Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) Сoncept of Cyber Immunity of Industry 4.0 Sergei A. Petrenko Krystina A. Makoveichuk Department of Information Security Department of Informatics and Information Technologies Saint Petersburg Electrotechnical University "LETI" V.I. Vernadsky Crimean Federal University St. Petersburg, Russia Yalta, Russia S.Petrenko@rambler.ru Christin2003@yandex.ru Alexander V. Olifirov Department of Economics and Finance V.I. Vernadsky Crimean Federal University Yalta, Russia Alex.Olifirov@gmail.com Abstract — The article presents the development of the concept Turing, J. Von Neumann, M. Minsky, A. Church, S. Klini, D. of cyber immunity to protect the Industry 4.0 critical information Scott, Z. Manna, E. Dijkstra, Ch. Hoare, J. Backus, N. Wirth, D. infrastructure and the theory of self-healing machine computing. Knut, N. Khomsky, A. Kolmogorov, A. Ershov, V. Glushkov, The specified theory is based on the results of the scientific-applied A. Markov and others. They had laid the foundations of the sections of biological and cybernetic immunology. In the developed concept it was taken into account that the neutralization of mentioned programming, allowing mathematically strict malicious influences should not lead to a denial of service for the studying the possible computational structures, studying entire system and to a loss of the functional semantics of computability properties and modeling computational calculations. Using interrelated probative, verification and testing abstractions of executable actions. These results produced the programming, a model for restoring functional program leading scientific schools, which made a significant contribution specifications was developed. It was developed with separation by to the development of the synthesis methods of model levels: semantic (functional, logical and algebraic models are abstractions and specific software solutions. Including Russian defined to determine the base of functionally-logic specifications of scientific schools that have contributed: programs); syntactic (defined models to form automatic machines for the detection and neutralization of malicious influences); • Study of abstract data types and denotation semantics (Y. semantically syntactic (models are defined for applying the L. Ershov, Y. V. Sazonov); simplest forms of program calculation semantics based on • Automatic algebraic synthesis of programs (V. M. graphical, schematic, and network representations). In order to Glushkov, E. L. Yushchenko); prove the correctness of functional semantics of the "cleared" calculations, a mathematical apparatus of the similarity theory • Conceptual programming (E. H. Tyugu, G. E. Minz); and calculation dimensions were developed. The п-converter was • Automatic synthesis of programs, based on knowledge identified; this operator allows forming the required "passports" (D. A. Pospelov); of trusted computations in the conditions of disturbances. • Development of a logical and applicative approach to Calculations with "antibodies" are represented by regular functional programming (W. E. Wolfengagen); schemes in the system of algorithmic algebras of V. M. Glushkov. • Methodology of applied verification and testing of A semantically controlled translator based on formal automata with abstract memory was developed for the interpretation of the programs (V. A. Nepomniashchy, O. M. Ryakin, Y. V. input program of the trusted computations and type of actions. Borzov); • Methodology of symbolic modeling and intellectual Keywords — cyber immunity; Industry 4.0; self-healing; gyromates of cyber security (Y. G. Rostovtsev, A. G. vulnerabilities; antigens; antibodies; destructive code; neutralization Lomako, D. N. Biriukov). of malicious; critical infrastructure; functional semantics; semantic- syntactic models. However, in order to protect