition, well-structured, targeted and smart marketing strategies are necessary
to be developed in order to ensure strategic growth of the business sector and brand
awareness amongst existing and prospective customers. The proposed solution com-
bines Cloud computing and Grid technology with peer-to-peer networks through a
software that allows users to participate in a single, decentralized Cloud system and
use their workstations to allocate network resources. As a result, it partially or com-
pletely eliminates the need to use powerful, high-performance servers in virtual data
centers and, ultimately, reduces energy consumption and negative impacts on the
environment.
By applying Distributed Cloud technology, the dynamics of the system changes so
that users become sources and consumers at the same time. This is the very core value
of this technology as it enhances cost effective scalability and changes the way busi-
ness is conducted, through a dynamic, alive and self-adjusting business model.
The interchanging roles of customers and suppliers within such a participatory
business model encourages companies and entrepreneurs to focus more strongly on
the value that can be obtained through the P2P technology within the distributed
461
cloud, rather than the marketing of the product itself. Consumers are becoming more
and more informed about how technology works and what benefits each provider
gives them. This means, that shifting towards value creation and focus through cus-
tomer participation may actually help companies differentiate themselves from the
mass, attract more customers and, eventually, contribute to a new corporative culture.
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462
Automated Development of Markovian Chains for Fault-
Tolerant Computer-Based Systems with Version-
Structure Redundancy
BogdanVolochiy1, Oleksandr Mulyak2, Vyacheslav Kharchenko3
1
National University Lviv Polytechnic, Lviv, Ukraine
bvolochiy@ukr.net
2
RPC “PromTechnoServis Ukraine”, Kyiv, Ukraine
mulyak@prom-technoservice.com
3
National Aerospace University “KhAI”, Kharkiv, Ukraine
v.kharchenko@khai.edu
Abstract. Reliability design of fault-tolerant computer-based systems with ver-
sion-structural redundancy and multiply software updates involves solving num-
ber of issues. This paper outlines an availability model of the computer-based
systems which shows the algorithm for reliability behavior. For various configu-
rations of the computer-based systems, the use of the proposed model and prob-
lem-oriented software, ASNA represents the ability to automate constructed the
Markovian chains. This model includes a number of settings: failure rate of the
software; numbers of software updates; duration of software updates; the struc-
ture of the system’s hardware and reliability indicators. The proposed model for
the automated development of Markovian chains is subject to the adaptation of
the structure of the hardware of computer-based systems and/or the algorithms of
reliability behavior. This allows us to obtain a new model and the feasibility to
automate development of the Markovian chains.
Keywords. Markovian Chains, Automated Reliability Design, Fault-Tolerance
System, Version-Structural Redundancy, Common Sliding Standby, Hot
Standby, Cold Standby
Key Terms. Mathematical Modeling, Method, Software Systems.
1 Introduction
1.1 Motivation
Nowadays the developments of fault-tolerant computer-based systems (FTCSs) are
a part of weaponry components, space, aviation, energy and other critical systems. One
463
2
of the main tasks is to provide requirements of reliability, availability and functional
safety. Thus the two types of possible risks relate to the assessment of risk, and to en-
suring their safety and security.
Reliability (dependability) related design (RRD) [1-6] is a main part of development
of complex fault-tolerant systems based on computers, software (SW) and hardware
(HW) components. The goal of RRD is to develop the structure of FTCS tolerating HW
physical failure and SW designs faults and assure required values of reliability, availa-
bility and other dependability attributes. To ensure fault-tolerance software, two or
more versions of software (developed by different developers, using other languages
and technologies, etc) are used [7]. Therefore use of structural redundancy for FTCS
with multiple versions of software is mandatory. When commissioning software some
bugs (design faults) remain in its code [8], this leads to the shut-down of the FTCS.
After detection the bugs, a software update is carried out. These factors have influence
on the availability of the FTCS and should be taken into account in the availability
indexes. During the operation of FTCS it is also possible that the HW will fail leading
to failure of the software. To recover the software operability, an automatic restart pro-
cedure, which is time consuming, is performed. The efficiency of fault-tolerant hard-
ware of FTCS is provided by maintenance and repair.
Insufficient level of adequacy of the availability models of FTCS leads either to ad-
ditional costs (while underestimating of the indexes), or to the risk of total failure (when
inflating their values), namely accidents, material damage and even loss of life. Relia-
bility and safety are assured by using (selection and development) fault-tolerant struc-
tures at RRD of the FTCS, and identifying and implementing strategies for mainte-
nance. Adoption of wrong decisions at this stage leads to similar risks.
1.2 Related Works Analysis
Research papers, which focus on RRD, consider models of the FTCS. Most models
are primarily developed to identify the impact of one the above-listed factors on relia-
bility indexes. The rest of the factors are overlooked. Papers [4, 5] describe the relia-
bility model of FTCS which illustrates separate HW and SW failures. Paper [6] offer
reliability model of a fault-tolerant system, in which HW and SW failures are differen-
tiated and after corrections in the program code the software failure rate is accounted
for. Paper [8] describes the reliability model of the FTCS, which accounts for the soft-
ware updates. In paper [10] the author outlines the relevance of the estimation of the
reliability indexes of FTCS considering the failure of SW and recommends a method
for their determination. Such reliability models of the FTCS produce analysis of its
conditions under the failure of SW. This research suggests that MTTFsystem=MTTFsoft-
ware. Thus, it is possible to conclude that the author considers the HW of the FTCS as
absolutely reliable. Such condition reduces the credibility of the result, especially when
the reliability of the HW is commensurable to the reliability of the SW. Paper [11]
presents the assessment of reliability parameters of FTCS through modelling behavior
using Markovian chains, which account for multiple software updates. Nevertheless
there was no evidence of the quantitative assessments of the reliability measures of
presented FTCS.
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3
In paper [12], the authors propose a model of FTCS using Macro-Markovian chains,
where the software failure rate, duration of software verification, failure rate and repair
rate of HW are accounted for. The presented method of Macro-Markovian chains mod-
elling [12, 13] is based on logical analysis and cannot be used for profound configura-
tions of FTCS due to their complexity and high probability of the occurrence of mis-
takes. Also there is a discussion around the definition of requirements for operational
verification of software of the space system, together with the research model of the
object for availability evaluation and scenarios preference. It is noted that over the last
ten years out of 27% of space devices failures, which were fatal or such that restricted
their use, 6% were associated with HW failure and 21% with SW failure.
Software updates are necessary due to the fact that at the point of SW commissioning
they may contain a number of undetected faults, which can lead to critical failures of
the FTCS. Presence of HW faults relates to the complexity of the system, and failure to
conduct overall testing, as such testing is time consuming and needs substation financial
support. To predict the number of SW faults at the time of its commissioning various
models can be used, one for example is Jelinski-Moranda [14].
A goal of the paper is to suggest a technique to develop a Markovian chain for com-
plex FTCS with different redundancy types (first of all, structure and version) using the
proposed formal procedure and tool. The main idea is to decrease risks of errors during
development of MC for systems with very large (tens and hundreds) number of states.
We propose a special notation which allows supporting development chain step by step
and designing final MC using software tools. The paper is structured in the following
way. The aim of this research is calculating the availability function of FTCS with ver-
sion-structural redundancy and double software updates.
To achieve this goal we propose a newly designed reliability model of FTCS. As an
example a special computer-based system of space radio-technical complex is re-
searched (Fig.1). The following factors are accounted for in this model: overall reserve
of FTCS and joint sliding reserve of modules of main and diverse FTCS; the existence
of two software versions; SW double update; and automatic software reboot, if its fail-
ure was caused by the HW physicals fault.
Structure of the paper is the following. Researched FTCS is described in the sec-
ond section. An approach to developing mathematical model based on Markovian chain
and detailed procedure for the FTCS are suggested in the third and fourth sections cor-
respondingly. Simulation results for researched Markov’s model are analyzed in the
section 5. Last section concludes the paper and presents some directions of future re-
searches and developments.
2 Researched fault-tolerant computer based system with
structure-version redundancy
The researched FTCS with structure-version redundancy is shown on figure 1. To
ensure the minimal FTCS downtime, overall hot standby with other version of software
is used.
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4
Fig. 1. Fault-tolerant Computer Based System (1 – main system, 2 – hot standby, 3 – cold
standby, 4 – diverse system, DCS – Diagnostics Control System).
The FTCS consists of: a main system comprising modules; diverse system consist
of k - modules; for two systems, the common sliding standby of modules is envisaged,
the first module in hot standby and other in cold standby; a diagnostics control system
determines the state of HW and SW, and manages the redundancy; and a switch is
connected the modules to the main and diverse systems.
3 An approach to developing an availability model for FTCS
with software update and restarting
An approach to the development of availability model for FTCS with double soft-
ware updates and automatically software restart in the form of Markovian chains is
presented in figure 2. During the operation of computer based system there are the fol-
lowing states: S1, S4 and S7 – system operable states; S2, S5, S9, S10 –inoperable
states, in which SW updates, are conducted; S3, S6, S8 – inoperable states in which
software restart after physical failure is automatically conducted; S11, S12, S13 – in-
operable states in which HW is repaired after physical failure.
Fig. 2.Markovian chain which show the reliability behavior of computer-based system with dou-
ble software updates and automatic restart
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5
The system functioning after state S1 can unfold in four possible ways: the system
moves to state S9 with rate sw11 after failure of first software version; the system move
to state S3 with rate swerror, after temporary failure of SW; the system move to state S2
with rate up1=1/Tup1 (Tup1 – duration of bugs correction in software) after finished the
first version software operation (ready to use second version of software); the system
move to state S11 with rate hw, after physical failure.
The system functioning after state S4 can unfold in four possible ways: the system
move to state S10 with rate sw12 after failure of second SW version; the system move
to state S6 with rate swerror, after temporary failure of SW; the system move to state S5
with rate up2=1/Tup2 (Tup2 – duration of bugs correction in software) after finished the
second version SW operation (ready to use the third version of SW); the system move
to state S12 with rate hw, after physical failure. The system functioning after state S7
can unfold in two possible ways: the system move to state S6 with rate swerror, after
temporary failure of SW; the system move to state S13 with rate hw, after physical
failure. System moves from state S3and S6 to states S1 and S4 with a rate of rest=1/Trest
(Trest – duration of SW restart).
When the system is in state S2 and S5, it replaced the version of SW with rate
repl=1/Trepl (Trepl – duration of software replacement). The system moves from states
S9 and S10 to states S2 and S5 with rate up1=1/Tup1 (Tup1 – duration of bugs correction
in software) and up2=1/Tup2 (Tup2 – duration of bugs correction in software).
After commissioning of the computer based system starts debugging the software
and develops first update that takes time Tup1. Second update takes timeTup2 and in-
volves finding all bugs in SW. Therefore after first SW update, the numbers of bugs
decreases, and debugging software is more complex, and the development of second
update takes more time Tup2>Tup1.
The described approach to the development of availability model for FTCS with
software update and restart is used to build availability model of FTCS showed in figure
1.
4 Markov’s model for FTCS with software update and
restarting
The method of development Markovian chain of the FTCS is described in the mon-
ograph [9]. It involves a formalized representation of the object of study as a “struc-
tural-automated model”. To develop this availability model of the FTCS one needs to
perform the following tasks: develop a verbal description of the research object (fig.
1); define the basic events; define the component vector of states, which can be de-
scribed as a state of random time; define the parameters for the object of research, which
should be in the model; and shape the tree of the modification of the rules and compo-
nent of the vector of states.
4.1 The procedures to describe behavior of the FTCS
The FTTS behavior is described by the following procedures.
467
6
Procedure 1. Detection of failure of the FTCS (hardware failure, software failure,
temporary failure). Failure can occur in the main and diverse system.
Procedure 2. Detection of failure in the main or diverse subsystems of the FTCS.
Procedure 3. Connection of the module from hot standby to faulty subsystem.
Procedure 4. Connection of the module from hot standby to cold standby.
Procedure 5. Loading the software on the module with connections from cold to hot
standby.
Procedure 6. Software restart.
Procedure 7. Development the software updates.
Procedure 8. Repair (replacement) of the HW of the FTCS.
4.2 A set of the events for the FTCS
According to described procedures which determine the behavior of FTCS, a list of
events is composed. Events are presented in pairs corresponding to the start and the end
of time intervals to perform each procedure. From this list of events for “structural-
automated model” basic events are selected [9].
As a result of analysis, twelve basic events in particular were determined: Event 1 –
“Hardware failure of main system module”; Event 2 – “Software failure of the main
system module”; Event 3 – “Software fault of the main system module”; Event 4 –
“Hardware failure of the diverse system module”; Event 5 – “Software failure of the
diverse system module”; Event 6 – “Software fault of the diverse system module”;
Event 7 – “Module failure in hot standby”; Event 8 – “Termination of the procedure
of the hot standby module connection to non-operational system”; Event 9 – “Termi-
nation of the procedure of the cold standby module transfer to non-operational system”;
Event 10 – “Termination of the procedure of software reloading on the module with
failure feature in its software work”; Event 11 – “Termination of the procedure of SW
version renovation”; Event 12 – “Termination of the procedure of the HW repair”.
4.3 Components of vector states for the FTCS
Components of the vector state that can also be described as a state of random
time. To describe the state of the system, eleven components are used: V1
– displays the current number of modules in the main system (the initial value of
components V1 equal to n); V2 – displays the current number of modules in the
diverse system (the initial value of components V2 equal to k); V3 – displays the
current number of modules in hot standby (the initial value of components V3 equal
to mh); V4 – displays the current number of modules in cold standby (the initial value
of components V4 equal to mc); V5 – displays which software version is operated by
the main system (V5=0 – first version, V5=1 – second version, V5=2 – third version);
V6 – displays which software version operated by diverse system (V6=0 – first
version, V6=1 – second version, V6=2 – third version); V7 – displays the temporary
SW failure in the main system; V8 – displays the temporary SW failure in the diverse
system; V9 – displays the SW fault in the main system; V10 – displays the SW fault
in the diverse system; V11 – displays the number of non-operational units, due to
HW fault.
468
7
4.4 The parameters of the FTCS Markov’s model
Developing Markov’s model of the FTCS, its composition and separate components
should be set to relevant parameters in particular: n – number of modules that are the
part of the main system; k – number of modules that are the part of the diverse system;
mh –number of the modules in the hot standby; mc – number of the modules in the cold
standby; hw – the failure rate that is in main (diverse) system and in the hot standby;
sw11, sw12 – the failure rate of first and second software versions; swerror – the tempo-
rary failure rate of software; Tup1, Tup2 – duration of the first and second software up-
dates; Trest – duration of software restart on the module; Tswitch – duration of the module
connections of the slight standby; Trep– hardware repair duration.
4.5 Model of the FTCS for the automated development of the Markovian
chain with software update and restart
According to the technology of analytical modeling, the discrete-continuous stochas-
tic systems [9] based on certain events using the component vector state and the param-
eters that describe FTCS, and model of the FTCS for automated development of the
Markovian chains are presented on the table 1.
Table 1. Model “Structural-Automated Model” of the FTCS for the automated development of
the Markovian chains
Formula used
for the inten- Rule of modification compo-
Terms and conditions
sity of the nent for the state vector
events
Event 1. Hardware failure of main system module
V1:=n; V3:=V3-1;
(V1=n) AND (V3>0) AND (V9=0) V1· hw
V11:=V11+1
(V1=n) AND (V3=0) AND (V9=0) V1· hw V1:=V1-1; V11:=V11+1|
Event 2. Software failure of the main system module
(V1=n) AND (V3=0) AND (V9=0) V1· swerror V1:=V1-1; V7:=V7+1
(V1=n) AND (V3>0) AND (V9=0) V1· swerror V1:=n; V3:=V3-1; V7:=V7+1
Event 3. Software fault of the main system module
(V1=n) AND (V5=0) AND (V9=0) V1· sw11 V1:=V1-1; V5:=0; V9:=1
(V1=n) AND (V5=1) AND (V9=0) V1· sw12 V1:=V1-1; V5:=1; V9:=1
Event 4. Hardware failure of the diverse system module
V2:=k; V3:=V3-1;
(V2=k) AND (V3>0) AND (V10=0) V2· hw
V11:=V11+1
(V2=k) AND (V3=0) AND (V10=0) V2· hw V2:=V2-1; V11:=V11+1
Event 5. Software failure of the diverse system module
(V2=k) AND (V3=0) AND (V10=0) V2· swerror V2:=V2-1; V8:=V8+1
(V2=k) AND (V3>0) V2· swerror V2:=k; V3:=V3-1; V8:=V8+1
Event 6. Software fault of the diverse system module
469
8
(V2=k) AND (V6=0) AND (V10=0) V2· sw11 V2:=V2-1; V6:=0; V10:=1
(V2=k) AND (V6=1) AND (V10=0) V2· sw12 V2:=V2-1; V6:=1; V10:=1
Event 7. Module failure that is in the hot standby
(V3>0) AND ((V9=0) OR (V10=0)) V3· hw V3:=V3-1; V11:=V11+1
Event 8. Termination of the procedure of the hot standby module connection to
non-operational system
(V10) AND (V11>0) 1/Tswitch V1:=V1+1; V3:=V3-1
(V20) AND (V11>0) 1/Tswitch V2:=V2+1; V3:=V3-1
Event 9. Termination of the procedure of the cold standby module transfer to non-op-
erational CS
(V30) 1/Tswitch V3:=V3+1; V4:=V4-1
Event 10. Termination of the procedure of software reloading on the module with
failure feature in its software work
(V10) 1/Trest V1:=V1+1; V7:=V7-1
(V20) 1/Trest V2:=V2+1; V8:=V8-1
Event 11. Termination of the procedure of software version renovation
(V1 0 the unit UI is simulated at the inputs ZI J, which takes the
value calculated for the current word, and the word input to the DC input on DI J
clock cycles sooner or later. Generally this word can be any input word of the
considered mode. Therefore, the unit UI should be simulated for each of the input
words on the values of input ZI J which are accepted by it on all words of the
considered mode.
For inertial processes of change of the input data processed in DC, the model of
path AP can be refined taking into account the maximum possible step Δ of changing
the input words or the operands making them. Let Δ ≥ 1. Then the unit UI should be
simulated for each input word with number G on the values of input ZI J, which are
480
accepted in the range of words with numbers G Δ · DI J,, where G > Δ · DI J. For
G ≤ Δ · DI J the initial set value of input DI J are used. In case of Δ < 1, when the value
of the input word is changed no more than once per 1 / Δ clock cycles, the number
range is rounded to the value of G ] Δ · DI J [.
Building a model of the path AP is performed by analyzing the structure of the
pipeline taking into account quantity of the sections preceding the data processing
unit UI on its inputs ZI J. The quantity of these sections determines amount of clock
cycles required for data delivery from the inputs of the DC circuit to the unit UI. Let
HI J is the quantity of sections (clock cycles) preceding the input ZI J, and
HMAX = MAX(HI J). Then, the equality HI J + YI J =HMAX + 1 is carried out for unit UI
in clock cycle HMAX. This determines number of own word
YI J = HMAX + 1 – HI J, (3)
including current word YI for input ZI.
Substituting (3) in (2) determines the values of the distance DI J = | HI – HI J | in the
model of path AP by the structure of the pipeline DC.
3 Simulation of the Circuit of a Pipeline DC
The observability of the circuit point is calculated in the course of pipeline DC
simulation at the input data, which are determined taking into account the model of
path AP.
Simulation of DC is performed according to the following method. Examination of
all input words of the considered mode and examination of all points of the circuit on
the pipeline course will be organized. The value of the examined point is calculated at
a given input word and is complemented by an inverse value. Values of all following
points of the circuit are calculated for two values of the examined point before
reaching a check point or a point where results of calculations coincide. If the results
in a check point are inverted, all the points belonging to the path, refer to the 0-
observable or 1-observable depending on the values accepted by them. If at the
previous input words the point was identified as observed with opposite value, this
point refers to observable and is not considered at the following input words. Point
values with DI J > 0 are calculated on an extended set of input words. The simulation
is carried out taking into account all their values.
It should be noted that incomplete simulation of the DC circuit in case of a
restriction of the input data typical for considered mode leads to an underestimation of
the observability of points. This underestimation admitted for normal and emergency
mode conducts to false detection of PHP and their skipping, respectively.
Considering that controllability of the circuit points is estimated directly by their
values, i.e. it is much simpler than observability, and taking into account that
controllability is the upper bound of observability, the following method of PHP
identification is offered:
Comparison in sizes | RN | and | RE | of ranges RN and RE for the input data of
normal and emergency modes.
