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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Platform for Testing and Dynamic Control of Software Code Based on Dimensions*</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>Innopolis University</institution>
          ,
          <addr-line>Kazan</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>MIREA - Russian Technological University</institution>
          ,
          <addr-line>Moscow</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>V.I. Vernadsky Crimean Federal University</institution>
          ,
          <addr-line>Simferopol</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
      </contrib-group>
      <fpage>0000</fpage>
      <lpage>0003</lpage>
      <abstract>
        <p>A possible platform for test automation and dynamic control of software code based on authoring models and methods of invariants of similarity and dimensions is considered. The development of the mentioned platform allowed organizing dynamic control of the program code of modern applications of digital enterprises with high reliability and reasonable complexity.</p>
      </abstract>
      <kwd-group>
        <kwd>semantics of computing</kwd>
        <kwd>technology platform</kwd>
        <kwd>digital economy</kwd>
        <kwd>digital enterprise</kwd>
        <kwd>invariants of similarity</kwd>
        <kwd>dimensions</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>The relevance of research</title>
      <p>The relevance of developing a platform to automatize the testing and dynamic control
of the software code of digital platforms is explained by the need to ensure the required
quality and speed of development of the relevant software (Qa&amp;testing), and the
imperfection of known methods of testing and verification of the software code in the
context of a large-scale digital transformation of leading state and commercial
enterprises in Russia.
*</p>
      <p>
        Currently, the following main solutions are used to test digital enterprise
applications: Katalon (https://www.katalon.com/), TestComplete (http://tiny.cc/xyt5cz),
ReportPortal (https://reportportal.io), TestRail (https://bit.ly/2kfTbia), Aquality
Automation (https://aquality-automation.ru/) [
        <xref ref-type="bibr" rid="ref14 ref15 ref3">3, 14-15</xref>
        ].
      </p>
      <p>The advantages of the first Katalon solution (takes up 2.5% of the world market of
automated testing tools) include: own development environment with project
templates; developed components for analysis of test results; scripting tools (Record &amp;
Play). Disadvantages of Katalon include: lack of native support for Desktop application
automation; focus on applications written only in Java and Groovy programming
languages; lack of flexibility when distributed runs are needed; lack of web version and
user interface overload etc.</p>
      <p>The advantages of the second Test Complete, Smartbear Software solution (occupies
at least 5% of the world market of automated testing tools) include: support for different
types of interfaces; the ability to write scripts in different programming languages; a
well-established product support process. Disadvantages of Test Complete include: the
inability to store the testing history; limited IDE compared to Visual Studio, Idea
Jetbrains, etc.; the need for licensing (not distributed free of charge).</p>
      <p>The advantages of the third solution ReportPortal (occupies from 2.5% of the world
market of automated testing tools) include: support for most Test Runners; possibility
of a joint analysis of results; automatic analysis of test results. Disadvantages of
Reportportal include: limited ability to develop new tests; complex structure of stored
results.</p>
      <p>Advantages of the fourth Test Rail solution, An Idera Inc. (occupies up 7% of the
world market of automated testing tools) include: a functionally rich structure for
organizing tests; a REST API for integration with other systems; and a JIRA defect
tracking subsystem. Disadvantages of Test Rail include the lack of a system for generating
automated tests; and the lack of visual analysis of test results.</p>
      <p>Advantages of the fifth solution Aquality Automation (occupies up to 4% of the
world market of automated testing tools) include: a single user-friendly interface for
writing and maintaining tests; fast generation, development and launch of automated
tests for various types of products (web, mobile, desktop); advanced algorithms for
automatically determining the causes of test failures; formation, maintenance and
management of a set of tests for a product and a test data storage system; automatic
collection, aggregation and visualization of automated testing results; collection and
provision of access to testing artifacts for further analysis; reduction of labor costs for
regression testing by 15 times, the time of its implementation - by 5 times; integration
with continuous build systems, maintaining a lifecycle for detected test failures;
integration with cloud testing platforms.</p>
      <p>In practice, testing applications of the digital economy, the listed solutions have
shown themselves as follows. ReportPortal is effective for pre-scripted automated tests
that require analysis of test execution. TestRail is a convenient test storage tool but does
not allow using written tests to automate testing. TestComplete provides a tool to
automate the application interface but does not provide an analytic system to enable
launches and analysis. Aquality Automation combines solving most of the problems in
one interface and allows organizing the process of automated testing of digital economy
applications in general.