the critical information infrastructure of the Industry 4.0 in the face of increasing threats I. INTRODUCTION to information security, it was necessary to define the concept of cyber immunity and develop a new theory of self-healing A fundamental contribution to the formation and machine computing [13, 14]. This new theory was enriched by development of the theoretical and system programming was the results of the scientific-applied sections of biological (E. made by the outstanding scientists from all over the world: A. 93 Metchnikoff) (Figure 1, Figure 2), and cybernetic immunology Including under conditions of a priori uncertainty and (A. Tarakanov, D. Hunt, D. Dasgupta, P. Andyus). obfuscation of programs (Figure 3). II. THE BASIS OF THEORY OF SELF-HEALING MACHINE COMPUTING In the mentioned theory, by analogy with classical immunology (Figure 1, Figure 2), the antigen is understood to be some destructive program code, and the antibody is a synthesized metaprogram of this code neutralization. Model of immune protection of Industry 4.0 describes the causal relationship between "antigens" and "antibodies". That is, between vulnerabilities and program defects (manifested in the form of structural violations), modes of functioning (distorting the properties of programs), security incidents, caused by the destructive program tabs (changing the given standard algorithms of calculations) and metaprograms for their neutralization. Fig. 1. Structural and functional diagram of the biological system Immune protection of Industry 4.0 includes three key subsystems: Recognizer, Planner and Executor. Here, the Fig. 2. Phagocytic theory of E. Metchnikoff Recognizer is designed to recognize patterns (images) of Taking into account the requirements set forth above, we malicious code by its structural, correlation and invariants present the main goals of the organization of self-recovering features. The scheduler is intended for planning, i.e. creation of trusted computations C1, C2 and C3 by the following display corresponding plans and metaprograms of malicious code neutralization. The executor is intended for execution of the 𝐹𝐹0 ÷ 𝐹𝐹6 system (Figure 4). specified plans and metaprograms. As a result of these three In order to reach these goals, a number of research objectives subsystems operation, the required "purification" and formation were achieved. In particular, the model of restoration of of a trusted environment for calculations in the conditions of functional program specifications in the ideology of interrelated heterogeneous mass cyber-attacks by malefactors takes place. probative, verification and testing programming has been Whereas the classical immunology neutralizes antigens by developed (Figure 4). Here, the probative programming allowed physically destroying them (absorbing them), this is us to study the correctness of computational structures, unacceptable in cybernetic immunology. As far as the loss of a correctness of computability properties and stability of part of the functional program code can lead to denial of service calculations. These aspects were modelled by denotation, and impossibility to continue calculations as a whole. That is axiomatic and operational formal semantics of programs, why it was demanded that the functional semantics of respectively. calculations during the neutralization of malicious influences be Thus for an establishment of conformity between their invariable (constant) [1-7, 13-18]. Moreover, the critical functionally-logic specifications and physical design the information infrastructure of Industry 4.0 must be able to methods of annotated programs of N. Wirth, Ch. Hoare and E. recover from both known and previously unknown attackers. Dixtra were involved. 