481
In case | RN | > | RE | simulation of the DC is running at the input words of
emergency mode for determining the sets EO–0, EO–1, EO–2 and EO–3 of points with
observability of OE: 0, 1, 2 and 3. The points of the set EO–0 are excluded from
consideration as they cannot be PHP. For the other points, the simulation of DC is
running at the input words of normal mode for determining the sets NO–0, NO–1,
NO–2, NO–3 of points with observability of ON: 0, 1, 2, 3 and identification of PHP,
according to Table 1.
In case | RN | ≤ | RE | simulation of the DC is running at the input words of normal
mode for determining the sets NO–0, NO–1, NO–2 and NO–3 of points with observability
of ON: 0, 1, 2 and 3. The points of the set NO–3 are excluded from consideration.
The simulation of the DC is running at the input words of emergency mode to
determine the sets EC–1 and EC–2 of points with controllability of CE: 1 and 2. The
points of the sets NO–1 EC–1 and NO–2 EC–2 are excluded from consideration.
For the other points, simulation of the DC is running at the input words of
emergency mode for determining the sets EO–0, EO–1, EO–2, EO–3 of points with
observability of OE: 0, 1, 2, 3 and identification of PHP, according to Table 1.
4 Identification of Internal PHP in Circuits with the LUT-
Oriented Architecture
Modern I&CS are designed with the use of pipeline DC constructed on FPGA with
the LUT-oriented architecture. The feature of the circuits of such DC consists in a
table specifying logical functions in memory of LUT (Look-Up Table). The result of
function is read out (with use of the multiplexer) from memory of LUT with the
address which code is formed from arguments of function [15].
The bits of the LUT memory are considered as internal points of the DC circuit.
Stuck-at faults of an internal point can be caused by defect of memory bit or defect of
the multiplexer. The internal point of the circuit is controllable if the appropriate bit is
selected at the input data of the considered mode, and is uncontrollable otherwise. The
internal point is observable if the point of the LUT output is observable at a choice of
the appropriate bit of memory.
The set of all controllable internal points of the circuit can be calculated for each
mode by simulation of DC at all input words of this mode including additional words
for points with DI J > 0. All internal points addressed in memory of LUT belong to the
controllable.
Internal PHP of the circuit can be identified according to the following method:
For each LUT two sets NC and EC of internal points which are controllable
respectively in normal and emergency mode are determined. The set of CEN = EC \ NC
of the internal points addressed in emergency mode and not used in the normal one is
calculated. Internal points of a set of CEN are checked for observability in emergency
mode. If they are observable, refer to the set of PHP.
For example, the task of identifying internal PHP in the circuit of DC that
computes the function F(X) = 1 for X mod 3 = 0 and F(X) = 0 for other values of X,
where X = {x5, x4, x3, x2, x1}, X = 0 31. The circuit is evaluated for stuck-at faults for
the given ranges RN and RE of input data.
482
The solution is considered for the three DC functioning in I&CS in different
conditions:
a) RN = 0 23 and RE = 24 31;
b) RN = 0 15 and RE = 16 31;
c) RN = 8 23 and RE = 0 7, 24 31.
A description of the function F and ranges RN and RE are shown in Table 2.
Table 2. Description of the function F(x5, x4, x3, x2, x1) and ranges RN and RE
X for x5 Variables F for x5 Ranges RN and RE
1 0 x4 x3 x2 x1 1 0 a b c
16 0 0 0 0 0 1 0 0 16 0 16 0 16
17 1 0 0 0 1 0 0
18 2 0 0 1 0 0 1
19 3 0 0 1 1 1 0
20 4 0 1 0 0 0 0 RN RE RN
21 5 0 1 0 1 0 1
22 6 0 1 1 0 1 0
23 7 0 1 1 1 0 0 23 7 23
24 8 1 0 0 0 0 1 RN 24 RN RE 8 24
25 9 1 0 0 1 1 0
26 10 1 0 1 0 0 0
27 11 1 0 1 1 0 1 RE RN RE
28 12 1 1 0 0 1 0
29 13 1 1 0 1 0 0
30 14 1 1 1 0 0 1
31 15 1 1 1 1 1 0 15 31 15 31 15 31
The number of input words and the function values are shown in pairs of columns
separately for values x5 = 0 and x5 = 1. The ranges RE of emergency mode selected
dark color.
The circuit of DC designed on FPGA ALTERA Quartus II [16] is shown in Fig. 1.
x5 x4 x3 x2 x1
LUT
L1
1 LUT
F
L2
LUT 3
2
Fig. 1. The circuit of DC
483
The circuit consists of three LUT: LUT 1, LUT 2 and LUT 3, which implement the
functions L1(x3, x5, x1, x4), L2(x3, x5, x1, x4) and F(L2, x2, L1) described by codes
6BBD16, 97E916 and 0AA016, respectively.
Values of the variables x3, x5, x1, x4, arriving at the inputs of the LUT 1 and LUT 2
in emergency mode, and also calculated values of the functions L1, L2, F and FL1, FL2
are shown in Table 3.
Table 3. Description of input variables and functions for LUT 1 and LUT 2
Variables F for x2 FL1 for x2 FL2 for x2 X for x2
№ L1 L2
x3 x5 x1 x4 0 1 0 1 0 1 0 1
0 0 0 0 0 0 0 1 0 0 0 0 0 0 2
2 0 0 1 0 1 0 0 1 0 0 1 0 1 3
4 0 1 0 0 1 0 0 1 0 0 0 0 16 18
5 0 1 0 1 0 0 1 0 0 0 0 1 24 26
6 0 1 1 0 0 1 0 0 1 0 0 0 17 19
7 0 1 1 1 1 0 1 0 0 0 0 0 25 27
8 1 0 0 0 1 0 0 1 0 0 1 0 4 6
10 1 0 1 0 0 1 0 0 1 0 0 0 5 7
12 1 1 0 0 0 1 0 0 1 0 0 0 20 22
13 1 1 0 1 1 0 0 1 0 0 1 0 28 30
14 1 1 1 0 1 1 1 0 0 0 0 1 21 23
15 1 1 1 1 0 1 0 0 1 0 0 0 29 31
The functions FL1 and FL2 take the values of the function F for inverse value
according to L1 and L2 owing to the distorted value of internal point in the LUT
memory. Besides, the first column contains the numbers of sets of the input variables
equal to their decimal equivalent. They are also numbers of internal points disposed in
the LUT memory. The values of X are specified in two last columns for two values of
variable x2 = 0 and x2 = 1. Values of functions FL1, FL2 selected in Table 3 by dark
color are inversed to values of function F that defines the internal points of LUT
corresponding to them as observable.
According to Table 3 internal points which are observable in emergency mode for
the considered ranges of RN and RE compose the following sets:
a) 5, 7, 13, 15 to LUT 1 and 5, 7, 13 to LUT 2;
b) 4 – 7, 12 – 15 to LUT 1 and 4, 5, 7, 13, 14 to LUT 2;
c) 0, 2, 5, 7, 8, 10, 13, 15 to LUT 1 and 0, 2, 5, 7, 8, 13 to LUT 2.
Listed internal points are not used in the normal mode, i.e. are unobservable.
Therefore they belong to the set of PHP. In LUT 3 the same 6 internal points 1, 3 – 7
in all modes are used that excludes them from a set of PHP as CEN = and the output
of LUT 3 is an observable point. The quantity of PHP in DC for the considered three
cases makes respectively 7, 13 and 14 at total of internal points NDCC = 40. The
probability of decrease in fault tolerance of the DC upon transition to emergency
mode calculated by the formula (1) accepts values of 17.5%, 32.5% and 35% for
cases of a, b and c, respectively.
484
5 Conclusions
Two modes of operation characteristic for I&CS generate the problem of hidden
faults which can accumulate in normal mode and reduce fault tolerance of the DC in
the most responsible emergency mode. In single-mode systems such problem isn't
present as a hidden fault is never shown and if a fault was shown, it isn't hidden.
The success in the solution of a task of PHP identification where the problem of
the hidden faults occurs is determined by opportunities of an assessment in
observability of circuit points in each mode of I&CS. The correctness of this
assessment is provided with completeness of input data considered for each mode of
I&CS. The underestimated assessment leads to false detection of PHP or their
skipping. The offered model of the activated path specifies a set of input data for
determination of observability of points in circuits of pipeline DC. The method of
simulation of pipeline DC and method of PHP identification follows from this model.
The design of modern I&CS on FPGA defines an additional task of identifying in-
ternal PHP typical for circuits with LUT-oriented architecture. The offered method of
solving this task analyzes sets of internal points used in normal and emergency mode.
It should be noted that these sets determine the effectiveness of manual regulation
of the input data in the normal mode. This procedure is used in practice for solving
the problem of the hidden faults. Procedure reduces the effectiveness with different
sets and becomes completely meaningless in case of disjoint sets.
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The Control Technology of Integrity and Legitimacy of
LUT-Oriented Information Object Usage by Self-
Recovering Digital Watermark
Kostiantyn Zashcholkin and Olena Ivanova
Odessa National Polytechnic University, 1, Shevchenko Avenue, Odessa, Ukraine
(const-z@te.net.ua, en.ivanova.ua@gmail.com)
Abstract. The paper proposes the technology of control of integrity and
legitimacy of information object usage with the Look Up Table-oriented (LUT-
oriented) architecture. The technology is based on embedding the self-recovery
digital watermark into information objects of such kind. The technology is the
composition of approaches to forming the self-recovery digital watermarks in
the passive multimedia containers, and approaches to embedding the extra
information into LUT-containers. The process of embedding the extra
information occurs with the help of classification of container elements and
their purposeful modification within the set of the formed classes. The
procedure of immediate embedding the data at the level of LUT-container
elementary parts includes the value inversion of current processed LUT unit
and propagation of the inversion around all the inputs of LUT units connected
to the current unit output. The description of practical realization of the
proposed technology is represented.
Keywords: digital watermarks, control of information object integrity, control
of information object usage, information security, cybersecurity, IT systems
safety, steganography, LUT-oriented architecture, FPGA.
Key terms: Information Technology, Data, Object, Approach, Method.
1 Introduction: Topicality of the Problem and Aim of the Paper
The technologies of digital watermark (DWM) usage are one of the most effective
approaches to the comprehensive information security provision [1]. DWMs are
mainly used for:
1. the control of information object integrity;
2. the control of information object usage: information object copyright provision,
digital content authentication, the tracking of digital content move (including the
tasks of source retrieval of information leak).
DWM technologies are based on steganographical technique, with the help of
which the fact of DWM presence in an information object (DWM container) is
487
hidden. At the same time DWM can be read in the container if someone has a stego-
key possessing the set of access rules to DWM elements [2].
The control of information object integrity by DWM is based on embedding some
control data unit allowing to analyze the object integrity in an information object.
Hash sum calculated with the help of the definite hash-function is most frequently
used as such kind of data unit [3]. However such kind of control unit embedding
results in information object change and consequently violates its integrity by itself.
Under these conditions the so-called self-recovering DWMs possessing the ability to
recover the initial object value (a value, which it had before DWM embedding) in the
process of DWM reading from the object are used [4]. In order to control the integrity
the DWM extraction from information object, hash sum calculation and this hash sum
with DWM contents comparison is performed. The analysis of integrity control
guarantees the impossibility of the information object substitution or corruption.
Finally this provides the safety of functioning the information system processing the
given information object.
The control of information object usage legitimacy by DWM is based on
possibility of a copyright owner to embed DWM having the copyright owner
identifying data into the object. So it is only a copyright owner who possesses a stego-
key can check the DWM presence and its contents in the information object [5].
DWM technologies are actively used in the structure of Digital Rights Management
systems (DRM – systems), but the field of their usage is commonly limited with the
multimedia content protection: graphical, audio and video files [6], [7]. In performing
the tasks of control of information object usage legitimacy by DWM the recovery of
initial object value after DWM extraction is necessary.
In the present paper the author proposes the information technology of self-
recovery DWM usage in active hardware containers based on LUT-oriented
architecture (further LUT-containers). We can refer, for example, Field
Programmable Gate Array microchips (FPGA microchips) [8], which at present are
often used as an element base for computer and control system design, to such kinds
of containers. The main element of such containers is LUT units, which are the data
structure used to replace the calculation with prepared data search operation [9]. LUT
units in FPGA are normally represented in the form of RAM. In this case LUT unit
inputs are the address inputs of RAM. If the number of inputs equals n a LUT unit
stores 2n bits information and is capable of calculating the value of 1 n-argument
Boolean function.
Self-recovering DWMs have been developed and used in the field of control of
integrity and legitimacy of usage for passive multimedia containers, e.g. graphical,
audio and video files. However it is necessary to control not only the information
objects of such kind by DWMs. But the task of self-recovering DWM usage in active
containers performing some calculating or controlling function is not realized at the
moment. In the articles [10], [11] the techniques of DWM embedding in active LUT-
containers are proposed. But the techniques described do not possess the possibility to
recover the container original. So the aim of the given paper is to describe the
possibility of container original recovery after DWM extraction by developing the
technique of forming the DWMs in LUT-containers.
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2 The Information Technology of Embedding the Self-
Recovering DWM in LUT-Container
The information technology considered in the paper is a formal process of usage of
the proposed and already existing techniques as well as the means of information
processing, which provides DWM forming in LUT-container space.
The proposed information technology uses a set of Fridrich-Goljan-Du method
(further Fridrich method) approaches [12], [13] in the part, which is intended for
container recovery, and technique described in [10], [11] in the part intended for
DWM embedding in LUT-containers. Besides the represented technology uses such
peculiarities of LUT-containers as activeness, accurate data presentation, non-
autonomousness of their elementary parts [10].
The methods proposed in [10], [11] are based on the change of codes of a pair of
successively integrated LUT units, which does not alter this pair functioning. Assume
there is a pair of LUT units and the output of the first one is connected directly or
through a trigger to the address input of the second one. The inversion of all the bits of
the first unit code and a definite rearrangement of the bits of the second unit code does
not change the functioning of the given pair of units. It is the consequence of
equivalence of Boolean functions realized by the pair of units before and after values
inversion. The rearrangement of bits in the second unit code of the pair is produced
according to the rules depending upon the binary weight of its address input, which the
first unit output is connected to. The inversion of bits of the first unit code of the pair
gives the possibility to achieve the required value in a definite bit of a unite code. This
peculiarity is exactly used by the methods considered in [10], [11] for DWM embedding
in a LUT-container. However these methods are not able to recover the container original.
Fridrich method [12], [13] is based on the group processing – disjoint subsets of
elementary parts of a container with the help of two functions: Flipping-function F
and function of discrimination f.
Function of discrimination is used in Fridrich method on order to classify the
groups of elementary container parts by including them to the classes of regular,
singular and unused groups. To determine the function value in each of the container
groups we are to calculate the sum of pairwise subtractions with overlapping for
elementary container parts included in a group.
Flipping-function is used by Fridrich method to modify the groups according to
some rule possessing the characteristic of involution. In the proposed information
technology the LUT-container architecture peculiarities are taken into account and
this fact differs it from Fridrich method in the following features:
within the frames of the proposed technology in the course of DWM embedding
the modification of elementary parts exactly (LUT units) is performed but not the
groups of elementary parts of a container;
within the frames of the proposed technology the calculation of Flipping-function
F(x) unlike Fridrich method contains the LUT unit value inversion according to the
procedure mentioned in [10], [11]. The procedure is the invention of values of the
current processed LUT unit and propagation the inversion around the inputs of all
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the LUT units connecting to the current unit output. It is obvious that the Fridrich
method requirement concerning the presence of involution characteristics is
performed for the given type of Flipping-function, i.e. F(F(LUTi)) = LUTi where
LUTi is any valid value of some LUT unit;
unlike Fridrich method within the frames of the proposed technology a principle of
container element classification without calculating any function of discrimination is
determined. The element classification is organized as a determination of zero and
one value proportion in LUT unit codes. It is performed according to the following
principle: if LUT unit contains zero values more than one values it is classified as a
regular unit (R-unit); if a unit contains more one values than zero values it is
classified as a singular unit (S-unit); if the number of zero values of LUT unit equals
the number of its one values the unit is classified as an unused unit (U-unit).
Certainly, the rules of moving the container from one class to another defined by
Fridrich method are performed within the frame of the proposed approach as well:
F(LUTR) = LUTS;
F(LUTS) = LUTR; (1)
F(LUTU) = LUTU,
where LUTR, LUTS, LUTU – LUT units classified as R-unit, S-unit and U-unit,
respectively; F() – Flipping-function.
The succession of actions in the proposed information technology in DWM
embedding in LUT-container is as follows.
Stage 1. The movement about LUT-container units in the order determined by
embedding path is realized. During this action each of the LUT units refers to the
classes R-unit, S-unit or U-unit on the basis of the above mentioned classification
rules. According to the results of classification the binary RS-vector is formed in the
following way: if the next LUT unit is classified as R-unit then zero value is fixed in
RS-vector; if the next LUT unit is classified as S-unit then one value is fixed in RS-
vector; U-unit values are not fixed in RS-vector.
Stage 2. The obtained RS-vector compression is performed with the help of some
lossless compression algorithm. As a result of this the compressed vector RScom is
formed. It is obvious that RScom vector length is less than RS-vector length. Difference
of length of these vectors is denoted as ΔL.
Stage 3. DWM, which is a binary succession the length of which does not exceed ΔL
is added to vector RScom by concatenating. Vector RS* obtained after concatenation is
added with arbitrary binary values until it reaches the RS vector length. So:
RS* = RScom . DWM . Add, (2)
where “.” – operation of concatenation; DWM – watermark embedded into container;
Add – optional addition of vector RS* to RS vector length.
Stage 4. The movement about LUT units of container in the order determined by
embedding path is performed. In the course of this movement U-units are ignored,
and within R-units and S-units a mutual transition of one into another with the help of
Flipping-function is made according to the table.
490
Table 1. The rules of LUT-unit move from one class to another
Class of Value of a bit, The current Action
the current corresponding to the bit of vector
LUT-unit current LUT-unit RS*
LUTi LUTi in vector RS
R 0 0 —
R 0 1 Transformation LUTi to S-unit
S 1 0 Transformation LUTi to R-unit
S 1 1 —
The actions at the given stage leads to vector RS* embedding in a LUT-container.
Vector RS* contains DWM and a compressed vector RS (vector RScom) version in
accordance with equation (2). Thus except for a DWM itself the information
necessary for the original container value recovery is embedded in a container. The
rules represented in table 1 describe the actions providing the vector RS* embedding
in a LUT-container. If the corresponding current bits of vectors RS and RS* coincide
then no modification for the current LUT unit is produced. In the case of mismatch of
these bits the current LUT unit transition in the class corresponding to the current bit
value of vector RS* is performed.
Taking into account that the Flipping-function impact on LUT units occurs
according to the unit inversion rules represented in [10], [11] LUT-container
functioning does not change after DWM embedding.
3 Example of DWM Embedding According to the Proposed
Technology
Let us consider the example of described stages of DWM embedding in container
technology. In table 2 the hexadecimal values of codes of twenty LUT units
(i = 1…20), which are in some embedding path of a container are shown in the lines
“Unit code”.
Table 2. Initial values of codes of LUT units lying in embedding path
i 1 2 3 4 5 6 7 8 9 10
Unit code 51F0 FF96 56EC E8FE 2002 0008 8040 1000 0FF0 CCCD
n1 7 12 9 11 2 1 2 1 8 9
Class of unit R S S S R R R R U S
RS-vector 0 1 1 1 0 0 0 0 — 1
i 11 12 13 14 15 16 17 18 19 20
Unit code 0220 88F8 F128 3F00 0001 9B94 AABA A340 B0E1 EE00
n1 2 7 7 6 1 8 9 5 7 6
Class of unit R R R R R U S R R R
RS- vector 0 0 0 0 0 — 1 0 0 0
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For each of these units a number of one values (n1) in the unit code bits are
indicated. Depending on the proportion of amounts of one and zero values in the code
the unit is classified as R, S or U unit according to the above mentioned rules. In
accordance with the results of the classification a RS-vector is formed, in which zero
values correspond to R-units and one values – to S-units. U-units do not participate in
forming the RS-vector.