2</p>
    </sec>
    <sec id="sec-2">
      <title>Description of the proposed approach</title>
      <p>
        The proposed QA &amp; Testing platform for automated testing of digital economy
applications is based on several well-known and author's models and methods of software
testing and analytical program verification [
        <xref ref-type="bibr" rid="ref1 ref2 ref4 ref5 ref6 ref7 ref8">1-2, 4-8</xref>
        ].
      </p>
      <p>This platform includes a Web portal (Database, Backend and Frontend), as well as
corresponding modules for organizing and conducting automated testing of digital
economy applications. Thus, a web application provides an interface for developing
tests, grouping them into sets, and visualizing test results. This web application consists
of the following components: database; Database; Backend and Frontend component.
In this case, the components are packaged into a docker image and distributed further
in the form of an image. MySQL database is used as Database (it is possible to use other
well-known databases). The purpose of the Database is to store any static information:
descriptions of tests, launches and their results. SQL procedures are used to optimize
work with Database and speed up query processing.</p>
      <p>Backend is a portal with REST API for interacting with other platform components.
At the same time, the REST API is developed using technologies: Java, Servlet API,
Spring Framework. The Backend component contains methods for processing test
results from different test runners (for example, TestNG, JUnit, MSTest,
RobotFramework, etc.). The backend also provides interfaces for sending data to the platform,
including test results, new tests, etc.</p>
      <p>The frontend is responsible for visualizing the information received from the
database. The user graphical interface is developed using TypeScript, AngularJS, HTML5
technologies. Using the graphical interface, the user can analyze the results obtained in
the form of graphs, tables. Also, the user can flexibly manage data using filters and a
search system that provides hints based on historical and analyzed information.</p>
      <p>Also, the QA &amp; Testing platform contains several modules for automating
application types: web, mobile, desktop. Each such module can use various combinations of
free automation tools and programming languages. For example, a module for working
with Java is designed to automate testing of web applications and is an add-on to the
tool for working with a browser via WebDriver. This module allows you to automate
web tests for Chrome, Firefox, Safari, IExplorer, Edge. At the same time, tests can be
run under the control of an operating system with JDK version 8 and higher installed
on it.</p>
      <p>The QA &amp; Testing platform supports integration with the most popular Continuous
Integration systems (Jenkins, TeamCity, Azure VSTS, Atlassian Bamboo) to run
automated tests. At the same time, the system provides a common interface for launching
regardless of which Continuous Integration system the integration is configured with.
The launcher provides a set of parameters (data files, browser settings, applications,
etc.) that are used to automate testing a product with specified parameters.
2.1</p>
      <sec id="sec-2-1">
        <title>An example of checking the semantics of applications.</title>
        <p>Consider an operator of the form:</p>
        <p>A  B  C </p>
        <p>D  1 .</p>
        <p>E
In terms of dimensions, we obtain three corresponding dimensional equations (2–4):
(1)
(2)
(3)
(4)
(5)
(6)
(1)  lnA (1)  lnB (1)  lnC  0 ,
(1)  lnA (1)  lnD (1)  lnE  0 ,</p>
        <p>1 lnA1  0 .</p>
        <p>R 
1</p>
        <p>0 ... 0
0 1 ... 0
...</p>
        <p>If in (1) we consider a numeric constant as a variable (for example, with the name
CONST_1) of a certain dimension, then operator (2) will add six variables (A, B, C, D,
E, CONST_1) to the system of constraints. Equation (2) will also change - it will take
the following form:</p>
        <p>1 lnA1  (1)  lnCONST _11  0 .</p>
        <p>
          As a result, variable A will remain in the system with a nontrivial value until the
completion of the calculations [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ].
