ISSN 0236-235X (P)
ISSN 2311-2735 (E)

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Publication date:
16 September 2024

Articles of journal № 3 at 2023 year.

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Public date | Title | Authors

1. Constructing perfect normal forms of Boolean functions for circuit implementations of authentication protocols using Maple [№3 за 2023 год]
Authors: Olenev, A.A., Kalmykov, I.A., Kirichek, K.A.
Visitors: 1854
One of the promising areas of applying discrete mathematics are zero-knowledge authentication protocols based on modular residue class codes (MRCC). Using MRCC allows replacing a computing device that implements the operation of raising to a power modulo with a code converter. As a result, a complex computational operation is executable in one machine phase. It is obvious that the efficiency of code converters depends largely on the correct transition from the truth table to perfect normal forms of Boolean functions. The authors of this article have developed a software code and a graphical application for a computer that allows obtaining perfect disjunctive or conjunctive forms in accordance with the content of the truth tables described by the user and displaying the result in the corresponding field in mathematical form. Perfect forms can be obtained using the description of the truth table both in the form of minterms (maxterms) of a Boolean function using the logical variables true or false, and using the numbers of sets of minterms (maxterms). There is a possibility to choose the type of the obtained perfect form. The developed application contains reference data on its use. The software code and the entire graphical user interface are written using the built-in language of the Maple computer algebra system, as well as using the Maplet library. It was possible to create an interactive application that is user-friendly for non-professional programmers (mathematics teachers, students). For the convenience of the end user, the program is designed as a graphical application that requires only the Maple system installed. The developed application can be used by educational organizations that study the academic disciplines of mathematical logic, discrete mathematics or their sections.

2. Fast quantum search algorithm modelling on conventional computers: Information analysis of the halting problem [№3 за 2023 год]
Authors: Ulyanov, S.V., Ulyanov, V.S.
Visitors: 1578
The paper describes the simplest technique for simulating a quantum algorithm based on the direct matrix representation of quantum operators. This approach is stable and precise, but it requires allocation of operator’s matrices in the computer memory. Since the size of the operators grows exponentially, this approach is useful for simulating quantum algorithms with a relatively small number of qubits (e.g., approximately 11 qubits on a typical desktop computer). This approach enables relatively simple simulation of the operation of the solution quality control system and performance of a reliability analysis. A more efficient fast quality control simulation method is based on computing all or a part of operator matrices as needed on a current computational basis. This method makes it possible to avoid storing all or a part of the operator matrices. In this case, the number of qubits to be simulated (e.g., the number of input qubits or the number of qubits in the system state register) is affected by: (I) the exponential growth in the number of operations required to calculate the result of matrix products; and (II) the size of the state vector allocated in computer memory. It is reasonable if one embodiment of this approach involves simulating up to 19 or more qubits on typical desktop computer, and even more in a system with a vector architecture. Due to particularities of the memory addressing and access processes in a typical desktop computer (such as, for example, a Pentium PC), when a number of qubits is relatively small, the on-demand computing tends to be faster than the direct storage approach. The compute-on-demand approach benefits from applying the results of studying quantum operators and their structure that enables computing the matrix elements more efficiently. The paper considers effective simulation of Grover’s quantum search algorithm using a computer with classical architecture.

3. Developing a GH-graph proportional separation algorithm to form of object influence zones in complex technical systems [№3 за 2023 год]
Author: Muntyan, Е.R.
Visitors: 1766
The article suggests one of the possible solutions to the problem the object influence zones in complex technical systems (СTS). It considers the extended perimeter security system as a СTS example, investigates the interaction of its objects (elements). The objects of such a system are mobile or stationary security objects, quadrocopters, decision makers, possible potential perimeter violators; provided that quadrocopters have different technical characteristics, in particular, the their video camera surveillance radii differ. To simulate the process of interaction of security system objects, the authors use a model based on a fuzzy graph with different types of vertices and multiple and different types of connections (GH-graph). Multiple connections in the GH-graph are vector connections that combine several different types of connections into one. Such model allows setting all necessary relationships between system elements and at the same time, it has an advantage in the time of calculating distances compared to graphs using only same type and different types of connections. To solve this problem, the authors propose using GH-graph algorithmic modeling means, including the graph proportional separation algorithm and the means of calculating graph metrics. The paper defines the GH-graph splitting operation, defines the separation criteria: the proportionality of subgraphs by a given parameter and the possibility of subgraph intersection. The authors have carried out the synthesis of the GH-graph proportional separation algorithm in accordance with the criteria and shown the algorithm results using the example of the graph model considered. It is shown that using the proposed graph separation algorithm into proportional subsets and the means of calculating the metric characteristics of the obtained subgraphs make it possible to determine the system object influence zones in accordance with their technical parameters. The paper considers the possibilities of software implementation of the proposed algorithm.