As a result the RS-vector takes the value RS = 011100001000001000 consisting of
18 bits (the information about two U-units was not included in RS-vector). Then the
RS-vector is to be subjected to lossless compression. In the given example the
simplest way of compression on the basis of Huffman method is used for illustration
(in practice the more effective compression methods are to be used). For this purpose
the triads of RS-vector bits are taken as elementary characters and their frequency of
entering the vector is found. The triad “000” enters the vector twice, the triad “100” –
once, the triad “011” – twice. As a result of Huffman method we obtain the following
system of uneven prefix codes for the triads of RS-vector: “000” “11”, “100”
“100”, “011” “101”, “001” “0”.
As a result of usage of the obtained codes we can have 12 bits vector
RScom = 101100011011 instead of the initial triads in 18 bits RS-vector. RS and RScom
vector lengths difference is ΔL = 6. This value expresses the maximum amount of
DWM bits, which can be embedded in LUT units in the given example.
In table 3 the values of bits of the initial RS-vector and its compressed version
RScom are shown. Let us consider the example of addition of the 6-bits DWM –
DWM = 101010 to the vector RScom. As a result of concatenation of the vector RScom
and DWM embedded in DWM container we obtain vector RS* having the similar
length as to vector RS.
Table 3. Binary vector values
RS 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0
RScom 1 0 1 1 0 0 0 1 1 0 1 1
DWM 1 0 1 0 1 0
RS* 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0
Then according to the rules specified in table 1 the LUT-container modification is
performed. The aim of this modification is to adapt the LUT-unit classes lying in the
embedding path to the value of vector RS* containing DWM. As we see from table 1
the LUT-unit movement from one class to another is only performed when the values
of the corresponding bits of vectors RS and RS* do not coincide. The bits
characterizing with the absence of coincidence of such kind are distinguished in table
3. For the LUT-unit codes corresponding to the distinguished bits a Flipping-function
is applied and this leads to the movement of these units from one class to another.
In table 4 the values of LUT-unit codes after Flipping-function application to the
distinguished units (units, for which the class is to be changed). As a result of these
actions the RS-vector of units, which are in the embedding path takes a value of the
vector RS* and DWM is embedded into the LUT-container.
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Table 4. Values of LUT-unit codes after embedding the DWM in the container
i 1 2 3 4 5 6 7 8 9 10
Unit code AE0F 0069 56EC E8FE 2002 0008 8040 EFFF 0FF0 CCCD
n1 9 4 9 11 2 1 2 15 8 9
Class of unit S R S S R R R S U S
RS-vector 1 0 1 1 0 0 0 1 — 1
i 11 12 13 14 15 16 17 18 19 20
Unit code 0220 7707 0ED7 C0FF 0001 9B94 AABA A340 4F1E EE00
n1 2 9 9 10 1 8 9 5 9 6
Class of unit R S S S R U S R S R
RS-vector 0 1 1 1 0 — 1 0 1 0
4 The Proposed Procedure of DWM Extraction from LUT-
Container
Within the frame of the proposed technology the stego-key dedicated for data
extraction consists of the following four components:
key = (order, classification, RSrule, ΔL), (3)
where order – the information defining the order of move around LUT units in the
container (embedding path) for DWM embedding or extracting; classification –
concrete definition of the principle of LUT-unit classification (unit is considered to be
R-unit if the amount of parts in the unit code is more or less); RSrule – the rule of
interpretation of RS, RScom, RS* vector bit values: for R-units a zero value and for S-
units one value are fixed in the RS-vector and vice versa; ΔL – the difference between
the vector RS length and its compressed version RScom length.
The succession of actions of the proposed information technology in DWM
extracting and recovering the initial value of LUT-container is as follows.
Stage 1. The movement about LUT-container units in the order specified by
embedding path occurs. And along with this a binary vector RS’ is formed on the basis
of LUT-unit classification like in the case of embedding the information.
Stage 2. The obtained vector RS’ structure corresponds to the one of vector RS* (2)
formed in DWM embedding in container. The last ΔL bits of vector RS’ are DWM with
the possible addition to the necessary vector length. At this stage the reading of this bits
and DWM obtaining is performed.
Stage 3. The other vector bits are subjected to the procedure of decompression
opposite to compression, which is performed at the stage of embedding the
information. As a result a binary vector RSdecom is formed.
Stage 4. On the basis of information contained in vector RSdecom the recovery of
original container value is performed. The movement about LUT-units of the
container in the order specified by the embedding path and successive review of
vector RSdecom values are performed for this. In the course of this movement the U-
493
units are ignored and within R-units and S-units a mutual transition is made by
Flipping-function according to table 1.
For the example considered above DWM extraction can be described in the
following way. As a result of analysis of LUT-unit codes lying in the embedding path
the unit classification is performed and a binary vector RS’ = 101100011011101010 is
formed. From the vector end the ΔL = 6 bits containing DWM “101010” are taking.
The rest bits of the vector “101100011011” are subjected to decompression with the
usage of the table making the match between the uneven prefix codes of compressed
vector and the triads of decompressed vector bits. This leads to creation of binary
vector RSdecom = 011100001000001000, which coincides with the container vector RS
before DWM embedding in it. The given vector has the information for the original
value recovery of LUT-container. According to the rules of table 1 the LUT-unit
classes become the original ones and the container acquires the value it had before
DWM embedding.
5 Experimental Research of the Proposed Technology
Aims of the experimental research:
1. to show experimentally that LUT-containers, in which DWMs were embedded
with the help of the proposed technology acquire their original value after DWM
extraction;
2. to indicate the degree of change of the main characteristics of containers after
DWM embedding in them. The main characteristics are considered to be the
following ones: a) maximal clock signals frequency expressing the limits of
processing speed within the frames of one family of target chips; b) energy
consumption of the input-output system of a chip; c) energy consumption of the chip
core; d) thermal dissipation of a chip.
Environment for making the experiments. The hardware-software means based
on the chips FPGA Altera Cyclone II and CAD Altera Quartus II usage have been
developed for the experimental research. The group of scripts performing the
interaction with CAD Altera Quartus II for reading and recording the LUT-unit
contents was organized in TCL language. The read data processing subsystem itself is
realized in language C# within the frame of the platform .Net in accordance with the
proposed technology. The estimation of design characteristics mentioned above were
carried out by means of CAD Altera Quartus II Timing Analyzer (estimation of the
limit processing speed) and Power Play (estimation of energy consumption and
thermal dissipation). The states of container before DWM embedding and after DWM
extraction were compared by bit-by-bit analysis of configuration files of the
corresponding containers.
The Materials for experiments are 40 FPGA – projects of different
complexities and purposes. The hardware complexity of devices within the frames
of the given projects varies from 1,2% to 65% resource volume (logic cells, RAM
units) of target chip FPGA.
494
The process of making the experiments. The experiments for each of the researched
project consist of the following stages:
1. estimation of the main characteristics (processing speed, energy consumption,
thermal dissipation) for the device represented in the form of initial container;
2. embedding the random binary succession of DWM in container;
3. estimation of the main characteristics for a container having the embedded DWM;
4. DWM extraction from the filled container;
5. comparison of configuration files of the final and initial container states.
The results of experimental research. As a result of experiments a complete
coincidence of configuration files of the initial containers and the ones obtained after
DWM extraction for all of the 40 projects has been established. So due to the features
of self-recovery after DWM extraction from containers they take the original form
and their characteristics return to the initial values.
In the part of determining the degree of changes of the main container
characteristics (after DWM embedding) the following results were obtained. We
found that insignificant changes of container characteristics occurs as a result of
DWM embedding. Along with this the dependence of this change upon hardware
complexity and its structural peculiarities is extremely low. The difference between
the changes of characteristics for devices occupying 1,2% and the ones occupying
65% resource volume of the target chip FPGA is hundredths of a percent. On average
(for all of the researched 40 projects) the processing speed characteristic change is
0,18%, changes of energy consumption and thermal dissipation characteristics –
0,22%. As we see the change values are within the limits of error value of
measurement means.
The technology offered in the paper does not change the mutual connections of
LUT units but does change the values of the specific units codes. It is accordingly of
interest to learn whether the changes of units codes are able to influence on the FPGA
project features under such conditions. Except for the previously considered
experiment another experimental research of the influence of the values of LUT units
codes on the basic features of FPGA projects has been made with the participation of
one of the authors of the given paper. The description of this research and its results
are shown in [14]. In the above considered experiment a random binary succession
was embedded in various FPGA projects. This led to the fragmentary changes of LUT
units codes as in accordance with table 1 the codes of units change only in the two of
four cases of possible combinations of values of bits of vectors RS and RS*. In [14]
the extreme cases of codes change in all the involved LUT units of FPGA-project
were considered. In order to create such kinds of changes the projects of similar
structures, but with the LUT units codes containing minimum and maximum amount
of one value, respectively, were formed and compared. The projects were chosen to
deploy the resources of the corresponding FPGA chip in a maximum way. In table 5
the main results of comparison of such projects are represented. The projects with the
minimum and maximum amount of one values are marked in table 5 as Pmin and Pmax,
respectively. In the given table the following characteristics are represented:
maximum clock frequency F; dynamic and static power supply as well as the total
495
energy consumption of chip core obtained for the indicated clock frequencies; δ – a
relative energy consumption change in mass changes of the number of logical values
in the codes of LUT units of a project. All the families of chips used in the experiment
have the core power supply equal 1,2 V.
Table 5. The results of energy consumption and processing speed estimation
Total core energy Dynamic Static
Project
consumption (mA) power supply (mA) power supply (mA)
Cyclone II EP2C35F672C6
F = 420,18 MHz
Pmin 699, 17 629,98 69,19
Pmax 701,40 632,19 69,22
δ 0,31 % 0,34 % 0,04 %
Cyclone III EP3C40F780C6
F = 516,26 MHz
Pmin 495,6 491,49 4,11
Pmax 497,37 493,39 3,98
δ 0,35 % 0,38 % 3,16 %
Cyclone III LS EP3CLS70F780C7
F = 516,26 MHz
Pmin 494,6 482,91 11,69
Pmax 496,23 484,73 11,51
δ 0,32 % 0,37% 1,5 %
Cyclone IV E EP4CE30F29C6
F = 600,6 MHz
Pmin 477,42 470.42 7,00
Pmax 479,64 472,22 7,41
δ 0,46 % 0,38 % 5,5 %
The experiment results shown in table 5 demonstrate that in maximum mass
change of the number of one values correlation in LUT units:
1. the energy consumption of input output system for chips within a FPGA family is
retained at the same level;
2. the chip core energy consumption changes insignificantly within one family mainly
due to the dynamic component (maximum value of this change equals 0,46% for
chips EP4CE30F29C6 of family Cyclone IV E);
3. the maximum clock frequency expressing the extreme processing speed of devices
does not practically change within one FPGA family.
The results show that such important characteristics as productivity and energy
consumption are not practically dependent upon the type of Software code used in
FPGA-projects with the fixed hardware realization. So we can come to the
conclusions that according to the technology proposed in the given paper the DWM
embedding in a LUT-container does not substantially impact on the FPGA project
characteristics mentioned above.
496
6 Conclusions
The information technology proposed in the paper allows to perform DWM
embedding in containers with LUT-oriented architecture. The technology gives the
possibility to recover the initial state of container after DWM extraction from it. The
technology is based on the combination of DWM embedding method into LUT-
containers proposed in the given paper and the popular Fridrich method oriented at
the passive multimedia containers. Unlike Fridrich method the proposed technology:
uses less complicated Flipping-function taking into account the container
peculiarities;
does not include the discrimination function calculation in order to perform the
element classification of container;
performs information embedding at the level of the container elementary parts
(LUT-units) but not at the level of groups of elementary parts.
The degree of the proposed technology effectiveness is of qualitative nature and is
expressed in possibility to recover the initial LUT-container after DWM extraction,
which was absent before. The proposed technology can be used in developing the
hardware and software, which realize digital watermark embedding in computer and
control devices created on the LUT-oriented element base (e.g. FPGA or
programmable logic integrated circuits with the similar architecture). Such kind of
embedding allows to control the device configuration integrity makes the substitution
or corruption of configuration impossible, which is of vital importance for critical
domains. In addition it allows to control the legitimacy of usage of project
information and devices themselves at the different stages of CAD and life cycle:
synthesized FPGA project, configuration file FPGA, operating device.
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498
Functional Diversity Design of Safety-Related Systems
Ivan Malynyak
Stalenergo LLP
ivanmiros@gmail.com
Abstract. Traditionally, the application of safety voted-groups architectures is a
matter of redundancy, where hardware and software components are replicated
and become a source of vulnerabilities with decreased system reliability as a
whole, therefore necessity of functional diversity design is become essential.
Well known diversity approach for similar erroneous results mitigation is wide-
ly used, but combined software and hardware techniques to achieve necessary
safety system requirements without enlarged implementation of price isn’t yet
evolved. Avoidance of redundant complexity with limitation the number of
channel’s internal states could lead to common cause failures reduction and suf-
ficient level of residual risks.
Keywords. fault tolerant architecture, 1oo2D, 2oo3, redundancy, complexity,
control systems, diversity, common cause failures
Key terms. Process, Technology, Development, Reliability, SoftwareCompo-
nent
1 Introduction
Nowadays technology of control system is believed to be effective and safe, where
essential approaches are sufficiently exploited [1]. The current generation of instru-
mentation and control systems is highly integrated digital complexes which offer
better performance, versatility and additional diagnostic capabilities in comparison
with aged analog systems. But as far as systems become more safety-critical, all kinds
of possible vulnerabilities have to be taken into account.
This paper offers the concept of functional diversity design which is unfolded by
three steps from the problem, through different approaches to the implementation.
First of all, necessity of latent systematic faults elimination is assumed, where ques-
tion of misinterpreted functional requirements within the system becomes a main
framework for modern applications [2, 3]. Secondly, the approach to cover up to
99.9% faults without overhead in performance and power consumption based on
modern surveys is suggested [4]. And finally, new architecture based on reduced sys-
tem complexity which helps to make up savings in development life cycle stage with
higher availability and higher safety in railway industry is proposed.
499
To be accurate with terminology, the functional diversity design in this paper is not
assumed as different physical functions within determined process implementation,
but more broadly, where fundamental diverse technology is considered in a way of
inherent difference without any commonality in its nature. Even the most comprehen-
sive strategies approach are suffered from the common channel failures and possible
external influences or insufficient faults mitigation that can further contribute to the
potential concurrent vulnerabilities [2]. Indeed, all mentioned strategies assumed the
six different fault management techniques which solves equal project problems in
redundant channels, composed of sensors, computers and control elements with pur-
pose to take the process to a de-energized state when predetermined conditions are
violated.
As shown in Fig. 1, two types of well-characterized redundant architectures (2oo3
and 1oo2D) have equal functional structure schemes A B C and therefore cy-
cle’s synchronization procedures within sub-channels are required. As a result, extra
data connection lines between sub-channels are used to establish additional infor-
mation exchange and projects very often become fed up with wiring L and sophisti-
cated inter-channel redundancy management.
Input (data) Input (data)
Channel 1 Channel 2
A B C A1 B1 A2 B2
L
L
Safe Safe
control control
X1 X2 X1 X2
Z Z
Output Output
Fig. 1. Two types of well-characterized architectures 2oo3 (left) and 1oo2D (right)
Almost all created inter-channel data than is sent to hardware/software redundant
voting mechanism Xi which than implements safe control output function Z. Despite
the fact that diversity questions are deeply concerned and surveyed, the biggest issue
still lies in assumption of equal channel functional design, where the fundamental
problem took their roots [4, 5]. Of course, it’s easy to fit out the system with all kinds
of diversity techniques, but absence of overall differential approach can’t guarantee
prolonged operation without common cause vulnerabilities. The possibility of concur-
rent triggering the latent multi-channel failures is potentially hazardous and it’s like a
group of man walking simultaneously around a pit with averted eyes.
500
The way out could be found in “sequential” (or satellite) type of system architec-
ture, where parallel equivalent sub-channels are substituted with diverse ones as
shown in Fig. 2. The challenge is to cope with nature evolution, where necessity of
redundancy implements as sequential algorithm in embedded bundle of diverse enti-
ties [6]. The idea is already has been considered in [2], but existent architectural con-
text is still repeated virtual “OR” logic of distinct sub-channels. Even if functional
diversity is achieved through different control laws, elements and distinct functionali-
ty, the need of overall agreement among the sub-channels and data synchronization
may critically affect output values.
Input (data)
Channel 1 Channel 2
S1 X1 X2 S2
Control
L
L’
A1 A2
Z
Deenergize
Output
Fig. 2. Sequential architecture of safety redundant control systems 1oo2S
Data lines in sequential architecture 1oo2S are minimized to essential level with
safety functions are guaranteed to be executed correctly by de-energize signals. This
type of architecture isn’t widespread despite advantages of system simplicity because
of general established multichannel parallel approach used to cover safety issues.
Nevertheless, such direction may have its future in the light of necessity to drop over-
all system complexity to acceptable level for commercial use.
2 Redundancy
The challenge of providing redundancy management to meet certain requirements
for different application is complicated by the critical constraints of market cost and
schedule. Further evolution of redundancy management with its intricate synchroniza-
tion interfaces and overall complexity were already found to be potentially cata-
strophic [7]. This approach obviously was costly in a way of wiring and components
but from the other hand it’s offered rather simple and attractive macro level “black
box” design.
501
As one could see, the redundancy approach is well known and understandable,
where failures of elements could be easily found by comparison. For simple functions
it works greatly and reliability decreasing is not matter of consideration. But when
dozens of input and output were designed with redundancy management, cost of de-
veloping and physical implementation tended to increase exponentially. The result of
complexity already known and contained to be in faults propagation which leads to
unsafe concurrent failures of two or more identical parallel sub-channels [8].
More than that, the design to achieve necessary safety level leaded out into dupli-
cating functions almost at every step. Firstly, the safe input means at least of two sig-
nals to be monitored with safe outputs are based on the same repeating principal. Sec-
ondly, to achieve availability requirements the “design shape” just went on adding
next “channel 2”, but of course it could be more channels. And finally, when all com-
ponents are successfully placed, the intricately net of data communicating has to be
put over.
The first step down from “black boxes” design could be avoiding some needless
redundancies. As shown in Fig. 3, 1oo2D architecture is looked safe due to transpar-
ent functional scheme. Indeed, all inputs are duplicated and could be verified by other
neighbor. Moreover, output Z is drove from two channels by voting mechanisms Xi,
with ability to perform safety de-energized state.
Channel 1 Control
A1 B1
X1
Z
Input L Output
Relay
X2
A2 B2
Channel 2
Fig. 3. Decomposition of 1oo2D architecture
On the contrary, the sequential architecture approach could change the whole ap-
pearance of system design, where redundancy eliminating is only the first step to be
done. As shown in Fig. 4, the point of view lied in the basic sequential approach idea,
where elements of system are presented with non-symmetrical faults property. Let’s
describe it by simplified hardware model, which could be than enlarged on software
issues by substitution physical elements with similar software routines in a project.
For example, if “input” is implied as thermocouple, than implementing fixed cur-
rent with periodical caliber testing would guarantee possible input faults detection.
Indeed, the only fault is not detected by this approach is a rare gradual measurement
502
drift and by using high quality thermocouple with periodical external checkup this
could be solved and particular problem due to low possibility of such fault would be
eliminated. As a result, a thermocouple with measuring circuits is treated as single
element with non-symmetrical types of faults, where most likely defects in circuit
break or rapid measurement drift (op-amps or connecting line issues) are easily de-
tected. The non-symmetrical type fault output is treated in the same way, where satel-
lite sub-channel S drives relay Z safely through transformer X with inherently elimi-
nating shortcut failures. The main sub-channel A is connected to S with communica-
tion line where control data and both functional integrity is transferred. Each of sub-
channels could run safety function by de-energizing transformer in case of discrepan-
cy.
I=const
X Z
Input Control Output
S Relay
Calibre
L
Deenergize
A
Fig. 4. Simplified model of sequential architecture 1oo1S
As a result, sequential approach is constrained to build the system with strong
functional design separation between core algorithm A and routine input/output tasks,
whereupon for example the fast and simple satellite sub-channel S is prepared to deal
only with input/output X and functional integrity management. The effect would
come out of overall system complexity reduction, common cause failures elimination
and reliability enlargement due to algorithm simplification with functional diversifica-
tion.
3 Design of safety-related systems
The main aim of diversity is to perform safety functions achieved by monitoring
the behavior of number of sub-channels. The way safety ideas are implemented re-
minds “fractal” pattern, where general method of reiteration is repeated at every scale
of a project. It could be seen in software, where developer has no idea how his source
code would be eventually implemented into assembler language. The same thing is
happened in hardware, where design is implemented by pure repeating elements
based on monolithic integrated circuits without clear understanding of its full func-
tionality. As a result, each level of system decomposition is considered with increas-
ing uncertainty and the principle of aggregation with uncontrollable elements cascad-
ing may not be as reliable as it expected.