94 Fig. 3. State space of the system with "vaccinated" cyber immunity Fig. 5. The model of restoration of the functional program specifications Here, the level classification was made by analogy with the classification of formal languages by N. Khomsky. In the semantic class we chose models suitable for the construction of calculations, in the syntactic class we chose models that allow us to form automatic machines for the detection and neutralization of malicious influences. The class of semantic- syntactic models has allowed operating with the simplest forms of program calculation semantics in an effective basis of models types of graphical, schematic and network representation (Figure 6). At the same time, the control flow graph (CFG), Fig. 4. Goals and objectives of building a trusted synthesis system Yanov schemata and Petri nets were chosen to specify the model basis. In order to solve the specific problems of restoring the functional specifications of programs, a corresponding model As a result, the following architecture of the neutralization basis was developed (Figure 5) [1, 14]. system of malware and malicious software bookmarks was proposed (Figure 7) [3-5, 13, 14]. 95 The mentioned architecture includes three main subsystems. The first subsystem is intended for detecting defective program code fragments. The second subsystem sets suspicion that the detected defective code sections belong to destructive program bookmarks and forms a plan (metaprogram) for their neutralization. The third subsystem confirms the presence and forms a module for neutralizing destructive software bookmarks. In order to prove the correctness of functional semantics of the "cleared" calculations, a mathematical apparatus of the similarity theory and calculation dimensions were developed. In particular, the direct similarity theorem, which allows establishing the general scheme of representation of semantically correct calculations in the invariant (dimensionless) form, is formulated and proved 𝑥𝑥1𝑗𝑗 𝑥𝑥2𝑗𝑗 𝑥𝑥𝑛𝑛𝑛𝑛 (𝐷𝐷𝑖𝑖 � , ,…, , П1𝑖𝑖 , П2𝑖𝑖 , … , П𝑧𝑧𝑧𝑧−1 � = 0, (1) 𝑥𝑥1𝑗𝑗0 𝑥𝑥2𝑗𝑗0 𝑥𝑥𝑛𝑛𝑗𝑗0 where Fig. 6. Stratification of program models for calculation semantics research 𝑥𝑥1𝑗𝑗 𝑥𝑥2𝑗𝑗 𝑥𝑥𝑛𝑛𝑛𝑛 , ,…, - similarity invariants of calculations. 𝑥𝑥1𝑗𝑗0 𝑥𝑥2𝑗𝑗0 𝑥𝑥𝑛𝑛𝑗𝑗0 The direct similarity theorem allowed proving the statements about the necessary and sufficient similarity conditions of semantically correct calculations 𝑋𝑋(𝑘𝑘+1)𝑗𝑗 𝑥𝑥1𝑗𝑗 𝑥𝑥𝑘𝑘𝑘𝑘 ⎧𝑋𝑋(𝑘𝑘+1)𝑗𝑗 = 𝜑𝜑1 (П11 , … , П(𝑧𝑧1−1) ; 𝑥𝑥1𝑗𝑗0 , … , 𝑥𝑥𝑘𝑘𝑗𝑗0 ) 0 ⎪ 𝑋𝑋 𝑥𝑥1𝑗𝑗 𝑥𝑥𝑘𝑘𝑘𝑘 (𝑘𝑘+2)𝑗𝑗 = 𝜑𝜑2 (П12 , … , П(𝑧𝑧2−1) ; ,…, ) (2) 𝑋𝑋(𝑘𝑘+2)𝑗𝑗0 𝑥𝑥1𝑗𝑗0 𝑥𝑥𝑘𝑘𝑗𝑗0 ⎨ ⎪ 𝑋𝑋𝑛𝑛𝑛𝑛 = 𝜑𝜑 (П , … , П 𝑥𝑥1𝑗𝑗 𝑥𝑥𝑘𝑘𝑘𝑘 𝑚𝑚 1𝑚𝑚 (𝑧𝑧𝑚𝑚 −1) ; 𝑥𝑥 ,…, ) ⎩ 𝑋𝑋𝑛𝑛𝑗𝑗0 1𝑗𝑗0 𝑥𝑥𝑘𝑘𝑗𝑗0 where П1𝑖𝑖 = 𝑥𝑥1𝑗𝑗 ⁄𝐶𝐶1𝑗𝑗 , П2𝑖𝑖 = 𝑥𝑥2𝑗𝑗 ⁄𝐶𝐶2𝑗𝑗 , … , П𝑧𝑧𝑧𝑧−1 = 𝑥𝑥𝑛𝑛𝑛𝑛 ⁄𝐶𝐶𝑛𝑛𝑛𝑛 - similarity invariants, 𝐶𝐶𝑖𝑖𝑖𝑖 - multipliers of similarity ratios transformation, 𝜑𝜑𝑖𝑖 - functions of all or some relative data. Example. D For the assignment operator A ≔ B ∗ C + + 1, the E following relations must be performed between the abstract dimensions of the parameters (A, B, C, D, E, CONST_1): (1) ∗ 𝑙𝑙𝑙𝑙[𝐴𝐴] + (−1) ∗ 𝑙𝑙𝑙𝑙[𝐵𝐵] + (−1) ∗ 𝑙𝑙𝑙𝑙[𝐶𝐶] = 0, (1) ∗ 𝑙𝑙𝑙𝑙[𝐴𝐴] + (−1) ∗ 𝑙𝑙𝑙𝑙[𝐷𝐷] + (1) ∗ 𝑙𝑙𝑙𝑙[𝐸𝐸] = 0, (3) (1) ∗ 𝑙𝑙𝑙𝑙[𝐴𝐴]1 + (−1) ∗ 𝑙𝑙𝑙𝑙[𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑇𝑇1 ]1 = 0. The received relations allow defining unequivocally the standard (or passport) of semantically correct calculation. The calculation is semantically correct if the corresponding system of dimension equations has at least one component consisting of all non-zero components among the set of vectors-solutions. Fig. 7. Neutralization system architecture of the destructive software Let us suppose that this is not the case, and among these bookmarks parameters there appeared a parameter identically equal to zero at any values of other parameters. This indicates that the new 96 parameter is dimensionless. However, it is impossible because it one can find the transformation g, which connects two contradicts the