        </p>
        <p>
          Correctness assertion. Such a change in the status of numeric constants makes it
possible to determine the criterion for the semantic correctness of the Technological
platform of some digital enterprise in the following form [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]:
        </p>
        <p>Statement 1. For the semantic correctness of the Technological platform of a digital
enterprise, the system of dimensional equations built for it with regard to numerical
constants must have at least one solution vector among the set of solution vectors,
consisting of all nonzero components.</p>
        <p>Proof of the statement (by contradiction). The appearance among the variables
corresponding to dimensions, such that is identically equal to zero for any values of other
variables, means its dimensionlessness. However, this contradicts the condition for
constructing a system of restrictions, namely the introduction of dimensions for all
variables and process constants. The statement is proven.</p>
        <p>For the numerical verification of the criterion, based on the matrix S of coefficients,
we construct a system of equations for the dimension of the matrix R, which has a
special form:</p>
        <p>The matrix R in this form can be represented by the following formula:</p>
        <p>Rkn  Ekk | Ck(nk) ,
where E is the identity matrix, k and n are the number of rows and columns of the
original matrix S, respectively.</p>
        <p>To construct a matrix R, it is sufficient to use three types of operations:
1. addition of an arbitrary row of the matrix with a linear combination of other rows;
2. permutation of lines;
3. permutation of columns.</p>
        <p>
          The main course of the process of achieving a form is similar to the Jordan-Gauss
method (see, for example, [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]). The difference is as follows:
─ double pass of the algorithm: first in the forward (top to bottom), and then in the
opposite (bottom to top) direction;
─ permutation of columns in cases where a nonzero value in any cell within the first k
columns, which is not the first nonzero in a row, cannot be turned into zero due to
the absence of other nonzero members in this column [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ].
        </p>
        <p>As applied to the solution of the system of dimensional constraints, the matrix R is
identical to the matrix S, except for possibly performed column permutations. That is,
there is an equivalent</p>
        <p>(S  X  0)  (R  T  X  0) ,
where T is a square permutation matrix of dimension n  n corresponding to the
permutations of columns in S performed at the stage of constructing R. This result is due
to the nature of the transformations performed on the matrix S in the process of
constructing the matrix R.</p>
        <p>Correctness conditions. Formula (8) allows using not the matrix S, but the matrix
R when checking the semantic correctness. For this, we formulate the following
statement:</p>
        <p>Statement 2. For the first k values of the solution vector of the system of constraints
of the i-th component to be identically equal to zero, it is necessary and sufficient that
all the elements in the i-th row of the matrix C in the formula be equal to zero.</p>
        <p>Let us prove the necessity of the condition (by contradiction). Let there be at least
one nonzero element in the i-th row of the matrix C (for example, in position j). Then,
set equal to zero all (n – k) last variables except for the (k + j) th, we obtain the following
equality:
k
 0  x p  xi 
p1, pi
nk
 ci,q  0  ci, j  xk  j  0 
q1,q j
xi  ci, j  xk j ,
(7)
(8)
(9)
from which it follows that in this case, the variable xi is not equal to zero. We got a
contradiction. The necessity of the condition is proved.</p>
        <p>Let us prove the sufficiency of the condition. If all elements of the i-th row of matrix
C are equal to zero, we obtain the following equality:
k nk
 0  x p  xi   0  xk q  0 ,
p1, pi q1
(11)
(12)
from which the required identity is obtained directly.</p>
        <p>xi  0 .</p>
        <p>The statement is proven.</p>
        <p>The variables corresponding to the first k columns of the matrix R are basic
(independent) in the given system of dimension invariants. The variables corresponding to
the remaining columns of the R matrix are dependent. Thus, the above statement
determines the relationship between the incident of anomalous functioning of the
Technological platform of a digital enterprise and the situation when one of the basic variables
has the dimension "0". The reason for this relationship is that the situation of dimension
"0" is impossible according to the methodology for constructing a system of invariants
of dimension.</p>
        <p>Assessment of the results obtained. This technique (with complete construction of