503
Finally, the result of uncontrolled “fractal” implementation is come out as necessi-
ty of channel diversity due to providing predictable system behavior and is turned to
entity multiplication which has to be carefully verified [9]. Hereafter, when system is
installed, a well known golden rule is remained - “don’t change anything”.
Evolution of Nature shows that repeated and uncontrolled growth ultimately leads
to disaster, just look back on dinosaurs or cancer. So, the main idea of safety may lies
in capability of system predicting its behavior with reasonable complexity. For exam-
ple, for the implication to the brain size it could be said, that decision making mecha-
nism should be “large as you need and as small as you can” [10].
Looking forward at systems design, there is a time point when sufficient data of
failures is gathered and overall availability could be increased just due to better
maintenance understanding. Indeed, if its clear how light bulbs in mines are breaks
and what circumstance is preceded, then particular algorithm with appropriate feed-
back could lead to limited abundance of lighting control system or even eliminate
redundancy at all due to accurate prediction of failures with using certain planned
actions.
After thorough revision of prevail railway control systems it’s assumed, that archi-
tectures could be transformed into simplified 1oo2S variant, where all inputs and
outputs are designed with proper feedback (shown in Fig. 5).
Channel 1
X1 Control
S1
A1
Deenergize
L Z
Output
Input L’ Relay
L Deenergize
A2
S2
Control
X2
Channel 2
Fig. 5. Decomposition of 1oo2S architecture
For the preliminary evaluation of design safety advantages, it’s assumed that set of
proper input signals p P or faults q Q are used for all sub-channels A,B,C with set
of internal conditionals r R to implement safely output set Z or hazardous output set
Z’.
For 1oo2D architecture A B is assumed where diversity mechanisms within
sub-channel could be implemented or not. Working states when safety function oper-
ates normally is described by formula:
504
r,p: Arp=Brp, Z Z’= (1)
Nonworking de-energized output state where sub-channels’ internal conditions are
differ because of failure detection:
r,q,p: Arq≠Brp Arp≠Brq, Z= (2)
Hazardous state where sub-channels’ outputs synchronously being changed by la-
tent failure:
r,q: Arq=Brq, Z Z’≠ (3)
Sequential architecture 1oo2S is considered to be diverse on design level where
each sub-channel is used different technologies, logic and way of responding by na-
ture, therefore equation A S ≈ is assumed. Nevertheless, in order to provide
necessary safety technique, the idea of artificially divided sub-channels’ internal con-
ditionals alphabet is used and proper mapping of normal responses set within each
sub-channel is determined [11]:
r,p: Arp SA Srp AS, Z Z’ ≈ (4)
Here the SA is a set of sub-channel A mapping responses which are analyzed in S
and vice versa. Hazardous state where sub-channels’ outputs synchronously being
changed by latent failure are very rare due to functional diversity design:
r,p,q: Arpq Srpq ≈ (5)
In order to avoid potentially hazardous states, a number of conditions must be met
[2]. Let us assume A and S with internal symmetric difference feature and in theory
it’s possible to reach necessary level of identified errors possibility at 99.9%:
r,p,q: Arpq ¬ Srpq, Z Z’ ≈ (6)
One of the approaches to achieve channels’ software symmetric difference could
be based on “likely program invariants” idea with substitution invariants property of
critical parts for negations ones [12]. For example, if sub-channel A algorithm has
CASE operator for “what must be done”, than sub-channel’s S algorithm to control
this part of software should have operator for “what is not supposed to be done in any
case”.
This paper is regarded only as intention where distinguish functional design speci-
fications of sub-channels is took into account. The formulas (1-6) are correlated with
already developed theoretical foundation and mathematical models of multi-version
systems [11], where different diversity kinds r R are sequentially accumulated in
final diverse versions by special mapping of output signal set Zi Z.
505
4 Architecture diversity usage
The problem of common cause failures mitigation basically could be found in four
industries (aviation, chemical process, rail transportation and nuclear power plant)
that provide high failure-consequence consideration in evaluating the diversity.
The usage of diversity are described in [2] with guidance related to clear examples
of diversity (shown in Table 1).
Table 1. Summary of diversity usage
Diversity Aviation Railway Chemical NPP
Equipment x x x
Design x x
1oo2S
Function x x x x
Human x x x x
Signal x x x
Software x x x x
In spite of the intensive researches in area of multi-version systems, the distributed
nature of the rail network and the localized action for interlocks and train control, the
railway safety management is paid less attention to diversity implementation. By
stopping or slowing trains to inhibit access to occupied tracks, railways have a readily
accessible safe state by local de-energized “stop” configuration. This failsafe ap-
proach based on old all-relay interlocking system resulted in a practical emphasis for
identifying faulted conditions and stopping the affected trains until the hazard can be
cleared.
In the modern microprocessor interlocks and train control the system diversity us-
age is vital due to increased speed and shortened time between rolling-stocks. Moreo-
ver, unique set of input and output signals for every railway station imposed addition-
al constraints on control systems, which has to be flexible in configuration, safe in
operation and cost effective in realization.
The idea of sequential 1oo2S architecture could fill the diversity gap in domains,
such as traffic control, where collision avoidance is a key of operational safety but
with considerable economic constraints.
5 Conclusions
With respect to size and complexity of modern safety-critical application it could
be assumed, that one way to achieve necessary system requirements without enlarged
implementation price is functional diversity design optimization. This paper proposes
combined software and hardware applying, where overall system complexity would
not exceed the uncontrollably high level and would decrease developing time.
Sequential safety architecture 1oo2S combines the benefit of 1oo2D and 2oo3 sys-
tems with higher availability and higher safety levels. The price for this innovation
lies in additional functional requirements to successfully analyzing integrity of sub-
506
channels. The additional benefit from such approach could be significant protection
against vulnerability of most common cause failures when software design shortcom-
ings and hardware faults are came to light.
References
1. IEC 61508-3:2010: Functional Safety of Electrical/Electronic/ Programmable Electronic
Safety-Related Systems – Part 3: Software Requirements
2. Wood, R.; Belles, R., Cetiner, M. & et al. Diversity Strategies for NPP I&C Systems,
NUREG/CR-7007 ORNL/TM-2009/302, (2009)
3. Yastrebenetsky, M., Kharchenko, V.: Nuclear Power Plant Instrumentation and Control
Systems for Safety and Security. IGI Global, (2014).
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Advanced Digital Instrumentation, Control and Information Systems for Nuclear Power
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search Report No 1145, LAAS-CNRS, (2001)
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tial Circuits. IEEE Trans. Computer. 23(7), 736–739, (1974)
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agement/Fault Tolerance. Space Shuttle Technical Conference, NASA Conference Publi-
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8. Madden, W., Rone, K.: Design, Development, Integration: Space Shuttle Primary Flight
Software System. Communications of the ACM 27(9), 914–925, (1984)
9. Astrom, K., Murray, R.: Feedback Systems: an Introduction for Scientists and Engineers.
Princeton Univ. Press, (2008)
10. Davidson, I.: As Large as You Need and as Small as You Can: Implications of the Brain
Size of Homo Floresiensis. In Schalley, A., Khlentzos D.: Mental States. V.1: Evolution,
function, nature, pp. 35–42, (2007)
11. Kharchenko, V., Siora, A., Sklyar, V.: Multi-Diversity Versus Common Cause Failures:
FPGA-Based Multi Version NPP I&C systems, Proceeding of the 76th conference
NPIC&HMIT, Las-Vegas, Nevada, USA, (2010)
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507
Computer’s Analysis Method and Reliability Assessment
of Fault-Tolerance Operation of Information Systems
Igor P. Atamanyuk1, Yuriy P. Kondratenko2
1
Mykolaiv National Agrarian University, Commune of Paris str. 9,
54010 Mykolaiv, Ukraine
atamanyukip@mnau.edu.ua
2
Petro Mohyla Black Sea State University, 68th Desantnykiv Str. 10,
54003 Mykolaiv, Ukraine
yuriy.kondratenko@chdu.edu.ua
Abstract. In this paper there was obtained an calculation method of the assess-
ment of the probability of fail-safe operation of information systems in the fu-
ture instants of time. The method is based on the algorithm for modeling a pos-
teriori nonlinear random sequence of change of values of the controlled parame-
ters which is imposed a limitation of belonging to a certain range of possible
values. The probability of fail-safe operation is defined as the ratio of the num-
ber of realizations that fell in the allowable range to the total number of them,
formed as a result of the numerical experiment. The realization of an a posterio-
ri random sequence is an additive mixture of optimal from the point of view of
mean-square nonlinear estimate of the future value of the parameter analyzed
and of the value of a random variable, which may not be predicted due to the
stochastic nature of the parameters. The model of a posteriori random sequence
is based on the Pugachev's canonical expansion. The calculation method offered
does not impose any significant constraints on the class of random sequences
analyzed (linearity, stationarity, Markov behavior, monotoneness, etc.).
Keywords. calculation method, random sequence, canonical decomposition, es-
timation, probability.
Key Terms. computation, mathematical model.
1 Introduction
One of the most important problems that arises constantly in the process of infor-
mation and communication systems service is the problem of the estimation of system
reliability with the following making decision about the possibility of its further ex-
ploitation on the basis of the information about possible failures in the future [1-5].
The problem becomes especially important in the case when information system is
used for the management of the objects that relate to the class of critical or dangerous
and under the threat of accident objects (aircraft, sea mobile objects, nuclear power
stations, chemical industry plants etc.) [6-8]. The forecasting of failures is the primary
508
stage of the providing of the dependability of the systems of such class. However,
nowadays the problem of failures forecasting (in overwhelming majority cases) is
solved by means of informal methods and the decision about the possibility of de-
pendable exploitation of the corresponding information system is made on the basis
[9-11]:
─ qualitative and quantitative estimation of its current state;
─ the experience of the exploitation of the given and analogous information systems.
As far as information and communication systems (ICT) become more complicated
and also as far as there is the growth of requirements to the probability of their relia-
ble work, informal methods of making decision are becoming less and less effective.
Hence, the usage of stricter approaches to the estimation of the dependability and
reliability of ICTs functioning based on the quantitative estimations of future state of
experimental information systems is very important.
2 Statement of the problem
Accuracy of the obtained solutions for correspondent class of problems and the
time during which given solutions can be obtained are the most universal parameters
characterizing the quality of information system functioning. Stated parameters (accu-
racy and time) have stochastic character because of the presence of inner defects of
the system and uncontrolled external destabilizing factors. That’s why the problem of
the forecasting control of information system reliability can be formulated in the fol-
lowing way.
Without the restriction of the generality of the next calculations let us assume that
the state of the information system in exhaustive way is determined with scalar pa-
rameter X (accuracy or time of problem solution). The change of the values of the
parameter X in discrete range of points ti , i 1, I is described by random sequence
X X (i), i 1, I . The values of the parameter X must satisfy the condition
a x(i) b, i 1,I (1)
In the case of the crossing by parameter X the limits of acceptable area [a; b] the
failure of information system in the process of its functioning is registered. The state
of the system is controlled periodically in discrete moments of time t , 1, k by
measurement of the values x , 1, k of the parameter X where x , 1, k
is the realization of the random sequence X in the cut set t , 1, k . It is evident
that for the segment of the time [t1; tk ] the inequation a x( ) b, 1, k must be
correct. Otherwise as it follows from (1) under
x i a, i 1,I
509
or
x i b, i 1,I
on the interval of examination [t1; tk ] the failure would take place that would lead to
the suspension of the process of information system functioning.
The statement of the problem can be formulated in the following way: on the basis
of stated (measured) information about current values of the parameter X on the time
interval [t1; tk ] the conclusion about the usability of the information system to exploi-
tation in future moments of time ti , i k 1, I must be made.
Similarly the problem of providing of dependable functioning and forecasting of
the state of the technical systems or objects to the structure of which information sys-
tems or management-information systems enter in the form of components can be
formulated. Herewith the dependability of functioning and usability of such compli-
cated systems and objects certainly depend on reliability and fail-safety of all their
components..
3 Solution
Given that the value of the controlled parameter X changes randomly within the
forecast region, the probability of fail-safe operation becomes an exhaustive feature
of the safety of functioning of the information system examined.
P(k ) ( I ) P{a X (k ) (i) b, i k 1, I / x( ), 1, k}. (2)
The problem is thus reduced to the determination of the probability of non-falling
of the realization of the a posteriori random sequence
X (k ) (i / x( ), 1, k ),i k 1, I outside the limits of the permissible region [a; b] .
In [12], [13] there was proposed an approach to the estimation of likelihood (2)
through multiple statistical modeling of possible extensions xl (i), i k 1, I , l 1, L
of the random sequence analyzed { X } in the forecast region, verification for each
realization of condition (1) and calculation as a result of the required estimation ex-
periment P*(k ) ( I ) n L ( n is the number of successes). In this method, its canoni-
cal expansion [14] within the range of points analyzed is used as a model of the ran-
dom sequence ti , i 1, I :
i
X (i) M X (i ) V (i ), i 1, I , (3)
1
where V , 1, I - random coefficients: M [V ] 0, M [V V ] 0 for
, M [V ] D ;
2
510
(i), i, 1, I - nonrandom coordinate function: ( ) 1, (i) 0 under > i .
Elements of the canonical representation (3) are defined by the following recur-
sions:
i 1
V (i) X i M [ X (i)] V (i), i 1, I , (4)
1
i 1
Di M [ X 2 (i)] {M [ X (i)]}2 D 2 (i), i 1, I ; (5)
1
1
(i) {M [ X ( ) X (i)] M [ X ( )]M [ X (i)]
D
(6)
1
D j j ( ) j (i)}, 1, I , i , I .
j 1
Tipping in the expression (3) of known values X ( ) x( ), 1, k converts the a
priori random sequence into the a posteriori one:
i
X ( k ) (i) mx( k ) (i) Vvv (i), i k 1, I , (7)
v k 1
where mx( k ) (i) - linear optimal, by the criterion of mean square minimum of predic-
tion error, estimate of the future value of the random sequence X at the point ti
according to the known initial values of k .
Expressions for finding mx( k ) (i) have two equivalent forms of notation
M [ X (i)], if =0, i =1,I ;
mx( ) (i) ( 1) (8)
mx (i) [ x( ) mx( 1) ( )] (i), =1,k , i = +1,I ;
or
k
mx( k ) (i) M [ X (i)] ( x( ) M [ X ( )]) f ( k ) (i), i = k +1,I ; (9)
j 1
( k 1)
f (i) f (k 1) (k )k (i), k - 1;
f ( k ) (i) (10)
k (i), =k ;
Formation of possible extensions of random sequence { X } by the expression (7) is to
compute estimates mx(k ) (i),i k 1,I , generating one of the known methods of statis-
511
tical modeling of values of independent random coefficients V , k 1, I with the
required distribution law and transforming of the values obtained by the coordinate
functions (i), i, k 1, I .
The calculation method of forecasting of fail-safe operation of information systems
on the basis of the model (7) covers a fairly wide class of random sequences (non-
markovian, non-stationary, non-monotonic, etc.), but this representation of an a poste-
riori random sequence is optimal only within the framework of linear stochastic prop-
erties, thus reducing significantly the accuracy of prediction of random sequences,
which have non-linear links.
The clearing of this trouble is possible through the use on the basis of estimation
method of the probability of fail-safe operation of an information system of nonlinear
canonical expansion of the random sequence [15], changing values of the parameter
controlled:
i N 1
X (i) M [ X (i)] V( )1( ) (i), i 1, I . (11)
1 1
Elements of the expansion (11) are determined by the following recursions:
1 N 1 1
V( ) X M [ X i ] V( j )
( j)
V( j )
( j)
, 1, I ; (12)
1 j 1 j 1
1 N 1
D M [{ X M [ X ]}2 ] D j ( ){
( j)
}2
1 j 1
(13)
1
D j ( ){ } , 1, I ;
( j) 2
j 1
h( ) (i )
1
{M [ X ( ) X h (i)] M [ X ( )]M [ X h (i)]
D ( )
1 N 1 1
(14)
D j ( )
( j)
( )h( j ) (i ) D j ( )
( j)
( )h(j ) (i )}, 1, h, 1, i.
1 j 1 j 1
In the canonical expansion (11) the random sequence { X } is represented in the range
of points analyzed ti , i 1, I via N 1 the arrays {V ( ) }, 1, N 1 of uncorrelated
centered random coefficients. Vi( ) , 1, N 1, i 1, I . These coefficients contain
information on the values X (i), 1, N 1, i 1, I , and the coordinate functions
h( ) (i), , h 1, N 1, , i 1, I describe probabilistic links of the order h between
the sections t and ti , , i 1, I .
Block-diagram of the procedure for calculating the parameters of the canonical de-
composition is shown in Fig. 1.
512
The concretization of values X ( ) x ( ), 1, N 1, 1, k allows to move
from the a priori random sequence (11) to the a posteriori one:
i N 1
( ) ( )
X ( k ) (i) mx( k , N 1) (1, i) V 1 (i), i 1, I . (15)
k 1 1
The expression mx(k ,l ) (1, i) M [ X (i) / x ( j ), j 1, k , 1, N 1] is the conditional
expectation of a random sequence providing that values x ( j ), 1, N 1, j 1, k are
known and the process analyzed is fully specified by the discretized moment func-
tions M [ X ( )], M [ X ( ) X h (i)], , h 1, N 1, , i 1, I .
The computing algorithm mx(k ,l ) (1, i) M [ X 1 (i) / x ( j ), j 1, k , 1, N 1] has
two equivalent forms of notation [16]:
M [ X (i )], 0;
h
mx( ,l ) (h, i ) mx( ,l 1) (h, i ) ( xl ( ) mx( ,l 1) (l , ))h(l) (i ), l 1, (16)
mx( 1, N 1) (h, i ) ( x( ) mx( 1, N 1) (1, ))h(1) (i ), l 1
or
k N 1
mx( k , N 1) (1, i) M [ X (i)] x ( j ) F((( kj(N1)(1))
N 1) ) ((i 1)( N 1) 1), (17)
j 1 1
where
( 1)
F ( ) F( 1) ( ) k (i), -1;
F( ) ( ) (18)
( ), = ;
(mod N 1 ( )) ([ / ( N 1)] 1), for k ( N 1);
1,[ /( N 1)]1
( ) (19)
(mod ( ))
1,[ /(NN11)]1 (i), if =(i-1)(N -1) 1.
The simulation procedure of the a posteriori random sequence (15) assumes that
densities of random coefficients Vi( ) , 1, N 1, i 1, I are known. The simplest and
the most effective solution to the problem of determining these one-dimensional den-
sities is to use nonparametric parse type estimates [17]. Together with this the esti-
mate of the required density of distribution f (Vi( ) ) of the random variable Vi( )
according to L of its realization vi(,l ) , l 1, L is represented as
513
Fig. 1. Block-diagram of the procedure for calculating the parameters of the canonical decom-
position (11).
514
1 L
f L (Vi( ) ) g (ul ), (20)
dL l 1
where ul d 1 (vi( N ) vi(,N )
l ) , g (ul ) - certain weight function (kernel);
d - constant (blur coefficient).
The estimate (20) at all points of the determination region is obtained unbiased,
consistent and uniformly converges on the desired distribution density f (Vi( ) ) with
probability one, if the weight function fulfils the condition
g (u) 0 ; sup g (u ) ; lim ug (u ) 0 ; g (u )du 1 . (21)
u u
The constant d is selected depending on the number of observations subject to the
conditions
d 0; lim d ( L) 0 ; lim d ( L) L . (22)
L L
When selected as the kernel function g (u ) the uniform density distribution blur
coefficient is determined on the basis of the correlation
d 0,5sup vi(,N ) (N) (N) (N)
l vi,l 1 , vi,l vi ,l 1 , l 2, L. (23)
l
Thus, the offered calculation method of polynomial predictive control of fail-safe
operation of information systems consists of the following stages:
─ construction on the basis of the known a priori information
M [ X ( )], M [ X ( ) X (i)], , h 1, N 1, , i 1, I . of the canonical expan-
h
sion (11) of the random sequence of change of the controlled parameter X ;
─ determination from the formula (16) or (17) the values
mx (1, i) M [ X (i) / x ( j ), j 1, k , 1, N 1]
(k ,l )
of the conditional expectation
[t ...t ]
of the random sequence analyzed within the forecast region k 1 I using the
x ( j ), 1, N 1, j 1, k [t ...t ]
known values on the observation interval 1 k ;
─ multiple simulation of values of random coefficients
Vi( ) , i k 1, I , 1, N 1
under the distribution law (20) and formation using
the expression (15) of the set of possible extensions of the realization of the ran-
[t ...t ]
dom sequence within the forecast range k 1 I ;
─ verification of conditions of non-crossing by the paths obtained of the bounda-
[a; b]
ries of the admissible region of the controlled parameter change X and
determination of the estimate of the probability of fail-safe operation of the in-
515
formation system as the ratio of the number of successes to the total number of
the experiments conducted.