initial condition of semantic correctness of equivalent objects 𝑂𝑂𝑟𝑟1 and 𝑂𝑂𝑟𝑟2 so that 𝑔𝑔 = 𝐹𝐹(𝑂𝑂𝑟𝑟2 )−1 𝐹𝐹(𝑂𝑂𝑟𝑟1 ). calculations, which was to be proved. It is essential that a multi-model approach was proposed Also, a п-converter was identified; this operator allows solving the task of synthesizing programs of trusted forming the required "passports" of trusted computations in the computations which allowes describing abstract programs of the conditions of disturbances. trusted computations in structural-functional, logical-semantic Statement 1: Operator F is a п-converter if for each object and computational-operational aspects [8-12, 14]. Such a multi- 𝑂𝑂𝑟𝑟𝑖𝑖 ∈ 𝑀𝑀 and each element 𝑔𝑔𝑣𝑣 ∈ 𝐺𝐺𝑣𝑣 of the finite abelian model organization of calculations required the introduction of coordination, allowing taking into account the specifics and subgroup the ratio of features of each named functional model of calculations. This 𝐹𝐹 ∗ �𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 � = 𝐹𝐹 ∗ �𝑂𝑂𝑟𝑟𝑖𝑖 �𝑔𝑔𝑣𝑣−1 , 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (4) has led to the need to build an appropriate knowledge metamodel. As basic models in the knowledge system it was is true. proposed to use formal grammar, production system, automatic Proof. converter. Let F is п-converter and F* is corresponding mapping in the When choosing a meta-modeling apparatus, preference was subgroup 𝐺𝐺𝑣𝑣 . given to the system of algorithmic algebras (SAA) proposed by academician V. M. Glushkov. This made it possible to create an Let us assume that the objects to be compared are equivalent. algorithmic system equivalent in its visual capabilities to such Then classical algorithmic systems as Turing machines, Post products and Markov algorithms. Besides, the advantage of SAA is the 𝐹𝐹�𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 � = 𝐹𝐹�𝑂𝑂𝑟𝑟𝑖𝑖 �, 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (5) possibility to express structures of abstract programs of trusted calculations in a strict basis of Dijkstra types (sequence, or in terms of mapping branching, cycle) in the form of corresponding algebraic 𝐹𝐹 ∗ �𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 ��𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 � = 𝐹𝐹 ∗ �𝑂𝑂𝑟𝑟𝑖𝑖 ��𝑂𝑂𝑟𝑟𝑖𝑖 �, 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (6) formulas. This allowed developing a multi-faceted algebraic system of the form < 𝐴𝐴, 𝐿𝐿 > with a signature of operations ∆, Apply now to the left and right parts of this equality the where A is a set of operators; L is a set of logical conditions taking values from a set of {true, false, uncertain}. Here, the 𝐹𝐹 ∗ (𝑂𝑂𝑟𝑟𝑖𝑖 )−1 , 𝐹𝐹 ∗ (𝑂𝑂𝑟𝑟𝑖𝑖 )−1 𝐹𝐹 ∗ �𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 ��𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 � = signature ∆= ∆1 ∪ ∆2 consists of a system of ∆1 logical = 𝐹𝐹 ∗ (𝑂𝑂𝑟𝑟𝑖𝑖 )−1 𝐹𝐹 ∗ �𝑂𝑂𝑟𝑟𝑖𝑖 ��𝑂𝑂𝑟𝑟𝑖𝑖 � = 𝑂𝑂𝑟𝑟𝑖𝑖 , 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (7) operations that take on a value in a variety of conditions L and a based on the property of the existence of the group unit system of ∆2 operations that take on values in a variety of operators A. 𝐹𝐹 ∗ (𝑂𝑂𝑟𝑟𝑖𝑖 )−1 𝐹𝐹 ∗ �𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 �𝑔𝑔𝑣𝑣 = 𝑒𝑒, 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (8) In SAA < 𝐴𝐴, 𝐿𝐿 > the system of forming ∐ is fixed. It is the multiplying on the left by 𝐹𝐹 ∗ (𝑂𝑂𝑟𝑟𝑖𝑖 ), get final functionally complete set of operators and logical conditions. With the help of this set and by means of 𝐹𝐹 ∗ �𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 �𝑔𝑔𝑣𝑣 = 𝐹𝐹 ∗ �𝑂𝑂𝑟𝑟𝑖𝑖 �, 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (9) superposition of operations included in ∆, arbitrary operators and logical conditions of the set A and L are generated. The multiplying on the right 𝑔𝑔𝑣𝑣−1 , find the required ratio logical operations of the system ∆1 include generalized Boolean 𝐹𝐹 ∗ �𝑔𝑔𝑣𝑣 𝑂𝑂𝑟𝑟𝑖𝑖 � = 𝐹𝐹 ∗ �𝑂𝑂𝑟𝑟𝑖𝑖 �𝑔𝑔𝑣𝑣−1 , 𝑖𝑖 = 1, 2, … , 𝑚𝑚 (10) operations of disjunctions, conjunctions, and negation, as well as the operation of left multiplication of the condition by the The converse holds true. operator 𝛽𝛽 = 𝐴𝐴𝐴𝐴 and filtration. The following operations belong As a result, the following conclusions can be drawn: to the ∆2 set: composition of operators 𝐴𝐴 ∗ 𝐿𝐿, sequential execution of operators A and L, α - disjunction of operators, - п-converter is a mapping of a reference pair alternative execution of operators A and L, i.e. 𝐹𝐹: 𝑀𝑀 → 𝑀𝑀0 (11) ̀ 𝛼𝛼(𝐴𝐴 ∨ 𝐿𝐿) = 𝐴𝐴, 𝑖𝑖𝑖𝑖 𝛼𝛼 = 1; - Set of standards M0 represents a set of objects (similarity 𝛼𝛼 (𝐴𝐴 ∨ 𝐿𝐿) = 𝐿𝐿, 𝑖𝑖𝑖𝑖 𝛼𝛼 = 0; (14) invariants), which do not change values of their information 𝛼𝛼 (𝐴𝐴 ∨ 𝐿𝐿) = J, 𝑖𝑖𝑖𝑖 𝛼𝛼 = 𝜊𝜊. signs under the action of п-converter F, i.e. Here, the α-iteration of operator A under the condition 𝛼𝛼𝛼𝛼 {𝐴𝐴} 𝐹𝐹�𝑂𝑂𝑟𝑟𝑖𝑖 � = 𝑂𝑂𝑟𝑟𝑖𝑖 , (12) consists in checking the condition α, if this condition is false, then the execution of operator A is performed. - With the help of п-converter F and the corresponding mapping It should be noted that such a representation < 𝐴𝐴, 𝐿𝐿 > allows developing effective regularization procedures (reduction to a 𝐹𝐹 ∗: 𝑀𝑀 → 𝐺𝐺𝑣𝑣 (13) regular scheme (RS)) 𝐹𝐹(∐) and prove the theorem, which defines the principal possibility of a formal description of an 97 arbitrary and reconstructed algorithm and procedure of trusted calculations in RS. Thus, it is possible to formally describe the declarative, technological and procedural knowledge of trusted computations in the form of regular schemes. Statement 2. Calculations with "antibodies" are represented by regular schemes in the system of algorithmic algebras (SAA) of V. M. Glushkov. The modified technique of a composite programming allowed determining the effective sequence of operations of trusted calculations. For each operator's construction there were given operations and operands that make up the program of Fig. 9. Broadcast immunity antibody formation program trusted calculations. After checking the completeness of this program for compliance with the selected criteria, an executable program of trusted calculations was synthesized (Figure 8). III. CONCLUSION An overview of the new concept of cyber immunity of Industry 4.0. is presented in Figure 10. The following significant results have been obtained in the course of the concept development. Fig. 8. Creation of operator constructions of the trusted computing program A semantically controlled translator based on formal automata with abstract memory (AAM) was developed for the interpretation of the input program of the trusted computations and type of actions (Figure 9). The AAM consists of four elastic belts (EB), which contain: • Messages of functional automatons; • Reports of identified software bookmarks; • Neutralization and countermeasures scenarios; • Information messages of the broadcast procedures’ completion. Fig. 10. Possible immune protection methods of Industry 4.0 98 Theoretical results: Proceedings of SPIIRAS. - 2015. - Issue. 2 (39). - P. 5-25. DOI: http://dx.doi.org/10.15622/sp.39.1 1. Scientific-methodological apparatus of computer [6] Biryukov D.N, Lomako A.G. Denotational Semantics of Knowledge immunology of cyber-security based on the mechanisms of Contexts in Ontological Modeling of the Subject Areas of Conflict // "immune response" and "immune memory" of classical Proceedings of SPIIRAS. - 2015. - Issue. 5 (42). - P. 155-179. DOI: http://dx.doi.org/10.15622/sp.42.8 immunology. [7] Biryukov D.N, Rostovtsev Yu.G. Approach to constructing a consistent 2. Methodology of self-recovery of trusted machine theory of synthesis of scenarios of anticipatory behavior in a conflict // Proceedings of SPIIRAS. - 2015. - Issue. 