the matrix R) is the basis for the construction of optimized algorithms for testing the
criterion. As input data, the algorithm uses a matrix of dimension k  n with elements
from Z, the result of the work is a Boolean variable, which has the value "True" if the
criterion of semantic correctness is met and "False" otherwise. The intermediate results
of the algorithm are:
─ matrix C of dimension k  (n – k) with elements from the set of rational numbers Q,
corresponding to the matrix S in the form (8);
─ the value of kERR, equal to 0, if the criterion of semantic correctness is fulfilled, or
the number of the first row of the matrix C, consisting only of zero elements if a
violation of the criterion is found.</p>
        <p>In practice, when using the basic technique, a variation of the algorithm for
constructing the matrix R is possible, which consists in creating it directly during the
analysis of each operator of the computational process under study. The allocation of basic
variables and the necessary computational transformations over R are performed each
time a new line is added to it. The purpose of the modification is to have a matrix of
dimensionality constraints already reduced to the form (7) at each analysis step.</p>
        <p>This algorithm allows:
─ eliminate the computational costs associated with the late (within the framework of
the Jordan-Gauss algorithm) permutation of the matrix columns;
─ to reduce the number of computational operations during the selection of the identity
matrix on the left side of the matrix R.</p>
        <p>
          The algorithm requires additional storage of the permutation matrix T at the entire
stage of the analysis of the Technological platform of the digital enterprise and
somewhat slows down the access to the matrix elements. However, the use of efficient data
structures makes it possible to reduce the additional costs to a negligible amount. The
construction of the matrix R allows us to detect an incident of anomalous functioning
of the mentioned Technological platform before the end of the entire construction
(however, it is not at all necessary that the criterion of semantic correctness is violated at the
moment of adding information about a semantically incorrect operator). This fact is an
advantage of the modified technique in the case of a large number of erroneous packets
(intentionally or unintentionally generated). In this case, the receiving station L, having
not yet decoded the message completely, can decide to ignore it, thereby freeing up its
computational resources. This possibility of the technique can be used when it is
included in a layered system of protection against cyber attacks of the "denial of service"
class. The possibility of early rejection of the packet does not affect the average
statistical computational complexity under normal operating conditions. This is since in such
conditions the proportion of abnormal implementations of processes in the network
protocol stack should tend to zero [
          <xref ref-type="bibr" rid="ref3 ref4 ref5 ref6 ref7 ref8">3-8</xref>
          ].
3
        </p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>Conclusions</title>
      <p>
        The lack of proper tools for automated testing and analytical verification of digital
economy applications can lead to an organization:
─ significant financial losses due to complete failure of the system and shutdown of
work due to poor quality, incomplete or untimely testing;
─ loss of existing and potential clients due to failure to complete tasks on time;
─ loss of business reputation, which has been created over the years and has a value in
terms of investment and impact on income [
        <xref ref-type="bibr" rid="ref10 ref11 ref12 ref13 ref9">9-13</xref>
        ].
      </p>
      <p>Note that manual testing and analytical verification of digital economy applications
are not always effective, since there is a risk of missing defects due to the human factor,
as well as the need to attract a large number of highly qualified engineers,
mathematicians and testers (up to 50 people).</p>
      <p>The proposed solution - the QA &amp; Testing platform - for automated testing and
analytical verification of digital economy applications provides:
─ completeness, reliability and consistency of testing and dynamic control of the
program code of digital platforms;
─ the ability to dynamically control not only the structure but the semantics of digital
economy applications;
─ the efficiency of detecting “digital bombs” and destructive program code of digital
platforms;
─ reducing the cost of ensuring the security and cyber resilience of digital platforms in
the long term.</p>
      <sec id="sec-3-1">
        <title>This work was supported by the RFBR grant (No. 18-47-160011 p_a)</title>
      </sec>
    </sec>
  </body>
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