Increasing the reliability of the estimate of the probability of fail-safe operation on
the basis of the model (15) compared to (7) is achieved by using nonlinear stochastic
properties of the random sequence analyzed: there rises the accuracy of determination
of conditional expectation and reliability of possible paths of a random sequence in
the forecast region through the use in the process of simulation of an additional array
of random coefficients Vi( ) , i k 1, I , 2, N 1 . The gain in accuracy can be
estimated using the expression:
k N 1 k
mx( k , N 1) (1, i ) mx( k ) (i ) { D ( j )(1(j ) (i))2 D j2 (i)}1/2
j 1 1 j 1
e[(ak,)b] . (24)
ba
Let a random sequence X in the discrete row of points ti , i 1, I is set by in-
stant functions: M X l i pl 1 X l 1 i pl 2 ...X 2 i p1 X 1 i ,
l
j N , p j 1, i 1, i 1, I . Decomposition of random sequence X looks like
j 1
[18],[19]:
i 1 N 1
X i M X i V (1) (1)(1) , i V1 i
11(1) 1 1 1
i 1 M ( ) p '1
(l )
p 'l( l)1 '1( l ) 'l( l )
... ... V p(l ) ... p(l ) (l ) ... (l ) (25)
1 l 2 p1( l ) 1 pl(l )1 pl(l )2 11( l ) 1 l( l ) 1 1 l 1; 1 l
(1)(l )
p1 ... pl(l )1;1( l ) ...l( l )
, i , i 1, I ,
where
, if N ,
M
N , if N ;
0, if j 1, l 1 or l 1,
p'(j l )
v l j , if j 1, l 1, l 1;
1
'(l ) N l (jl ) , 1, l.
j 1
516
The casual coefficients of canonical presentation (9) are defined by the expres-
sions:
1 N 1 1
V1 X 1 M X 1 V (1) (1)(1) , V (1) ( )
1 (1) 1
1 (1) 1
1 1 1 1
1 M ( ) p1'( l ) pl'(l1) 1'( l ) l'( l )
( )
(1)1 , ... ... V p(l ) ... p(l ) (l ) ... (l ) (26)
1 2 l 2 p1( l ) 1 pl(l )1 pl(l )2 11( l ) 1 l(l ) 1 1 l 1; 1 l
( )
(l1)
p1 ... pl(l )1;1( l ) ...l( l )
, , 1, I .
The coefficients V ,...
1 n 1;1 ,... n
which contain information about the values
X n n1 ... X 1 are calculated as
V ,...
1 n 1 ;1 ,... n
X n n1 ... X 1 M X n n1 ... X 1
N 1 ( ,... n 1 ;1 ,... n )
V (1) ( ) (1)1
1
,
1 1(1) 1 1
1 M ( ) p1
'( l )
pl'(l1) 1'( l ) l'( l )
... ... V p (l ) ... p(l ) (l ) ... (l )
1 l 2 p1( l ) 1 pl(l )1 pl(l )2 11( l ) 1 l( l ) 1 1 l 1; 1 l
( ,... n 1;1 ,... n )
(l1)
p1 ... pl(l )1;1( l ) ...l( l )
,
(27)
n 1 p1'( l ) pl'(l1) 1'( l ) l'(l )
... ... V p(l ) ... p(l ) (l ) ... (l )
l 2 p1( l ) 1 l 1; 1
pl(l )1 pl(l )2 1 1( l ) 1 l( l ) 1 1 l
( ,... n 1 ;1 ,... n )
(l1)
p1 ... pl(l )1;1( l ) ...l( l )
,
p1*( n ) pn*(n1) 1*( n ) n*( n )
( ,... ; ,... )
... ... V p ( n ) ... p( n ) ( n ) ... ( n ) p( n1) ... pn(n1) 1( n ) ...n( n ) , .
n 1; 1
pl(n1) pl(n2) 11( n ) 1 n( n ) 1
n n 1; 1
p1( n ) 1 1 1 n
In (27) parameters p1*(n) ,..., pn*(n1) ; 1*(n) ,..., n*(n) are calculated by the following
expressions:
517
, if 1, p( n)1 , 2, n,
pj ( n) (28)
v l , if p 1 1 , 2, n.
( n)
, if i 1, ( n) , i 2, n;
i 1
i j
j ( n) i 1
(29)
N n i j , if j i 1 , i 2, n.
( n) ( n)
j 1
The values * , 1, n 1; *i , i 1, n, are the indexes of casual coefficient
V * ... *
1 n 1 ; 1... n
* * which proceeds V1...n1;1...n in canonical decomposition
(25) for the moment of time t :
1. * , 1, n 1; *i i , i 1, k 1; *k k 1;
j 1
* j N n j *m , j k 1, n; if k 1, j 1, j k 1, n;
m 1
2. , 1, k 1; *k k 1; * j n j, j k 1, n 1; *i N n i
*
j 1
*m , i 1, n, if i 1, i 1, n; k k 1 1; j j 1 1; j k 1, n 1;
m 1
3. 0; *i 0; V * ... * ; * ... * ( ) 0, if , 1, n 1; i 1, i 1, n.
*
1 n 1 1 n
The expressions for the determination of the dispersion D1 , of casual coeffi-
cients V1 are:
1 N 1 ( )
2
D1 M X 21 M 2 X 1 D (1) (1)1 ,
1 (1)
1
1
1 1
1 1 2
( )
D (1) (1)1 ,
1
1 1
(1) 1
(30)
1 M ( ) p '1
(l )
p 'l( l)1 '1( l ) 'l( l )
... ... D p(l ) ... p(l ) (l ) ... (l )
1 l 2 p1( l ) 1 pl(l )1 pl(l )2 11( l ) 1 l(l ) 1 1 l 1; 1 l
2
( )
(l1) (l ) (l ) ( l ) , , 1, I .
1
p ... p
l 1; 1 ... l
518
Dispersions D ,...
1 n 1;1 ,... n
of casual coefficients V ,...
1 n 1;1 ,... n
are
defined as
D ,...
1 n 1 ;1 ,... n
M X 2 n n1 ... X 21
1 N 1
M 2 X n n 1 ... X 1 D (1)
1 (1) 1
1 1
2
( ,... ; ,... )
(1)1 n 1 1 n ,
1
1 M ( ) p '1
(l )
p 'l( l)1 '1( l ) 'l( l )
... ... D p(l ) ... p(l ) (l ) ... (l )
1 l 2 p1( l ) 1 pl(l )1 pl(l )2 11( l ) 1 l( l ) 1 1 l 1; 1 l
2
( ,... ; ,... )
(l1) n(l)1 (l1) (nl ) ,
1
p ... p
l 1; 1 ... l
(31)
n 1 p '1( l ) p 'l( l)1 '1( l ) 'l( l )
... ... D p(l ) ... p(l ) (l ) ... (l )
l 2 p1( l ) 1 l 1; 1
pl(l )1 pl(l )2 11( l ) 1 l( l ) 1 1 l
2
( ,... ; ,... )
(l1) n(l)1 (l1) (nl ) ,
p1 ... pl 1;1 ...l
p1*( n ) pn*(n1) 1*( n ) n*( n )
... ... D p ( n ) ... p( n ) ( n ) ... ( n )
n 1; 1
pl(n1) pl(n2) 1 1( n ) 1 n( n ) 1
n
p1( n ) 1 1
2
( ,... ; ,... )
( n1 ) n(n1) 1( n ) n( n ) , , 1, I .
1
p ... p
n 1; 1 ... n
The coordinate functions of canonical decomposition (25) are defined by the for-
mulas:
─ to describe the relationship between the value X 1
and X am i bm1 ... X a1 i
519
D
1 1
(b1...bm 1;a1...am ) , i M X X i b ... X i am
m 1
a1
1
1
M X 1 M X am i bm 1 ... X a1 i
1 N 1 ( )
D (1) (1)1 , (1)1 , i
(b ...bm 1;a1...am )
1 1(1) 1 1 1 1
1 1 (32)
( )
D (1) (1)1 , (1)1 , i
(b ...bm 1 ;a1...am )
1 1
1(1) 1 1
1 M ( ) p '1
(l )
p 'l( l)1 '1( l ) 'l( l )
... ... D p (l ) ... p(l ) (l ) ... (l )
1 l 2 p1( l ) 1 pl(l )1 pl(l )2 1 1( l ) l 1; 1
l( l ) 1 l
( )
(l1)
p1 ... pl(l )1;1( l ) ...l( l )
, (pb(1l...) ...bmp(l1);a1(...l )a...m)(l ) , , 1, I .
1 l 1; 1 l
─ to describe the relationship between the value X n n1 ... X 1 and
X am i bm1 ... X a1 i
(b1 ,...bm 1;a1 ,...am ) , i
1 ,... n 1 ;1 ,... n D ,...
1
M X ...X
n
n 1
1
1 n 1 ;1 ,... n
X am i bm 1 ... X a1 i M X n n 1 ... X 1
(33)
M X am i bm 1 ... X a1 i M X n n 1 ... X 1
M X i bm 1 ... X i
am a1
1 N 1 ( ,... n 1 ;1 ,... n )
D ( (1)
j)
(1)1
1 1
, (b(1)1...bm 1;a1...am ) , i
11(1) 1 1
520
1 M ( ) p '1
(l )
p 'l( l)1 '1( l ) 'l( l )
... ... D p(l ) ... p(l ) (l ) ... (l )
1 l 2 p1( l ) 1 pl(l )1 pl(l )2 11( l ) 1 l( l ) 1 1 l 1; 1 l
( ,... n 1;1 ,... n )
(l1)
p1 ... pl(l )1;1( l ) ...l( l )
, (pb(1l ,...
)
bm 1 ;a1 ,...am )
... p ( l ) ( l ) ... ( l )
, i
1 l 1; 1 l
n 1 p '1
(l )
p 'l( l)1 '1( l ) 'l( l )
... ... D p(l ) ... p(l ) (l ) ... (l )
l 2 p1( l ) 1 l 1; 1
pl(l )1 pl(l )2 11( l ) 1 l( l ) 1 1 l
( ,... n 1;1 ,... n )
(l1)
p1 ... pl(l )1;1( l ) ...l( l )
, (pb(1l ,...
)
bm 1; a1 ,...am )
... p ( l ) ( l ) ... ( l )
, i
1 l 1; 1 l
p1*( n ) pn*(n1) 1*( n ) n*( n )
... ... D p( n ) ... p( n ) ( n ) ... ( n )
n 1; 1
pl(n1) pl(n2) 11( n ) 1 n( n ) 1
n
p1( n ) 1 1
( ,... ; ,... ) , 1, I .
( n1) n(n1) 1( n ) n( n ) , (1n ) m(n1) 1( n ) m ( n ) , i
(b ,...b ;a ,...a )
p1 ... pn 1;1 ... n p1 ... pn 1;1 ... n
Tipping in the expression (3) of known values X ( ) x( ), 1, k converts the a
priori random sequence into the a posteriori one:
X i M X i mx( I N 1, I N 2,..., I 1;1,1...1, ) 1, i
i 1 N 1
V (1) (1) , i V1 i
(1)
k 11(1) 1 1 1
(34)
i 1 M ( ) p '1
(l )
p 'l(l)1 '1(l ) 'l(l )
... ... V p(l ) ... p(l ) (l ) ... (l )
k 1 l 2 p(l ) 1 p(l ) p(l ) 1 (l ) 1 (l ) 1 1 l 1; 1 l
1 l 1 l 2 1 l
(1)(l )
p1 ... pl(l )1;1(l ) ...l(l )
, i , i k 1, I .
Values of conditional expectation are defined as
( x i mx( 1...n 1;1...n , ) b1...bm1; a1...am , i
521
M X am (i b )... X a1 (i ) , 0;
m 1
( *1... *n 1; *1...... *n , )
mx b1...bm1; a1...am , i x n n1 ...x1
m( 1... n 1; 1...... n , ) ... ; ... ,
* * * *
n 1 1
x 1 n
(b ...b ;a ...a )
x i 1... m 1; 1......m , i ,if *1 0,..., *n 0;
1 n 1 1 n (35)
( p '( n 1) ... p'( n 1) ; '( n 1) ... '( n 1) , )
mx 1 n2 1 n 1
b1...bm1; a1...am , i x n n1 ...
1
...x mx
( p1'( n 1) ... pn'( n 21) ;1'( n 1) ... n'(n11) , )
1... n1;1... n ,
1 m 1 1 m , i , if * 0,..., * 0.
( b ...b ; a ...a )
1... n 1;1...... n 1 n
Technology of predictive control of fail-safe operation on the model (35) is the
same as using the expression (15).
4 Conclusion
Thus, there we obtained an calculation method for the estimation of the probability
of fail-safe operation of information systems in the future instants of time. The tech-
nology is based on the model of the canonical expansion of the a posteriori random
sequence of changes of the parameter controlled. Estimation of the probability of fail-
safe operation of a information system based on the results of the numerical experi-
ments is determined as a relative frequency of an event characterized by belonging of
the realization to the allowable region on the forecast interval. The calculation method
offered does not impose any significant constraints on the class of random sequences
analyzed (linearity, stationarity, Markov behaviour, monotoneness, etc.). The only
constraint is the finiteness of variance that is usually performed for real random pro-
cesses. In contrast to the known solutions [12], [13] the suggested estimation proce-
dure for fail-safe operation of information systems allows for nonlinear stochastic
properties of the random sequence analyzed, which improves the accuracy of the pre-
dictive control procedure.
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523
Distributed Datastores: Towards Probabilistic
Approach for Estimation of Reliability
Kyrylo Rukkas and Galyna Zholtkevych
V.N. Karazin Kharkiv National University
4, Svobody Sqr., 61022, Kharkiv, Ukraine
galynazholtkevych1991@gmail.com
Abstract. This paper focuses on the contradiction that follows from
Brewer’s Conjecture for distributed datastores: the need to deliver qual-
itative data to the user requires a guarantee of consistency, availability
and stability of the system at the same time, but Brewer’s Conjecture
claims that this is impossible. To overcome this contradiction in the pa-
per it is suggested to estimate statistically violation of these guarantees.
To implement this idea the interdependencies between the guarantees
and indicators of information quality are considered, different kinds of
models specifying the general architecture and behaviour of datastores
are described, and, finally, the basic metrics of guarantee ensuring are
defined. This consideration allows us to formulate several problems that
have both theoretical aspects and engineering applications for the im-
provement of the technology of distributed data processing.
Keywords: distributed datastore, CAP-theorem, information quality,
statistic metrics, simulation
Key Terms: DistributedDataWarehousing, ConcurrentComputation
1 Introduction
Nowadays, any kind of human activity requires an infrastructure to support effi-
ciently the corresponding process of decision making. A modern answer to such
a requirement is an information system that is an integrated set of components
to collect, store and process data, to deliver information, knowledge, and digi-
tal products. Today the development trend of Information and Communication
Technology is a wide use of networking technologies. Therefore a typical modern
information system is a distributed data processing system with a distributed
datastore.
Now it is generally accepted that a distributed datastore should guarantee
the following properties: consistency (C), availability (A), and partition tolerance
(P). They are discussed in papers [5] and [1], but this discussion is too implicit.
These works had been critically reviewed in [2]. This criticism is based on the fact
that nobody had so far given explicit and rigorous definitions of these guarantees.
Taking into account this remark we accept the following understanding as the
origin point of our research:
524
consistency means that all replicas of any data unit contain the same data at
the same time point;
availability means that a datastore eventually returns a response (either a
success report or a failure notification) on each request;
and finally, partition tolerance characterizes the ability of a datastore to con-
tinue to operate despite arbitrary message losses or failure of part of the
system (sometimes to refer to this ability the more general concept fault-
tolerance is used).
In the ideal case a distributed datastore should provide these guarantees.
In contrast to relational datastores like SQL databases that satisfy ACID prop-
erties and ensure the system safety, non-relational datastores do not provide
complete safety for the information system. As known Brewer’s conjecture [5],
being called sometimes CAP theorem, says that it is impossible to maintain si-
multaneously all three CAP-guarantees in asynchronous or partially synchronous
network and maintain safety in this way. Taking into account that synchroniza-
tion of a distributed datastore decreases essentially system throughput we study
consequences of Brewer’s conjecture for asynchronous distributed datastores.
A lot of research had been wasted at the consideration of CAP-guarantees.
As it is impossible to implement all three of them, we suggest a new approach:
to characterise stochastically that each of these requirements is fulfilled or not
(see Sec. 5) and do the best for a consumer - provide him with mechanisms used
in different datastores for restoring the validity of the CAP-guarantees.
This supposition leads us to the need to develop a simulation framework for
supporting numerical experiments to study these mechanisms.
As we said above, the principal objective for an information system design
process is to provide a consumer with qualitative information just in time. There-
fore we should understand how information quality (IQ) and the CAP-guarantees
are connected. In order to clarify this interconnection we give some model of in-
formation quality and determine its indicators that depend on providing the
CAP-guarantees in Sec. 2.
In Sec. 4 we present the conceptual model of a distributed datastore proposed
as a background for the framework that should be developed. In Sec. 3 we dis-
cuss briefly the models for maintaining the consistency property in distributed
systems. And finally, in Sec. 5 we give rigorous definitions for stochastic criteria
of the CAP-guarantees providing, which is based on the presented conceptual
model.
Further to avoid cumbersome formulations we shall say ”CAP-properties”
instead of ”ensuring CAP-guarantees”.
2 Interrelations between IQ model and CAP-properties
The problem to identify Information Quality (IQ) model was widely described
and discussed in [3], [8], [4]. On our opinion, this discussion had been compactly
summarized in [7]. The information represented in these sources correlates with
525
data quality standards in [6]. Below we give the list of IQ indicators according
to this paper:
accessibility is the indicator that characterises the extent of availability and
fast retrievability of information;
appropriate amount of information is used to denote if the scope of infor-
mation is appropriate for the task at hand;
believability means that the information is considered as true and credible;
completeness evaluates whether information is sufficiently broad and deep to
solve the task at hand;
concise representation characterises the compactness of data representation;
consistent representation means that all the information processes operate
with the same data;
ease-of-manipulation envisages that information is easy manipulated and
applied to different tasks;
free-of-error means that information is correct and reliable;
interpretability characterises that information is in appropriate languages,
symbols and units, and the definitions are clear;
objectivity denotes that information is considered as unbiased and impartial;
relevancy envisages that information is applicable and helpful for the task at
hand;
reputation determines that information should be highly regarded in the terms
of its source or content;
security is satisfied if the access to information is restricted appropriately in
accordance with the access rights;
timeliness is fulfilled if information is up-to-date for the task at hand;
understandability means that information is well-comprehended;
value-added assumes that information is beneficial and provides advantages
from its use.
These indicators are used to define different views of an information system.
We stress that the consideration is given from the next points of view: product
and service quality. These quality indicators are also classified taking into ac-
count different views, namely, system specifications and consumer expectations.
Therefore they had been grouped in a two-dimensional Table 1 presented below.
(See more complete description of this classification in [7]).
Focusing on our subject, we consider only those of indicators, that depend
on CAP-properties. Let us explain the reasons that has motivated us to take
exactly these indicators of IQ model.
Obviously, by the definition the consistency has the direct impact on the
consistent representation indicator. Also, consistency ensures the correct infor-
mation, thus the free-of-error indicator directly depends on it. Furthermore, if
the consistency is fulfilled, there may be a lot of replicas in the system, that
is decreasing the concise representation indicator. And one can simply see that
the consistency definition involves up-to-date information and then timeliness
immediately depends on the consistency. Consistency does not have an influence
526
Table 1. Information Quality Model
Conforms to Specifications Meets or Exceeds
Consumer Expectations
Product Sound Information: Useful Information
Quality
– Free-of-Error – Appropriate Amount
– Concise Representation – Relevancy
– Completeness – Understandability
– Consistent representation – Interpretability
– Objectivity
Service Dependable Information: Usable Information:
Quality
– Timeliness – Believability
– Security – Accessibility
– Ease-of-Manipulation
– Reputation
– Value Added
on the accessibility, because if the consistent information is received, it does not
necessarily mean that it was retrieved quickly and easily.