1 (38). - P. 94-111. DOI: calculations with the required functional semantics of http://dx.doi.org/10.15622/sp.38.6 calculations. [8] Gruber T. A translation approach to portable ontology specifications. // Scientific and practical results: Knowledge Acquisition, 1993, V. 5, I. 2, pp. 199 - 220. DOI: 10.1006/knac.1993.1008. • Approach to deobfuscation and normalization of logical [9] Gruber T. Toward Principles for the Design of Ontologies Used for structures of calculations using a system of equivalent Knowledge Sharing? // International Journal Human-Computer Studies, 1995, V. 43, I. 5–6, pp. 907 - 928. DOI: 10.1006/ijhc.1995.1081. transformations of Janov's schemes. [10] Guarino N., Musen M. Applied ontology: The next decade begins // • Method of combined verification of semantics of Applied Ontology. - 2015. - V. 10, no. 1, pp. 1-4. DOI: 10.3233/AO- 150143. calculations on the basis of similarity invariants and [11] Kotenko, I.V. Intelligent mechanisms of cybersecurity management // In provocative load testing. Risk and security management. Proceedings of the Institute of System • Methods of generating trusted program algorithms on the Analysis of the Russian Academy of Sciences, 2009, Vol.41, pp.74-103. [12] Nardi J., Falbo R., Almeida J., Guizzardi G., Pires L., Sinderen M., basis of synthesis of calculations in the system of Guarino N. An Ontological Analysis of Value Propositions. Published in: algorithmic algebra and scenarios of permits. Enterprise Distributed Object Computing Conference (EDOC), 2017 IEEE 21st International. Quebec City, QC, Canada, 10-13 Oct. 2017, pp. • Computer immunology technology for cybersecurity and 184 - 193. DOI: 10.1109/EDOC.2017.32. private methods of detecting and neutralizing destructive [13] Petrenko, A.S., Petrenko, S.A., Makoveichuk, K.A., Chetyrbok, P.V. software bookmarks and program vulnerabilities. Protection model of PCS of subway from attacks type «wanna cry», «petya» and «bad rabbit» IoT, 2018 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), 2018, REFERENCES pp. 945-949. DOI: 10.1109/EIConRus.2018.8317245 [1] Ashby W.R. (1991) Principles of the Self-Organizing System. In: Facets [14] Petrenko, S.A., Makoveichuk, K.A. Ontology of cyber security of self- of Systems Science. International Federation for Systems Research recovering smart Grid In CEUR Workshop Proceedings, 2017, Vol-2081, International Series on Systems Science and Engineering, vol 7. Springer, pp. 98 – 106. http://ceur-ws.org/Vol-2081/paper21.pdf Boston, MA. DOI: https://doi.org/10.1007/978-1-4899-0718-9_38 [15] Pospelov D. A. The modeling of reasoning. Experience in the analysis of [2] Barabanov A.V., Markov A.S., Tsirlov V.L. Methodological Framework mental acts. - M .: Radio and communication. - 1989. - 184 p. (In for Analysis and Synthesis of a Set of Secure Software Development Russian). Controls, Journal of Theoretical and Applied Information Technology, [16] Leontiev V., Gordeev E. On the Algebraic Immunity of Coding Systems. 2016, vol. 88, No 1, pp. 77-88. Voprosy kiberbezopasnosti [Cybersecurity issues], 2019, No 1 (29), pp. [3] Biryukov D. N Cognitive-functional memory specification for simulation 59-68. DOI: 10.21681/2311-3456-2019-1-59-68. of purposeful behavior of cyber systems // Proceedings of SPIIRAS. - [17] Pospelov D. A. Thinking and automatons. - Moscow: Soviet radio. - 1972. 2015. - Issue. 3 (40). - C. 55-76. DOI: http://dx.doi.org/10.15622/sp.40.5 - 224 p. (In Russian). [4] Biryukov D.N, Lomako A. G, Petrenko S. A. Generating scenarios for [18] Sheremet I. A. Augmented Post Systems: The Mathematical Framework preventing cyber attacks // Protecting information. Inside. - 2017. - No. 4 for Data and Knowledge Engineering in Network-centric Environment. (76). (In Russian). Berlin, 2013. 395 p. [5] Biryukov D.N, Lomako A.G, Rostovtsev Yu.G. The appearance of anticipatory systems to prevent the risks of cyber threat realization // 99