4. On one trend in the development of algorithms implemented in decision support systems [№3 за 2023 год]
Authors: Sayapin, O.V., Tikhanychev, O.V., Bezvesilnaya, A.A., Chiskidov, S.V.
Visitors: 1658
The article considers the issues of implementing effective control algorithms for complex human-machine systems in modern conditions. The subject area analysis shows that recently, algorithms based on simple but reliable methods are increasingly used in management practice; their use was previously problematic due to high computational costs. The practical use of such methods has become possible due to the computer technology development and the growth of the bandwidth of data transmission networks. As an example of implementing such algorithms, the authors consider the methods for forming control actions using the control process visualization using virtual reality technologies. The relevance of the work is determined by the fact that in the conditions of control of dynamic spatially distributed ergodic systems, existing control methods and technologies do not always provide the required efficiency. At the same time, effective management is the key to the successful application of any systems. Based on the analysis of a typical control cycle and the shortcomings of the currently used control algorithms, the article synthesizes proposals for using models based on direct calculations and exhaustive search methods. As an example, it considers the use of models based on virtual reality tools for applying a visual algorithm reducing the current state of the controlled system to the required state to achieve a goal. The proposed algorithm logically complements the algorithms for solving optimization problems and information retrieval, being in the general trend of the development of algorithmization of decision support systems in favor of simplifying the methods used.

5. A research on concurrent binary tree properties [№3 за 2023 год]
Authors: Grachev, V.G., Ushakov, A.S.
Visitors: 1318
The navigation simulator software “Marine Operation Simulation System” (MOSS) implements the automatic construction technology for a global terrain 3D-model based on the recursive subdivision algorithm with a locally adaptive level of detail control. The algorithm is entirely implemented on the graphics adapter (GPU) and uses massive parallel data processing in compute shaders. The recursive subdivision algorithm is based on using a binary tree; however, classical binary trees explicitly described using pointers are not applicable to GPU implementations due to architectural features. To ensure the parallel execution of the algorithm, the authors use a specialized parallel data structure that is a concurrent binary tree (CBT). The article describes the prerequisites for creating a CBT structure and considers its construction stages from using an implicit binary tree up to representing a binary tree as a binary field augmented with a reduced sum of leaf nodes. The required RAM amount to accommodate a CBT of a given depth is theoretically substantiated. There is an analysis of the algorithmic complexity of constructing a CBT and iterating over its leaf nodes. The article presents and analyzes the results of comparative synthetic performance tests of a concurrent binary tree performed on a central processing unit (CPU) and GPU, as well as the results of the practical application of CBT in MOSS.

6. A method of deformation of functionally defined objects using graphics processing units [№3 за 2023 год]
Authors: Vyatkin, S.I., Dolgovesov, B.S.
Visitors: 1670
The article discusses a method of modeling deformation of elastic functionally specified objects. Deformation and animation of three-dimensional objects are important functions, but require a large number of calculations. Modeling elastic dynamic objects is used in computer graphics, biomechanics and robotics applications. The aim of the work is to develop a method for modeling deformation of elastic objects on a graphics processor. The subject of the study is the Chebyshev and Jacobi methods and their use in projective dynamics. The theoretical significance of the work is in the combination of Chebyshev and Jacobi methods for solving problems of deformation and animation of surfaces, where the problem is a large number of calculations. Projective dynamics can be effectively accelerated using the Chebyshev method. The practical significance is in implementing the method on a GPU. The combination of the Chebyshev method and the Jacobi method for projective dynamics is optimally implemented on a GPU, since the calculations are well parallelized. As a result, we get a simple implementation that does not require additional libraries to solve this problem and has a small memory. The method does not need to refactorize the matrix with each system change, which is used in direct calculation, and requires large computational costs. When testing the proposed method, we used free form patches based on grids of basic triangles. Testing shows that this approach accelerates the projective dynamics by about one order of magnitude when the Jacobi solution is used at the global stage.

7. Compensation of various types of uncertainties when controlling a technical object using intelligent controllers [№3 за 2023 год]
Author: Ignatyev, V.V.
Visitors: 1736
The article presents the research results on the development of hybrid intelligent controllers, which make it possible to ensure the effectiveness of the technical object control, including one functioning under uncertainty. The article is devoted to the issues of compensation of various types of uncertainties in controlling a technical object using intelligent controllers. It also gives a generalized classification of uncertainties and proposes a new classification with the definition of its types that are compensated using the developed methods and algorithms. The uncertainty types are parametric uncertainty, uncertain-ties caused by external influences, linguistic uncertainty. The author highlights linguistic uncertainty and gives methods for its compensation based on a control approach based on a combination of a classical control theory, fuzzy logic, neural network technologies and genetic algorithms. As a part of the demonstration of the approach, the author presents a general description of the entire process of obtaining the desired control for a technical object, including the one operating under conditions of uncertainty. The paper demonstrates the results of the work of the developed methods for controlling technical objects using intelligent controllers based on self-organization of knowledge bases. The basis of the methods is a self-organization algorithm of robust knowledge bases without involving an expert and automating the process of generating control rules. The implementation of these algorithms in control models makes it possible to obtain the desired control for technical objects including those functioning under uncertainty represented by linear or nonlinear mathematical models of the first, second, third order, including the ones with a delay. The presented simulation results confirm that the implementation of the hybrid control approach allows obtaining the desired control of a technical object including the one functioning under uncertainty.