Now we tell about the availability interrelations. Firstly, reasoning from the
availability definition (see Sec. 1) the accessibility directly depends on the avail-
ability measurement. Secondly, the free-of-error indicator definition involves re-
liable data that is delivered just-in-time, so it also has a direct dependence on
the availability. Evidently, it does not impact on the consistent representation
and concise representation indicators; also it is not tightly connected with the
timeliness indicator. Further in this paper we shall determine availability more
strictly: we shall denote the availability as the meantime between a request and
the response on it. And following from that definition, with improving availabil-
ity the speed of retrieving data is increased, but it does not mean that these
data are up-to-date.
The last group of interrelations is about the partition tolerance. It has an
impact on the consistent representation, free-of-error, accessibility and timeliness
quality indicators. The thing is that the perfect partition tolerance fulfillment
ensures the successful response from a distributed datastore. In its turn, the
successful response must always contain consistent, correct, reliable and up-to-
date information. Otherwise the system answer is counted as an error message.
Therefore greater probability to get the successful response gives higher values
of indicators mentioned above.
Evidently, it does not have any influence on the concise representation in
contrast to the consistency.
We summarize this connection in Table 2.
The endorsement of some interrelations and the discovering their behaviour
can be obtained by the further experiments. The rest of indicators of IQ model
527
Table 2. Interrelations between IQ Indicators and CAP-requirements
Consistency Availability Partition Tolerance
Consistent + +
representation
Free-of-Error + + +
Concise +
representation
Accessibility + +
Timeliness + +
depend on the quality of the information system that provide information datau-
nits and we are not interested in them.
3 Brief overview of Models for Distributed Systems
The distributed datastores are various, therefore it is necessary to have tools for
their analysis. The simplest classification is related to the ratio of read and write
operations quantity. This classification should be reasonable from the point of
view of three pillars that maintain all distributed systems: consistency, availabil-
ity, partition tolerance. Hence the list will be as follows:
– Systems with domination of read operations (decision support or retrieval
systems);
– Systems with domination of write operations (online transaction processing
systems);
– Systems without explicit domination of read or write operations (business
systems).
This classification is based on the quantity of read and write operations. It is
important to know for us, because it may require different mechanisms for each
type of system.
In this section we tell about the way to verify consistency and maintain the
probability of its fulfillment following [10, Chapter 7]. An appropriate way to
increase this probability is replication – making copies of new data units at each
node and their updating.
Traditionally, consistency is discussed in the context of read and write op-
erations in distributed systems. Following the book mentioned above there are
two consistency models for different distributed systems: data-centric and client-
centric ones. They are applied for different types of distributed systems. The first
one, data-centric consistency model is a model for wide usage: online transaction
and business systems mentioned above. It involves many types of consistency,
such as continuous, sequential, causal and combined one, called grouping opera-
tions. The protocols for these consistency types are more complex than protocols
in the second model. That is because data-centric model should be usable for
systems where a lot of write operations may occur and spoil all the data units.
528
For instance, imagine if two employees in a company use the same datastore.
They need to modify some file. And, unfortunately, it turns off that two employ-
ees download the file from the data storage and modify it in a different way and
in different places. First one upload the file back and later the second one does
the same. But the problem is that the file is modified in different places and
there will be some conflicts. This is the simplest example, but if this datastore is
distributed on many servers, there are a lot of copies of files in the data storage
and more people use the same distributed system, it causes a complete mess in
the storage. Therefore these protocols for controlling consistency should prevent
such errors when a lot of write operations may occur.
The second one, client-centric model, is used for retrieval systems, where
mostly read operations occur, but write ones are rare. Thus it is very costly and
not necessary needed to use complex protocols. That is why for this model there
exist such a type of the consistency as eventual consistency that ensures such a
guarantee for the distributed system that eventually all the data units become
same and consistency is fulfilled. The protocols for the client-centric model are
also invented (see more in [10, Chapter 7]).
So as soon as we described different types of distributed datastores and es-
tablished the problem to use different models and protocols for datastores that
we focused on, we can go to the next section, where we specify the architecture
and important behaviour elements for a distributed datastore.
4 Conceptual and Behavioral Model of Distributed
Datastore
Above we described the general accepted model of the information quality that
determines indicators which are needed for our research purpose, described mod-
els that are used for distributed datastore to satisfy consistency guarantees. But
in order to come to the estimation step for the distributed datastore guarantees,
obviously, we should also discuss the model of a distributed datastore.
Therefore in this section we represent the model of such systems in two views:
structural and behavioural. Below there is given the structural one (Fig. 1).
The main component of our system is a distributed datastore. By definition
it is a set of nodes (servers) connected by links between each other. Each node
may have one or more neighbours. That is why this entity is composed of nodes
and links. Obviously, each link is two-sided and a node entity may have many
incidences.
Every node stores data units in replicas. If a node receives a new data unit
it finds the data unit with the same identifier and replaces the old replica.
Nodes are classified into ready, busy and dead ones. If a node is busy or dead
it ignores all the messages, so in this case the request will be lost. That is why
the behaviour in this case is trivial.
The behaviour of a ready node is represented below, in the activity diagram
(see Fig. 2).
529
Request to Response
1 1
receives sends
DistributedDatastore
2..m 1..n
Node incidence Link
2 *
1
allocation
1..*
Replica replication DataUnit
1..* 1
Fig. 1. Conceptual model
To present the behaviour in clear and understandable way, we separate more
complex method of node handle request from the general behavioural view and
show it in Fig. 3.
5 Distributed Datastores: Basic Prerequisites and
Metrics
As said above the leading idea of this paper is to suggest an approach for esti-
mating probabilistic metrics of CAP-properties.
It is generally accepted (see [9]) that a distributed datastore is a computer
network where information is stored on more than one node, often in a replicated
fashion.
Moreover, it is important to mention that a researcher has the possibility to
observe datastore events in the sequence according to physical time while each
530
Node behaviour
receive
request
search required [dataUnit has been found]
handle request
dataUnit on the node
[dataUnit has not been found]
redirect
request
Fig. 2. Behaviour of node
Handle request
[write] [read]
update required read
dataUnit on this node required dataUnit
send
response
send
response
broadcast updating
for all dataUnit replicas
Fig. 3. Behaviour of handle request method
531
datastore node considers the sequence of events with respect to its local time
only. Also we assume that datastores at study meet the eventual consistency
requirement [10]. It means that after an isolated read request for any data unit
all its replicas eventually have the same value.
Let us represent a short case study in order to understand the motivation to
apply the probabilistic approach in asynchronous distributed datastore.
Let us suppose that there is the unreliable node in a distributed system that
fails and recovers over over some time. At the initialization moment when nodes
are established each node has the probabilistic distribution of recovering time
and time of failure. In a distributed system links that bind nodes may also fail.
To be able to calculate the probability of partition tolerance fulfillment we need
to take into account these distributions in our research.
For now we are ready to describe how we apply the probabilistic approach
in our studying by giving the rigorous definitions of CAP-properties. To do this,
we describe a distributed datastore using the following mathematical model.
Our model is a tuple (N, L, ∂, D, r), where
N is a finite set, whose elements correspond to nodes of a dis-
tributed datastore;
L is a finite set, whose elements correspond to links of a distributed
datastore;
∂ : L → 2N is a mapping that associates each link with two nodes that it
connects;
D is a finite set, whose elements correspond to stored data units;
r : D → 2N is a mapping that associates each data unit d with a subset of
nodes that store its replica.
Thus, firstly, let us introduce the consistency metric. Taking into account
that the consistency is the property when for each data unit its replicas have the
same value, we shall consider the probability that all data units at distributed
datastore are consistent at a certain time moment. Therefore we define the con-
sistency metric in the following manner.
Definition 1 (Consistency metric). Let σt ∈ {0, 1} be the random variable
that represents one of two events at time point t ≥ 0:
σt = 0 corresponds to the event “there exists a data unit that is not
consistent at the time point t” and
σt = 1 corresponds to the event “all data units are consistent at the time
point t”.
Then the consistency metric C(t) at time point t is defined by the formula
C(t) = Pr(σt = 1) . (1)
The second metric estimates the availability guarantee. We propose to mea-
sure the extent of availability as meantime between two events: the request has
been received by the datastore and the corresponding response 1 has been sent
by the datastore. More, formally:
1
This response is either a successful report on request or an error message.
532
Definition 2. Let τt be the time interval between a request receiving at the time
point t and the corresponding response. Then the mean response time is defined
by the formula
T (t) = E[ τt ] . (2)
Finally, to estimate the third guarantee, called the partition tolerance, we
consider the ability of a datastore to survive network partitions, so that the
performance of the datastore does not suffer. This definition is more complicated.
Let us consider some time point t . At this instant some nodes are alive, but other
ones failed. We denote by Nta the set of alive nodes (Nta ⊂ N ). Similarly, we
denote by Lat the set of alive links that connect alive nodes.
Definition 3. We shall say that a data unit d ∈ D is reachable from a node
n ∈ Nta at time a a
T point t if there exists a path in the graph (Nt , Lt ) from n to
′ a
some n ∈ Nt r(d) .
Now we can introduce the metric for the partition tolerance using the previous
definition.
Definition 4. Let ζt ∈ {0, 1} be the random variable that represents one of two
events at time point t ≥ 0:
ζt = 0 corresponds to the event “there exists a data unit that is not
reachable from some alive node at time point t” and
ζt = 1 corresponds to the event “all data units are reachable from any
alive node at time point t”.
Then the partition tolerance metric P (t) at time point t is defined by the formula
P (t) = Pr(ζt = 1) . (3)
6 Conclusion
In this paper we have started studying the problem of the quality for distributed
datastores. We have proposed the approach to measure the quality properties
of a datastore. Therefore we have described CAP-properties and have built the
metric system for CAP-properties estimation. We have described the indicators
of the information quality and have found interrelations between the information
quality and distributed datastores’ properties basing on [7].
In order to have a view of the datastore and be able to work with it we
have built its structural and behavioural model and based on this knowledge,
we specified probabilistic characteristics for CAP-properties measurement.
Thus, the following steps for the problem set in the paper have been done:
– Formulation of understanding the idea: what are CAP-guarantees for dis-
tributed datastores indeed;
– Description of the information quality indicators;
– Investigating the connection between CAP-guarantees and information qual-
ity model;
– Building the structural and behavioural models for a distributed datastore;
533
– Forming ”CAP-metrics” as the main idea for studying the quality of dis-
tributed datastores.
These steps give us possibilities to study CAP-properties fulfillment using
the following background: the fault-tolerance mechanisms for asynchronous sys-
tems, concurrent programming, algorithms of data propagation in distributed
systems, probably, some issues of internet strategy, Queueing Theory, Mathe-
matical Statistics. Fault-tolerance protocols can be used to invent the algorithms
for maintaining the partition tolerance guarantee. Obviously, a researcher should
have the good background in Graph Theory, Probability Theory and Concurrent
Programming in asynchronous distributed systems. Also, as we need to repre-
sent experimental results, it is necessary to imitate the model of a distributed
datastore.
Summing up now we might set following problems:
– To simulate the model of a distributed datastore;
– To study different mechanisms to estimate the degree of ensuring each guar-
antee applying specified metrics;
– To analyse discovered mechanisms and their composition;
– To integrate these mechanisms with simulated asynchronous distributed
datastore;
– To estimate theoretically the total time complexity for all provided mecha-
nisms;
– To carry out the experimental estimation.
Acknowledgment. Authors express a deep gratefulness to Grygoriy Zholtkevych
and Iryna Zaretska for their help and their criticism.
References
1. Brewer, E.: CAP Twelve Years Later: How the ”Rules” Have Changed. Computer,
IEEE Computer Society. Vol. 45, No. 2 (2012)
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markburgess.org/blog_cap.html (2012)
3. CRG. Information Quality Survey: Administrators Guide. Cambridge Research
Group, Cambridge, MA (1997)
4. English, L.P.: Information Quality Applied: Best Practices for Improving Business
Information, Processes and Systems. Wiley (2009)
5. Gilbert, S., Lynch, N.: Brewers Conjecture and the Feasibility of Consistent, Avail-
able, Partition-Tolerant Web Services. ACM SIGACT News. Vol. 33, No. 2, pp.
51–59 (2002)
6. ISO 8000-1:2011. Data Quality. International Organisation for Standartization
(2011).
7. Kahn, B.K., Strong, D.M., Wang, R.Y.: Information Quality Benchmarks: Product
and Service Performance. Comm. ACM. Vol. 45, No. 4 (2002)
8. Kovac, R., Lee, Y.W., Pipino, L.L.: Total data quality management: the case of
IRI. Conf. on Information Quality (Cambridge, MA), pp. 63–79 (1997)
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9. Pessach, Ya.: Distributed Storage: Concepts, Algorithms, and Implementations.
CreateSpace Independent Publishing Platform (2013)
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(2nd Edition). Prentice-Hall, Inc. (2006)
535
Direct Partial Logic Derivatives in Analysis of
Boundary States of Multi-State System
Elena Zaitseva1, Vitaly Levashenko1, Jozef Kostolny1, Miroslav Kvassay1
1
University of Zilina, Department of Infromatics, Univerzitna 8215/1,
010 26, Zilina, Slovakia
{elena.zaitseva, vitaly.levashenko, jozef.kostolny,
miroslav.kvassay}@fri.uniza.sk
Abstract. Multi-State System (MSS) is mathematical model that is used in
reliability engineering for the representation of initial investigated object
(system). In a MSS, both the system and its components may experience more
than two states (performance levels). One of possible description of MSS is a
structure function that is defined correlation between a system components
states and system performance level. The investigation of a structure function
allows obtaining different properties, measures and indices for MSS reliability.
For example, boundary system’s states, probabilities of a system performance
levels and other measures are calculated based a structure function. In this paper
mathematical approach of Direct Partial Logical Derivatives is proposed for
calculation of boundary states of MSS.
Keywords. Multi-State System, Multiple-Valued Logic, Direct Partial Logic
Derivatives, Boundary State
Key Terms. Reliability, Model, Approach, Methodology, ScientificField
1 Introduction
Reliability is a principal attribute for the operation of any modern technological
system. A principal issue in reliability analysis is the uncertainty in the failure
occurrences and consequences. With respect to the complexity of the system and the
modeling of their behavior, a distinctive feature of the system reliability analysis is a
comprehensive and integrated manner [1]. Focusing on safety, reliability engineering
methods aim at the quantification of the probability of failure of the system. In paper
[1] presents detail analysis of reliability engineering state and define principal
problems in this scientific discipline. According to [1] one direction of reliability
engineering is estimation of a complex system based on Multi-State System (MSS)
reliability analysis methods.
MSS is mathematical model used in reliability analysis for system with some
(more that two) levels of performance [1, 2]. This mathematical model has been
exploited in reliability engineering since 1975 [3-5]. Principal advantage of this
mathematical model is detail description of investigated object. MSS permits to
536
define and investigate several performance levels: from perfect function to fault. The
typical Binary-State System allows evaluating only two system states as functioning
and failure. Other states, for example, as partly functioning or functioning with
restrictions are not analyzed in case of Binary-State System use. But extra states and
performance levels in the mathematical model dramatically increase size of this
model and computational complexity of its analysis. Therefore the MSS has not been
used intensively in reliability analysis. There is other aspect to restrict the application
of MSS. It is absent of effective methods for MSS analysis.
According to analysis in paper [2] there are four groups of methods for MSS
analysis that are based on different mathematical approach: an extension of Boolean
models to the multi-valued case, the stochastic process as Markov process, the
universal generation function methods and the Monte-Carlo simulation techniques.
For example, Markov processes are used to analyze the system state transition process
[6]. The universal generation function application is useful in optimization problem
[7]. The Monte-Carlo simulation as a rule is used for reliability assessment of system
with large number of components [8]. The methods based on extension of Boolean
models to the multi-valued case were developed historically the first [9, 10].
According to these methods MSS is represented and defined by the structure function.
This function is defined the conformance of the system performance level and
components states. As a rule for the structure function definition and representation is
used Boolean functions [10, 11]. Only in separated publications the structure function
with some values has been considered [9, 12]. In papers [13, 14] the correlation of
Miltiple-Valued Logic (MVL) function and structure function was analyzed. The
interpretation of the structure function as the MVL function allowed using the
mathematical approach of MVL in the analysis of the MSS structure function. In
paper [14] the application of Logical Differential Calculus for MSS reliability
analysis has been proposed. The Logic Differential Calculus is used for analysis of
dynamic properties of MVL function and this approach can be applied for analysis of
dynamic behaviour of MSS that is determined by the structure function.
In the paper [14] the basic conception of application of Direct Partial Logic
Derivatives (it is part of Logical Differential Calculus) in MSS reliability analysis has
been considered. The proposed method permits to investigate the influence of one
system component state change to the system performance level. The new indices for
quantitative analysis of such influence have been defined. The application of these
derivatives for calculation of importance measures (Structural Importance, Birnbaum
Importance and Criticality Importance) has been investigated in paper [15, 16]. The
algorithm for calculation of Fussell-Vesely Importance based on Direct Partial Logic
Derivatives has been proposed in [17].
In this paper new application of Direct Partial Logic Derivatives for MSS
reliability analysis based on the structure function is considered. The new algorithm
for calculation of boundary states of MSS is proposed. This algorithm is based on
representation of MSS by the structure function (section 2). This section includes the
conception of boundary states of MSS for every performance level. The special
structures of MSS (parallel and series) and their structure function are considered in
the section 2 too. These types of system are typically employed in reliability analysis
[18]. The short description of conceptions of Direct Partial Logic Derivatives with
respect to one variable and with respect to variable vector are presented in the section
537
3. The calculation of MSS boundary states for every system performance level is
considered section 4.
2 MSS Structure Function
2.1 Structure Function of MSS
Consider the system of n components. Each component of this system has m
states: from the complete failure (it is 0) to the perfect functioning (it is m-1). The i-th
system component state is denoted as xi (i = 1, …, n). Suppose, that this system has m
performance level too: from the complete failure (it is 0) to the perfect functioning (it
is m-1). The dependence of the system performance level on components states is
defined by the structure function (x) identically:
(x1, x2,…, xn) = (x): {0, 1, …, m-1}n {0, 1, …, m-1}. (1)
The function (1) agrees with the definition of a MVL function [19]. Therefore the
mathematical approaches of MVL can be used in quantification analysis of MSS. But
the structure function (1) allows representing the very small class of real system for
which the number of system performance levels and number of every component
states are equal. As a rule, the real-world system has different numbers of states for
different components. And the number of performance levels can be different too.
Therefore the structure function of real-word system must be defined as:
(x): {0, 1, …, m1-1}…{0, 1, …, mn-1} {0, 1, …, M-1}, (2)
where mi is number of states for i-th system component (i = 1, …, n) and M is number
of a system performance levels.
The equation (2) can be interpreted as a MVL function. But some formal changes
allow transforming this structure function definition into an incompletely specified
MVL function. This transformation suppose the interpretation of the function (2) as
incompletely specified MVL function for maximal value of number mi and M:
mmax=MAX{m1, …, mn, M}. In this case, the structure function (2) is defined as:
`(x): {0, 1, …, mmax-1}n {0, 1, …, mmax -1}. (3)
The interpretation of the structure function (2) as an incompletely specified MVL
function (3) permits to use mathematical approaches of MVL without principal
restriction for analysis of properties of the structure function (2).
538
For example, consider the simple service system (Fig. 1) in a region from paper
[17]. This system consists of three components (n = 3) – service point 1 (x1), service
point 2 (x2) and infrastructure (x3). This system has four performance levels: 0 – non-
operational (no customer is satisfied), 1 – partially operational (some customers are
satisfied), 2 – partially non-operational (some customers are not satisfied), 3 – fully
Fig. 1. A simple service system.
Table 1. The structure function of the simple service system
Components states x3
x1 x2 0 1 2 3
0 0 0 0 0 0
0 1 0 1 1 2
1 0 0 1 1 2
1 1 0 2 3 3
Table 2. The structure function of the simple service system represented as an incompletely
specified MVL function
Components states x3
x1 x2 0 1 2 3
0 0 0 0 0 0
0 1 0 1 1 2
0 2
0 3
1 0 0 1 1 2
1 1 0 2 3 3
1 2
1 3
2 0
2 1
539
2 2
2 3
3 0
3 1
3 2
3 3
operational (all customers are satisfied). Next, we assume that the service points are
only functional (state 1) or dysfunctional (state 0). The infrastructure can be modelled
by 4 quality levels, i.e. from 0 (the quality of the infrastructure is poor) to 3 (the
quality is perfect). The structure function of this system according to (2) is defined in
Table 1 (m1 = m2 = 2, m3 = 4 and M = 4). The structure function of this system as an
incompletely specified MVL function is shown in Table 2 (mmax = 4).
2.2 Series and Parallel MSS
There are some typical structures in the reliability engineering: series, parallel, k-
out-of-n and bridge. Every system of these structures has single valued definition for
Binary-State System (Fig.2).
The series system: The k-out-of-n system:
n
(x) = i1 xi (x) = ( z k xi )
z
x1
x1 x2 … xn
x2 k/n
…
xn
The parallel system:
n
(x) = x
i 1 i
The bridge system:
(x) = (x1x2)(x4x5)(x1x3x5)(x2x3x4)
x1
x1 x2
x2
… x3
xn x4 x5
Fig. 2. Graphical and mathematical interpretation of typical structures of Binary-State System.
The extension of mathematical definition of the structure functions of these
system for the MSS has some variants. For example, in paper [24] the structure
functions of series, parallel and k-out-of-n MSS are defined based on the
interpretation of mathematical equations of these system in terms of MVL. Structure
540
functions of these MSS in MVL terms are declared by OR () and AND () MVL
functions: OR(a, b) = MAX(a, b) and AND(a, b) = MIN(a, b). According to [24]
structure functions parallel, series and k-out-of-n MSS are declared
- for parallel MSS as:
n
(4)
(x) = x = MAX(x1, x2, …, xn),
i 1 i
- for series MSS as:
n
(5)
(x) = i1 xi = MIN(x1, x2, …, xn),
- for k-out-of-n MSS as:
(x) = ( zk xi ) MAX(MIN1 ( xi , xi ,...,xi ),...,MIN w ( xi , xi ,...,xi )) ,
z 1 2 k 1 2 k
(6)
w n!/(k!(n k )!) .
In paper [27] other declaration of these MSS are presented in which a system
performance level depends on the number of functioning components. In Table 3
some structure functions of parallel MSS of two components (n = 2) with three states
(m1 = m2 =3) and three performance level (M = 3) are shown. All these structure
function in case of Binary-State System are parallel system. The series MSS can be
defined similarly.
Table 3. The structure functions of parallel MSS (n = 2, m1 = m2 = M = 3)
Components states Structure function of parallel MSS
x1 x2 1(x) 2(x) 3(x) 4(x)
0 0 0 0 0 0
0 1 1 1 1 1
0 2 2 1 1 1
1 0 1 1 1 1
1 1 1 2 1 1
1 2 2 2 1 2
2 0 2 1 1 1
2 1 2 2 1 2
2 2 2 2 2 2
Therefore the typical structures of MSS have no single valued mathematical
definition, because there are the set of structure functions of MSS that can be agreed
with one Binary-State System. The structure function allows defining MSS explicitly.
Therefore the structure function is preferable form of MSS mathematical
representation.
541
2.3 Boundary States of MSS
The conception of boundary states has been proposed for Binary-State System
firstly. The boundary state is defined as state for which the failure of one system
components or some components causes the fault of a system [20]. The boundary
state of MSS must be defined for every system performance level [2]. In papers [21,
22] the boundary states of MSS are interpreted as minimal cut/path sets. Authors of
[23] introduced conception of Lower (Upper) Boundary Points of MSS for system
performance level j (j =0, …, M-1). The boundary states for system performance level
j and component i (i = 1, …, n) (named as exact boundary states) has been proposed
and considered in papers [24, 25]. In paper [26] and [17] the correlations of these
boundary states with Lower (Upper) Boundary Points and minimal cut/path sets are
shown accordingly.
The exact boundary states have been considered in paper [25]. These states are
system states for which the change of the i-th component state from s to ~ s causes the
~ ~ ~ ~
system performance level change from j to j (s, s {0,…, mi -1}, s s and j, j
~
{0,…, M -1}, j j ). The exact boundary state is defined by the exact boundary
vector unambiguously. Illustrate the correlation of a system exact boundary state and
an exact boundary vector by the example for the service system in Fig.1.
Determine the exact boundary states of this service system for which the failure of
the first component causes the system failure as the change of the system performance
level from state “1” to “0”. According to Table 1, there are two situations that agree to
this condition. They are possible for the failure of the second component and the third
component state “1”or “2”. These exact boundary states can be presented as vector
states: x = (x1, x2, x3) = (1 0,0,1) and x = (x1, x2, x3) = (1 0,0,2). Note that the
boundary state x = (x1, x2, x3) = (1 0,0,3) does not satisfy the condition because the
system performance level changes from “1” to “2” depending on the failure of the
first component in this case.
One of possible mathematical approaches for the definition of the exact boundary
states in MVL is Logical Differential Calculus, in particular the Direct Partial Logical
Derivatives. Consider the application of this mathematical approach for analysis of
structure function of MSS.
3 Direct Partial Logical Derivatives
3.1 Direct Partial Logical Derivative with respect to one variable
The mathematical tool of Direct Partial Logic Derivatives has been proposed in
[25] for calculation of an exact boundary states of a MSS. The Direct Partial Logic
Derivative with respect to variable xi for the structure function (1) permits to analyze
~
the system performance level change from j to j when the i-th component state
changes from s to ~s :
542
1, if ( si , x ) j and (~ ~ (7)
~ ~ si , x ) j
( j j ) xi ( s s )
0, other ,
where (si , x) = (x1,…, xi-1, s, xi+1,…, xn); ( ~s , x) = (x1,…, xi-1, ~s , xi+1,…, xn); s,
~ ~ ~
s {0,…, mi -1}, s ~ s and j, j {0,…, M -1}, j j .
For example, investigate the influence of the first component failure to the fault of
the simple service system in Fig.1. The Direct Partial Logic Derivative
(10)/x1(10) allows to calculate the system state for which this failure causes
the system break down. The calculation of this derivative is shown in Fig.3 in form of
flow graph. The derivative (10)/x1(10) has two non-zero values that agrees
with state vectors: x = (x1, x2, x3) = (1 0,0,1) and x = (x1, x2, x3) = (1 0,0,2).
According to definition of the Direct Partial Logic Derivative (7) for these system
state the failure of the first system component causes the system failure too. Therefore
the service system fails after the failure of the first service point if the second service
point isn’t functioning and the functioning of the infrastructure conforms to state one
or two. The system states x = (x1, x2, x3) = (1 0,0,1) and x = (x1, x2, x3) =
(1 0,0,2) are exact boundary states for the first system component failure and the
system performance level 1.
x1 x2 x3 (x) (10)/x1(10)
0 0 0 0 0
0 0 1 0 1
0 0 2 0 1
0 0 3 0 0
0 1 0 0 0
0 1 1 1 0
0 1 2 1 0
0 1 3 2 0
1 0 0 0
1 0 1 1
1 0 2 1 x = (1 0,0,1)
1 0 3 2 x = (1 0,0,2)
1 1 0 0
1 1 1 2
1 1 2 3
1 1 3 3
Fig. 3. Calculation of the Direct Partial Logic Derivative (10)/x1(10).
The Direct Partial Logic Derivative (7) allows investigating boundary states of a
MSS for which component state xi change from s to ~ s causes the system
~
performance level change from j to j . Therefore, this derivative allows calculating
exact boundary states of the i-th system component for MSS performance level j that
agree to state vectors x = (x1, x2,…, xn). All possible changes of the i-th system
543
component and their influence to MSS performance level can be investigated based
on the Direct Partial Logic Derivative (7). But this derivative permits to investigate
the influence of one component only. The Direct Partial Logic Derivative with respect
of variable vector investigate the system state changes depending on changes of states
of some system components.
3.2 Direct Partial Logical Derivative with respect to variable vector
A Direct Partial Logic Derivatives of a structure function (x) of n variables with
respect to variables vector x(p) = (xi1, xi2, …, xip) reflects the fact of changing of
~
function from j to j when the value of every variable of vector x(p) is changing from
s to ~
s [15]:
1, if ( si ,...,si , x ) j and (~ ~
~ si ,...,~
si , x ) j (8)
( j j ) xi ( s (p) ~
s (p)) 1 p 1 p
0, other .
In (8) a change of value of iq-th variable xi form si to ~si agrees with a change of
q q q
i -th MSS component state form s to ~s (q = 1, …, p and p < n). So, changes of
q iq iq
some components states correspond with change of a variables vector x(p) = (xi1, xi2,
…, xip). Every variable values of this vector changes form si to ~si . So, vector x(p) q q
can be interpreted as components states vector or components efficiencies vector.
For example, consider the simple service system (Fig.1) failure depending on fault
of the first service point and reduction of functioning of infrastructure from state 2 to
1. This system behavior can be presented by the Direct Partial Logic Derivative
(10)/x1(10) x3(21). The calculation of this derivative is shown in Fig.4 by
the flow graph.
The derivative (10)/x1(10) x3(21) has two values and one of them is
non-zero value that agrees with state vector: x = (x1, x2, x3) = (1 0, 0, 2 1). This
state vector define of the service system failure depending on the failure of the first
service point and deterioration of the infrastructure functioning from state 2 to state 1.
Therefore the system state x = (x1, x2, x3) = (1 0, 0, 2 1) can be interpreted as
exact boundary state for the first and the third system components of the system
performance level 1.
The Direct Partial Logic Derivative with respect to variable vector (8) allows
investigating boundary states of a MSS for which simultaneous changes of p
components states from si to ~si (q = 1, …, p and p < n) causes the system
q q
~
performance level change from j to j . Therefore, the Direct Partial Logic Derivative
with respect to variable vector allows calculating exact boundary states for MSS
performance level j of the i-th system component.
544
x1 x2 x3 (x)
0 0 0 0 (10)/x1(10)x3(21)
0 0 1 0 1
0 0 2 0
0 0 3 0
0 1 0 0
0 1 1 1 0
0 1 2 1
0 1 3 2
1 0 0 0
1 0 1 1
1 0 2 1 x = (10,0,21)
1 0 3 2 x = (10,1,21)
1 1 0 0
1 1 1 2
1 1 2 3
1 1 3 3
Fig. 4. Calculation of the Direct Partial Logic Derivative (10)/ x1(10) x3(21).
4 The Calculation and Estimation of Exact Boundary States of
MSS based on Direct Partial Logic Derivatives
The exact boundary state of MSS are defined based on the condition that fixed
system performance level change depending on the appointed change of one system
component state or specified changes of some components states. The Direct Partial
Logic Derivative with respect to one variable (7) and the Direct Partial Logic
Derivative with respect to variable vector (8) can be used to investigate change of the
~
system performance level from j to j that are caused by specified changes of one or
some system components states. These derivatives have non-zero values of the
structure function for system states that satisfy for specified condition: the system
~
performance level change from j to j depending on specified changes of one or some
system components states. Therefor the exact boundary states can be defined as
system states that conform to non-zero values of derivatives (7) and (8).
The exact boundary state for MSS performance level j depending on the i-th
j j
~
system component xi is indicated by vector state x = (x1,…, xi,…, xn) =
s ~s
~
(a1,…, si,…, an) for which (a1,…, si,…, an) = j and (a1,…, ~si ,…, an) = j . This
state is calculate as non-zero value of Direct Partial Logic Derivative (7). The exact
boundary state for MSS performance level j depending on p components xi1, xi2, …,
545
j ~j
xi p xi ...xi is indicated by vector state x = (x1,…, xi ,…, xi ,…, xn) =
s ~s s ~s
1 p 1 p
i1
i1 i p ip
(a1,…, si1,…, si p,…, an) for which (a1,…, si1,…, si p,…, an) = j and
~ ~ ~
(a ,, s ,, s ,, a ) j . This state is calculate as non-zero value of Direct Partial
1 i1 ip n
Logic Derivative (8).
Consider estimation of the system boundary states for coherent MSS. There are
next assumptions for structure function of coherent MSS [2]: (a) the structure
function is monotone and (s)=s (s{0, …, m-1}) and (b) all components are s-
independent and are relevant to the system.
Every system component is characterized by the probabilities of its state:
pi,s = Pr{xi = s}, s = 0, …, mi -1. (9)
.
The probability of every boundary state (a1, …, si, …, an) for MSS performance
level j depending on the i-th system component change from s to ~ s is calculated
based on the probabilities of components states:
j j
~
(10)
p( a ... s ... a ) xi p1,a pi 1,a pi ,s pi 1,a pn,a .
s~s
1 i n 1 i 1 i i 1 n
The probability of boundary state for MSS performance level j depending on the i-
th system component states changes is calculated as:
j j j j
~ ~
(11)
p xi p( a ... s ... a ) xi .
s~s s ,~s s~s
1 i n
Next measure is defined the probability of boundary state of MSS performance
level j depending of all component state change from s to ~
s :
j j n j j
~ ~
(12)
p x p xi .
s~s i1 s~s
The probability of MSS performance level change depending on the change of the
i-th system component from state s to ~
s is calculated according to:
546
j j
~
(13)
p xi p xi .
ss j , ~j s ~s
~
The probability of MSS performance level change depending on all change of the
i-th system component state is generalization of previous equation:
p xi p xi .
(14)
s ,~s s ~s
The similar measures to (10) - (14) can be defined for estimation of exact boundary
j ~j
state for MSS performance level j of p components xi1, xi2, …, xip xi ...xi .
s ~s s ~s 1 p
i1 i1 i p ip
Consider some examples for calculation of measures (10) - (14) for the simple
service system in Fig.1. The components states probabilities for this system are
defined in Table 4. Consider this system failure depending to the first components.
The Direct Partial Logic Derivative (10)/x1(10) represents this system
behavior (Fig.3). This derivative has two non-zero values that conform to two
boundary states x1 : x = (1,0,1) and x = (1,0,2).
1 0
10
Table 4. The components states probabilities of the simple service system
0 Components states
x1 x2 x3
0 1 0 1 0 1 2 3
pi,s 0.3 0.7 0.2 0.8 0.2 0.6 0.1 0.1
The probabilities of boundary states for the system failure depending the first
component break down x1 are calculate according to (10) and are:
1 0
10
p(101) x1 p1,1 p2, 0 p3,1 0.084 and p(102) x1 p1,1 p2, 0 p3, 2 0.014
10 10 (15)
10 10
The probability of boundary state for this system failure depending on the first
component is calculated based on (11) as:
547
p x1 p(101) x1 p(102) x1 0.098 .
10 10 10 (16)
10 10 10
Therefore according to (16) the service system failure depending on the breakdown
of the first service point is 0.098. By the similar way the probability of this system
failure depending on the breakdown of the second service point is calculated and this
probability is p x2 0.098 .
10
10
There are three boundary states for the system failure depending the fault of
infrastructure (the third component): p( 011) x3 0.144 , p(101) x3 0.084 and
10 10
10 10
p(111) x1 0.336 . Therefore the probability the service system fault caused by the
2 0
10
failure of the infrastructure is 0.564.
Other probabilities of this system failure or deterioration of the performance level
are calculated according to (10) – (14) similar.
5 Conclusion
The mathematical background for application of mathematical methods of MVL
for reliability analysis of MSS is considered in this paper. The correlation of the
structure function and MVL function are shown and proved by means of the
conception of incompletely specified MVL function. This background allows using
Direct Partial Logic Derivatives for analysis of MSS structure function.
Mathematical approach of Direct Partial Logic Derivatives in MVL is used for
investigation of dynamic properties of MVL function. The analysis of boundary
values of MVL function is possible based on these derivatives too. In this paper the
investigation of boundary values of the structure function of MSS and definition of
MSS exact boundary states based on these valued are considered. Conception of exact
boundary states is defined as boundary states for fixed MSS performance level change
depending on change of the appointed change components state. This conception is
extended for exact boundary states depending on changes of some components states.
New measures for estimation of MSS boundary states estimation are introduced
and considered in the paper. The analysis of MSS based on the exact boundary states
has not limits for the numbers of components (n) and states for every component (mi ),
and system performance levels (M) according to the theoretical background. But in
real-world applications these numbers have important influence to the structure
function dimension (number of structure function elements) that is calculated as:
Nstructure function dimension = m1 m1 … mn
As a rule the number of system performance levels (M) and number of component
states (mi ) are defined between two and seven. The increase of the structure function
548
dimension depending on the number of components (n) is illustrate in Fig.5.
According to the investigation in papers [15 – 17] the Direct Partial Logical
Derivatives is applicable for systems which have dimension less than ten millions
elements. So the proposed method can be used for the MSS at least ten components.
Fig. 5. Calculation of the Direct Partial Logic Derivative (10)/ x1(10) x3(21).
Acknowledgments. This work was partially supported by grant of Scientific Grant
Agency of the Ministry of Education of Slovak Republic (Vega 1/0498/14) and the
project "Innovation and internationalization of education - instruments for increasing
quality of the University of Žilina in the European educational space".
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Automation of Building the Safety Models of Complex
Technical Systems for Critical Application
Bohdan Volochiy1, Bohdan Mandziy1, Leonid Ozirkovskyy1
1
Department of Theoretical Radio Engineering and Radio Measurement, Lviv Polytechnic
National University, 12 Bandera str., 79013 Lviv, Ukraine
bvolochiy@ukr.net, bmandziy@lp.edu.ua, l.ozirkovsky@gmail.com
Abstract. In this paper the improvement of method of automated building of state
space models of complex technical systems for critical application was proposed.
On the basis of the developed model with the split state of critical failure the
reliability and safety indexes of studied system can be obtained. Developed
approach allows to estimate of reliability and safety indexes, that makes the
impact of maintenance strategies on safety and reliability, impact of the fault
tolerance on safety to be considered. This will increase the accuracy (certainty)
of efficiency indexes estimation of complex technical systems for critical
application.
Keywords. Reliability, Reliability Engineering, Safety, Modeling, Complex
System.
Key Terms. Reliability, MathematicalModel, MathematicalModeling
1 Introduction
Modern technical systems belong to the class of complex systems, which have the
following properties [1,2]:
presence of large number of elements which interact according to the given
fuctional algorithm, that causes the great dimention of reliability mathematical
model (from tens to hundreds of thousands of differential equations);
elements of the system can be characterized by several types of failures (such
as breakage and short circuit);
in the case of multifunctional systems the situations when not all functions are
fully performed or are performed simultaneously or are performed with the
deterioration of relevant characteristics can happen. Therefore the definition
of "system failure" is complicated;
the failure of complex system for critical application can affect the human
casualties or material damage, so these systems must be fault-tolerant (the
ability to function normally in conditions of failures of individual elements)
and safety (resistance to accidents). These properties are achieved by
introduction of various kinds of redundancy (structural, algorithmic, time,
551
etc.), that leads to complexity of structure and internal behavior algorithm of
the system as a result of the introduction of control functions, fault isolation
and function recovery.
Thus, the designers of complex technical systems for critical application (CTSCA)
must provide the high level of reliability and safety of the project, and thus they meet a
number of contradictions, namely: contradiction between the complexity of the system
and its reliability (more complex system has lower reliability), the contradiction
between reliability and safety (to increase the level of safety it is necessary to induce
additional subsystem of security, locking, emergency stop, etc., that reduces reliability).
Increasing of reliability through the use of fault-tolerant configuration does not increase
the level of safety. At the same time the applying of appropriate maintenance strategy
increases both reliability and safety. At the design stage, these contradictions are solved
by multivariate mathematical modeling of CTSCA, comparative analysis of
alternatives and selection of the best one. Note that the system reliability analysis
involves the study of the process of transition from state to state in the state space as a
result of failure or restoration of certain elements of the system. In the general approach
for forming reliability models these models are formalized and describe the interaction
of elements of the system while its performing from the reliability position. These
models reflect the degree of each element influence on the reliability in the whole. The
study of safety includes, in addition, the analysis of the transition of system failures due
to accident and determines the characteristics of this process.
Due to complexity of modern technical systems the multivariate analysis without
automation of model building and estimation of reliability and safety indexes on its
basis are not available in many cases. So often, especially for safety estimation, it is
replaced by building one variant of the model followed by the combination of obtained
results with expert evaluation of safety and recommendations to bring them up to
acceptable values.
Nowadays reliability behavior modeling of CTSCA and its safety modeling are
carried out independently of each other, using different types of models, which in the
case of reliability take into account some properties of the system, but in the case of
safety – completely different, although in reality these properties are interrelated and
can’t be separated.