8. USB connections control in the local network of computers running under Astra Linux SE [№3 за 2023 год]
Authors: Baranov, A.V., Korepanov, P.M., Lepeshev, I.A.
Visitors: 2153
The constant growth of information security requirements, as well as a major trend towards import replacement in the system software, have led to the widespread use of infrastructure solutions based on the domestic Astra Linux Special Edition (SE) operating system. Astra Linux makes it possible to build secure computing systems including supercomputers for processing confidentional information. At the same time, the audit of connecting USB devices to computers is one of the most important problems of ensuring information security. An analysis of the existing open access works shows the lack of turnkey solutions working in the Astra Linux SE environment. The article discusses a possible technological stack of such solution. The technological stack includes besides Astra Linux the RabbitMQ message-broker sofware, the Flask micro web framework, the PostgreSQL database, and the USBRip forensics tool for keeping track of USB event history on Linux machines. The proposed modular structure of the software USB connections audit system is considered. It includes the modules for collecting USB connections artifacts on controlled computers, the collected information aggregation module, and the module for checking the USB device connection permissions. The proposed structure and technological stack were implemented as a prototype of the software system called ALUMNUS. The prototype was deployed and tested in the secure segment of the MVS-10P OP supercomputer installed at the Joint Supercomputer Center of the Russian Academy of Sciences.

9. Organization of adaptive data routing in electric power complexes using ontological fuzzy classifiers [№3 за 2023 год]
Authors: Fedulov, A.S., Lazarev, A.I.
Visitors: 1781
The paper discusses the theoretical aspects of the machine learning application methods, in particular, the adaptation of deep models to the TCP/IP network topologies management in electric power complexes. The subject of the research in the paper is the author's approach to the organization of centralized network segments management in the field under consideration. The study of the interaction subjects in electric power units processes on the basis of the developed ontological models allowed to identify the main properties of multiformat data that may represent vulnerabilities for exploiting vulnerabilities. The practical significance of the research is represented by the development of a multi-module structure for tracking, classifying and predicting changes in consumed traffic, due to which it is possible to increase the efficiency of complex corporate network structures. Practical testing of existing algorithms for obtaining hash functions was carried out - the results allowed to conclude that it is advisable to use the basic BLAKE3 encryption algorithm as the main mechanism for verifying the authenticity of clients in comparison with the SHA-384, SHA-512, SHA-224, MD5 algorithms. The analytical implementation of the fuzzy character-by-character comparison algorithm as a decision-making module is given - this also allowed to confirm the relevance of the proposed approach when working with fuzzy data structures. As the main solution to these problems, an implemented approach to flexible management of the electric power plants segment represented by a complex of generating, electric grid, power supply and other companies is proposed. The main result of the proposed solution is the possible changes centralized analysis approach, taking into account adaptation to network loads based on selected ontological variables. Additional features in the implementation of this approach are compatibility with existing hardware network devices due to the unique architecture of the topology built.

10. An architecture of the decision support system for monitoring a technical condition of critical equipment [№3 за 2023 год]
Authors: Yemelyanov, V.A., Chernyi, S.G., Yemelyanova, N. Yu.
Visitors: 1660
The paper solves an applied problem of improving the existing system for diagnosing critical lined equipment without its decommissioning. The relevance of the work is due to the need to increase the level of automation and objectivity of decision-making during operation of critical lined equipment to prevent accidents in production. The purpose of the study is designing the architecture of a decision support system for monitoring the technical condition of critical lined equipment. As for research methods, for high-level architecture design of the decision support system in the process of monitoring the technical condition of critical lined equipment, we used the architecture modeling language ArchiMate. An object-oriented approach (including object-oriented analysis, object-oriented design and programming) and the unified modelling language UML were used to design the static system structure in the form of the main entities that are responsible for implementing the system functionality to support decision making on the admissibility of using critical lined equipment. As a result, there is a developed model of the top-level architecture of the decision support system for monitoring the technical condition of critical lined equipment. The developed software for a decision support system for monitoring the technical condition of critical lined equipment makes it possible to generate recommendations regarding the operating modes of critical lined equipment. The developed software was tested in the conditions of metallurgical production in the technological process of diagnosing mobile mixers PM350 at the Alchevsk Iron and Steel Works.

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