This approach is explained by the reliability models complexity as well as safety
models and respectively by huge time costs for their building and by significant
computational costs for their analysis with taking into account only the important
nuances of CTSCA behavior. The dimension of reliability models of modern systems
can reach hundreds and thousands equations. The safety model is, unlike the reliability
model, complex logical function that contains hundreds and thousands arguments.
Experience shows that the "manual" building of reliability models of fault-tolerant
systems even with small number of elements (10) without software usage requires time-
consuming procedure of dozen hours. If you change the parameters of the state graph
you need to rebuild the new one and the probability of making errors in the model is
very high when the chances of detection them is very low, also the time of restructuring
the state graph is comparable with the time of construction its first version. Manual
building of safety models as fault tree and the risk indexes estimation on its basis
552
(minimal cut set) is comparable to the complexity of the building the reliability models
as graph of states and transitions.
From the above it arises the urgent task of further improvement and development of
automated methods for modeling reliability behavior of CTSCA which are focused on
reliability and safety indexes estimation.
2 The Current State of Modeling the Reliability and Safety of
Complex Technical Systems Critical Application and
Directions for Its Improvement
For reliability estimation of CTSCA nowadays there are enough formal and in some
cases software implemented approaches, but for safety estimation there are only
partially formalized methodologies which involve manual building of logical and
probabilistic models in GUI. These models provide the automated determination of
selected safety indexes - risk indexes (minimal cut sets).
Well-known software suites such as RAM Commander (ALD, Israel) [3], PTC
Windchill QualitySolutions (PTC, USA) [4], ReliaSoft Synthesis Master Suite
(ReliaSoft USA) [5], Item Toolkit (Item Software, USA, UK) [6], Reliability
Workbench (Isograph, US, UK) [7] allow building reliability models as reliability block
diagrams (RBD) with the automated estimation of reliability. Models as graph of states
and transitions are built manually with further automation of reliability analysis.
For safety estimation these software suites have graphical tools for forming fault
trees in manual mode with the automated determination of minimum cut sets and
special tools to carry out FMEA / FMECA analysis. The main advantage of these
software suites is that they contain integrated frameworks of elements models
(electronic, electromechanical, mechanical, etc.) in accordance with international
standards: MIL-HDBK-217, Telcordia SR-332, IEC TR 62380, 217Plus, FIDES, which
are required for reliability and safety analysis.
In monograph [1] the general principles of automation of building reliability models
as matrix of states and transitions and matrix with subsequent transition to the graph of
states and transitions are given as guidelines and recommendations. Also, this approach
does not have tools to analyze safety. In monograph [8] the fundamental principles of
logical and probabilistic models as fault trees for the reliability and safety estimation
are provided. Actually, this approach is widely used to analyze safety indexes, namely,
risk by the minimal cut sets determination. However, this approach isn't formalized and
in the case of CTSCA it requires significant time costs for building the fault tree and
computational costs for the analysis of safety indexes. In addition, any changes in the
structure of the system require the construction of its new model. Therefore, for
multivariate analysis at the design stage this approach is rarely used, it is usually
provided for certification, when the structure of CTSCA is established.
Currently the most powerful method for building reliability models of CTSCA is the
state space method. It allows us to adequately reflect the functional and reliability
behavior of CTSCA. Generated by this method model is represented by yhe system of
linear differential equations of Chapman-Kolmogorov which adequately describes all
553
the features of system behavior that allows us to obtain standardized and non-
standardized reliability indexes, which are required by developer at design stage.
However, for the analysis of safety and risk, in particular, this mathematical tool is not
used in practice, although there are attempts to use it for building dynamic fault trees
[10]. Practical use of state space method [11] is limited at the design stage, due to
cumbersome models, the phase space of which is equal to 103 .. 104 equations, and for
multivariate analysis, in most cases, it is replaced by simplified evaluation using
standard models.
In work [2] the method of automated generation of state space for behavior analysis
of CTSCA basing on formalized description of the designed object in the form of
structural-automatic model is described. It allows us to automate the process of
reliability models building and to significantly reduce the time costs of multivariate
analysis.
Structural-automatic model (SAM) consists of three sets of data [2]. The first set is
state vector (SV), which describes all the formalized list of states using variables - SV
components. The SV components are variables which describe the state of the system
elements. State vector may contain additional components which are used to track the
status of additional features, such as counter of current number of repairs of each item;
counter of all repairs; counter of total number of failed items and so on.
The second set is constants - set of formal parameters which characterize the
structure of the system and its properties, namely the number of parts on the system
configuration, the number of reserve elements, their failure rate and intensity of
renewals, limited number of updates and more.
The third set is tree of modification rules of state vector components (TMRSVC),
which is given in tabular form and reflects the consequences which come after the
failure or recovery of certain elements under certain conditions. The components of
TMRSVC are the events, which can occur with elements (failure or recovery of
element, reserve connection etc.), the set of logical conditions that defines combinations
of values of state vector components, which take place for this event, and the
modification rules of states vector components (MRSV). Each condition corresponds
to the formula for calculating the intensity transition (FCIT). The event result is the
change of SV component and transition from one state of system to another in
accordance with the rules of transition. If certain elements inherent in more than one
type of failures (such as breakage and short circuit), the probability of which is known,
in such cases, use the set of formulas for calculate the probability of alternative
transitions (FCPAT), for each of which the certain rule from MRSV is used.
Time-costs for build the SAM by experienced developer are 1-30 hours, depending
on the complexity of the system. These costs justifies itself in multivariate analysis of
fault-tolerant systems, because the next correction of the model, even with significant
changes in the structure of the system takes time from tens of minutes to several hours.
This approach is implemented in ASNA software[2, 11]. Input data about the
researched object for software module ASNA should be submitted in the form of SAM,
which is formalized description of the structure and reliability behavior of system (the
rules of transition from one state to another during the failure and recovery of elements).
Basing on SAM software module ASNA generates the list of all possible states of the
554
system, the table of transitions from one state to another, which is transformed into the
matrix of intensities of transitions when entering numerical values of intensities of
failures and recovery of the system. Therefore, basing on the matrix of intensities
ASNA module automatically forms the system of differential Chapman-Kolmogorov
equations and solves it by Runge-Kutta-Merson method. As a result the user gets the
time dependences of probabilities of system being in each of the possible states. Basing
on this information, the user can define standardized reliability indexes of system
(availability function, probability of failure, failure flow parameter, MTTF, etc.), and
arbitrary parameters that may be needed for the "thin" study of the system (probability
of downtime, probability of having at least N employable elements when using a certain
number of renewals, etc.).
This approach focuses on estimation reliability indexes for reliability design and
efficiency indexes for functional design. To use this approach to the safety indexes
estimation the improvement both the graph states and transitions (to display emergency
situations) and description of the state vector and principles of SAM building is needed.
In particular, in work [12] it is proposed to combine the approach outlined in the
monograph [1] with reliability block diagram GUI, allowing us to integrate into SAM
designed method of RBD visualization and determine system operation conditions.
Developed interface allows entering data not only for method of RBD visualization,
but also for reliability model of the whole system. However, this approach has several
limitations considering maintenance strategies and tools for monitoring and
diagnostics. In addition, this approach focuses exclusively on building reliability
models.
Thus, among the known approaches there were not found ones which allow
determining the reliability and safety indexes for the same behavior model of CTSCA
with taking into account all behavior features of the system while disability, accidents,
downtime, etc. Hence the task of updating SAM and state space method for their
adaptation to the problems of multivariate analysis and safety indexes estimation.
3 Improvement of the State Space Method and Its Formalization
for Safety Models Building
The state space method combining with formalized description of the systems in the
form of SAM is the powerful tool for the study of both functional and reliability indexes
of CTSCA STSVP that allows us to perform multivariate analysis with minimal time-
cost. Significant advantages of the state space method is that it provides the set of all
states of CTSCA and determine the probability rates getting in or staying in any of
them. This property is particularly relevant when the operation of the system allows the
states of reduced functionality or partial disability. In addition, you can see the quantity
of reliability increase when entering certain types of redundancy and their cost. These
properties make it possible not only to investigate the reliability of CTSCA when
carrying in redundancy or changing its behavior algorithm, but also to analyze the
impact of these actions on safety, which we understand as the risk of emergency in case
of failure of each element of system.
555
This index according to [13, 14] is called minimal cut set. Minimal cut set (MCS) –
is a minimal combination of events which lead to catastrophic system failure. If when
any of event is removed from the MCS the remaining events collectively cannot cause
to catastrophic system failure [13].
Thus, when designing CTSCA we must have a single model that is based on the state
space method and provides:
adequate reflection of system behavior while disability;
consideration of strategies for maintenance and repair;
consideration of controls and diagnostics;
possibility of obtaining reliability indexes (probability of faultless work ,
availability, MTTF, MTBF);
possibility of obtaining safety indexes (MCS);
consideration of system downtime;
the opportunity to obtain indexes of economic efficiency;
to carry out the multivariate analysis.
To achieve this goal it is necessary to make a number of modifications of the state
space method, as described below. The behavior of CTSCA is described by graph of
states and transitions. Vertices of graph are the states in which the system can be. These
states are characterized by probabilities. Edges of the graph are the possible transitions
from state to state and are characterized by the transition intensities.
In all known methods the catastrophic failure condition is a combination of all
inoperable states, which are united in one state. This is used, on the one hand, to obtain
the required reliability indexes when only operable states are used, on the other hand,
inoperable states significantly increase the phase space, dimensionality of which is
great.
Therefore, for safety indexes estimation (MCS), you must split the state of
catastrophic failure (CF) in separate states. Thus, the set of inoperable states contains a
subset of accidents (AS1, ..., ASi, ...), accordingly to CTSCA (Fig. 1). Each of these
accidents can be represented by the corresponding fault tree.
The dimension of the system of differential equations Chapman - Kolmogorov
increases proportionally to the expansion of phase space and the system of equations
consists of two parts - the equations that describe the operable states (Pi (t)) and the
equations that describe inoperable states (Qj (t)).
The solution of the equation system can be implemented by analytical methods
(matrix exponential, Laplace transform) and numerical methods (Runge-Kutta,
Rosenbrock). As a result of solution the probability distribution of CTSCA being in all
states is obtained.
The next step is filtration of obtained probability distribution for the separation of
states to operable and inoperable. Filter is in this case the condition of critical failure.
As a result of filtration, we obtain a set of probability of CTSCA being in operable
states {Pi (t)} and the set of probability of CTSCA being in inoperable states {Qj (t)},
where i is the serial number for operable states and j is the serial number for inoperable
states.
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Split state of CF АS1 АS2 АS3
Fig. 1. Graph of state and transitions with split state of catastrophic failure
From the resulting set of operable states the necessary reliability indexes are formed
and from the set of inoperable states the MCS – combination of inoperable states, when
the critical failure definitely will occur – are obtained.
As the number of inoperable states is equal to 101..102, for automated MCS
obtaining, an algorithm for finding all combinations of inoperable states, which refer to
critical system failure, should be developed. This means that this element is one of the
most critical parts of the system. In the case of fault-tolerant systems, CTSCA is just
that, the combination of several elements is possible. It is considered that as more
inoperable states are included in MCS so the less vulnerable system is and so the effects
of its failure will not be catastrophic for human life and health and the environment.
If vulnerable elements, which form inoperable states, which are included in MCS,
are replaced by more reliable or reserved, the risk of accident is reduced in times. Thus,
the MCS are necessary for designer to make reasonable redundancy in a new version
of designed CTSCA. So due to the effect of redundancy input we can quantify the rate
of risk reduction:
Krr=Cm/Cn, (1)
where
Cm – MCS before redundancy input;
Cn – MCS after redundancy input;
Generalized diagram of technique of estimation of safety and reliability indexes
basing on the graph of states and transitions with the split failure state and using SAM
is shown in Fig. 2. According to it, the automated algorithm for obtaining MCS was
developed. The input data for the algorithm is the set of inoperable states (MCS),
derived from the binary SAM.
The binary SAM is the SAM of the CTSCA, in which all elements of structure are
displayed by individual SV components and can take only of two values: zero and one.
The binary SAM, which, unlike to original SAM [2], makes a possibility to describe
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the structure and behavior of CTS without unification of states of its structure elements.
In addition, the binary SAM allows obtaining split failure state, in which states of
CTSCA subsystems failures can be discerned with the given level of detail
representation.
CTSCA analysis
Binary SAM development
Automated forming of graph of
states and transitions with split
failure state
Forming of differential equations of
Chapman - Kolmogorov
Solving the differential equations of
Chapman -Kolmogorov
Obtaining the distribution of
probability of CTSCA being in
states
Operable states selection Inoperable state selection
Reliability indexes estimation MCS computation
Forming of FT basing on MCS
Fig. 2. Generalized diagram of technique of estimation of safety and reliability indexes basing
on the graph of states and transitions with the split failure state
Procedure of filtering inoperable states from whole phase space is carried out by the
analysis of the state vector component, comparing them with the critical failure
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condition. If the element is operable, the value of its corresponding SV component is
greater than zero. If the element failed and led to accident, the component will be equal
to zero.
While the algorithm development it is taken into account that:
at least one MCS is presented in the sysytem;
cut set of the system is inoperable state, when system falls into catastrophic
failure condition;
MCS of the system is the state, when the system is in catastrophic failure but
taking off at least one of the elements that are failed in this MCS, the
catastrophic failure of the system can not occur at all.
Definition of MCS is provided in two stages: stage of MCS obtaining and stage of
estimation their probability values.
Stage I. For MCS finding the following procedures are used: MCS sorting; MCS
determination.
At this step it is necessary to sort obtained array of inoperable states of the system
on the feature of the smallest number of events that led to the accident of the system.
Further, basing on sorted array of inoperable states the MCS are defined. As a result of
the proposed procedures the array of MCS is presents as a matrix.
Stage II. Determination of MCS probability is performed by the following
procedures: determination of MCS from all cut sets; sum of MCS probabilities; forming
of array of MCS and their probability values.
According to this stage we must create a matrix that consists of four columns – the
first column is a serial number of MCS – N; the second column is SV component and
its value; in the third column the numbers of states, which are attended by the
corresponding MCS, are recorded. So in the fourth column there are recorded obtained
probabilities of MCS as a result of this procedure. Also at this stage procedure of
comparison of the system states is used.
The procedure for obtaining probability values of MS is the sum of probability
values of being in respective states, whose numbers were found in the previous
procedure, i.e., in the states that are recorded in the third column corresponding to the
MCS matrix. As a result, the fourth column is filled with appropriate MCS probabilities
value.
An example of the usage of developed method of MCS definition. Fault-tolerant
system consists of five modules A, B, C, D, E. Modules A, B, D are the main operable
configuration that provides performance of system functions and modules C and E are
reserve modules. Modules A and B are reserved by module C. The entire system is
reserved by module E. All modules have the same failure intensity = 0,001, and the
observation period is T = 100 h.
The RBD of the fault-tolerant system is shown in Fig. 3:
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On the basis of developed binary
E SAM of the fault-tolerant system,
which consists of set of formal
parameters (Fig. 4), SV
А B D components and failure condition
(Fig. 5), the tree of modification
rules of state vector (Fig. 6),
С which is the input to the software
Fig. 3. The RBD of the fault-tolerant module ASNA, the graph states
system and transitions was obtained in the
automatic mode (Fig. 7).
Fig.4. The set of formal parameters
Fig .5. State vector components and failure condition
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Fig.6. The tree of modification rules of state vector
Basing on the obtained graph of states and transitions the software module ASNA
formed mathematical model of the system as a system of Chapmen - Kolmogorov
differential equations. After its solving the probability of being in every possible state
was obtained. Probability of system being in operable state is 0.9894, and the
probability of failure is equal to:
Qf = 1 - 0,9894 = 0,01061
λD
λE λC
BCDE λC λD
BDE BCE λE
λB
λC λB λB
λE λD
CDE DE λA CE
λA λC
λA
ADE ACE
λC λD λE
ACD
λD λC
λE
λA BCD λB BE
λB λA
λB
λB E SF
λC CD λA λE
ABC ABD
λA λC
DE AE λE
λD λA ACD
λE
λD
λE λD ABE λB
λB λA
λC λE
ABCE
λE λD
λA λB
ABD
λA λB
ABC λC
λD
Fig. 7. Graph of state and transitions
On the basis of the graph of states and transitions according to developed algorithm,
it was determined that after simultaneous failure of modules E and D the system fails
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in general. Next, other two combinations which also lead to failure of the whole system
are ACE and BCE. Thus, these three combinations make the MCS. The next stage was
the determining of the values of the probability of each of these combinations.
Substituting logical expression of MCS DE: ((V4 = 0) AND (V5 = 0)) instead of failure
condition the MCS value of probability simultaneous failure of combination of modules
E and D was obtained, which is QDE = 0,009. Similarly, substituting logical expression
of MCS ACE and BCE instead of failure condition we get: QACE = 0,00084; and QBCE
= 0.00084. The calculated MCS is shown in Table. 1.
Table 1. Minimal cut sets of the system
Failed The number of failed Percentage
MCS values
modules modules values, %
E, D 2 0,009 84,6
A, C, E 3 0,00084 7,92
B, C, E 3 0,00084 7,92
Validation of the
developed method. To
validate the developed
method it was
implemented the a
fault tree building for
the system (Fig. 8)
according to the
approach [8] and the
values of the
probability of failures
for each MCS were
calculated. It was
considered that the
results obtained by
fault tree are accurate
and they were
compared with results
which are shown in
Fig.8. Fault tree Table 1.
The validation was
performed using
specialized software suite RAM Commander by ALD Service. For RBD the fault tree
was set up (Fig. 8) and MCS were obtained by tools of RAM Commander and are
shown in Fig. 9.
The comparison shows that the calculated values of MCS, which were obtained from
fault tree using software suite RAM Commander coincide with the values obtained
from the graph of states and transitions with the split failure state using binary SAM.
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The developed approach (Fig. 2) allows us to get the MCS in automatic mode without
fault tree construction.
Fig. 9. Minimal cut sets basing on fault tree
4 Expanding the Functionality of the Program ASNA for the
Safety Analysis of CTSCA
For building complex models, which are focused on determination of the reliability
and safety indexes it is most advisable to take as a basis the graph of states and
transitions with split state of catastrophic failure and method for its automated
construction using binary SAM. However, the biggest problem for the designer, in this
case, is the construction of the binary SAM because its formation requires from the
developer not only the deep knowledge of the nuances of functionality of designed
CTSCA but also thorough knowledge about techniques of construction the formalized
graph of states and transitions that is the whole direction in complex systems designing.
Therefore, the next urgent task is to automate the construction of binary SAM-based
graphical representation of the system as a RBD. This will speed up the development
of SAM, reduce the time cost in degree and obtain both reliability and safety indexes.
Principles of this automation were laid in works [12, 15]. At the same time, we note
that this approach narrows the class of the analyzed systems because it does not allow
us to analyze complex technical systems that are described by queuing systems,
flowcharts, etc. behavior algorithm.
According to approach [12] the visualization software for RBD of technical system,
which makes it possible the automatic construction of graphic images of flow diagram
of technical systems and the formation of conditions of their functioning and failure,
was developed. Using the developed software the information about the system is
transmitted as input to the ASNA software for further calculations of reliability indexes
accordingly to the number of elements in the node, the number of renewals and
maintenance crews, time range, intensity of failures and recoveries for each of elements
of analyzed system.
In order to extend the functionality of the ASNA software for safety analysis of
CTSCA it is needed to combine binary SAM methodology with the approach [12]. It is
necessary to modify the SAM as follows:
Every element input in the RBD is accompanied by the creation the next set of SV
components, the number of elements corresponds to the number of components:
Item1, Item2, … ,Itemi,… → V11, V21, … , Vi1, …
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The initial value of each component is equal to one: Vi1=1;
Type of connection of RBD elements (serial, parallel, combined) is given by the
inoperable condition
If the limited number of renewals of system is planned, for each item is added
another SV component – counter of repairs:
→ V12, V22, … , Vi2, …
The initial value of each component is equal to zero: Vi2=0
If the number of renewals is unlimited, the additional component isn’t added;
Each RBD element is assigned to line of binary SAM as follows:
Event Condition FCIT FCPAT MRSV
Failure of module і Vi1=1 i 1 Vi1=0
If the system is renewable, in addition to each RBD element, another line is
assigned to binary SAM as follows:
Event Condition FCIT FCPAT MRSV
Repair of module і (Vi1=0) AND µi 1 Vi1=1
(Vi2