A Numerical Aggregation Method for Finite-State Machines Using Algebraic Operations
- Authors: Menshikh V.V1, Nikitenko V.A1
-
Affiliations:
- Voronezh Institute of the Ministry of Internal Affairs of Russia
- Issue: No 6 (2023)
- Pages: 66-75
- Section: Information Technology in Control
- URL: https://ogarev-online.ru/1819-3161/article/view/292106
- DOI: https://doi.org/10.25728/pu.2023.6.6
- ID: 292106
Cite item
Full Text
Abstract
This paper considers the problem of synthesizing finite-state machines (FSMs) based on algebraic methods. The aggregation operations of FSMs are numerically implemented using symbolic matrices that describe their functioning. An algebra is defined for these matrices as follows: the carriers are matrix elements and special symbols, and the signature includes two operations serving to determine actions over these symbols. As a result, it becomes possible to define an algebra of symbolic matrices whose signature includes three operations. The classical operations over FSMs are represented in matrix form based on the algebra of symbolic matrices. Next, special operations over FSMs are constructed involving classical operations over them. Special operations are constructed considering the constraints and requirements of the subject area. A numerical example of FSM synthesis––the joint activity of two functional groups in an emergency zone––is provided.
About the authors
V. V Menshikh
Voronezh Institute of the Ministry of Internal Affairs of Russia
Email: menshikh@list.ru
Voronezh, Russia
V. A Nikitenko
Voronezh Institute of the Ministry of Internal Affairs of Russia
Email: vitalijnikitenko82043@gmail.com
Voronezh, Russia
References
- Калман Р.Э., Фалб П.Л., Арбиб М.А. Очерки по математической теории систем (пер. с англ.) / Под ред. Я.З. Цыпкина, Э.Л. Наппельбаума. – М.: Едиториал УРСС, 2004. – 400 с. [Kalman, R.E. Falb, P.L., Arbib, M.A. Topics in Mathematical System Theory. – New York: McGraw Hill, 1969. – 358 p.]
- Villa, T., Yevtushenko, N., Brayton, R.K., et al. The Unknown Component Problem: Theory and Applications. – Cham: Springer, 2012. – 311 p.
- Меньших В.В. Петрова Е.В. Теоретическое обоснование и синтез математической модели защищенной информационной системы ОВД как сети автоматов // Вестник Воронежского института МВД России. – 2010. – № 3. – С. 134–143. [Men'shih, V.V., Petrova, E.V. Teoreticheskoe obosnovanie i sintez matematicheskoj modeli zashchishchennoj informacionnoj sistemy OVD kak seti avtomatov // Vestnik Voronezhskogo instituta MVD Rossii. – 2010. – No. 3. – P. 134–143. (In Russian)]
- Меньших В.В., Петрова Е.В. Применение методов теории автоматов для моделирования информационных процессов // Вестник Воронежского института МВД России. – 2009. – № 1. – С. 121–130. [Men'shih, V.V., Petrova, E.V. Primenenie metodov teorii avtomatov dlya modelirovaniya informacionnyh processov // Vestnik Voronezhskogo instituta MVD Rossii. – 2009. – No. 1. – P. 121–130. (In Russian)]
- Hartmanis, J., Stearns, R. Algebraic Structure Theory of Sequential Machines. – New York: Prentice-Hall Inc., 1966. – 211 p.
- Меньших В.В., Самороковский А.Ф., Середа Е.Н., Горлов В.В. Моделирование коллективных действий сотрудников органов внутренних дел. – Воронеж: Воронежский институт МВД России, 2017. – 236 с. [Men'shih, V.V., Samorokovskij, A.F., Sereda, E.N., Gorlov, V.V. Modelirovanie kollektivnyh dejstvij sotrudnikov organov vnutrennih del. – Voronezh: Voronezhskij institut MVD Rossii, 2017. – 236 s. (In Russian)]
- Zhong, G., Zhai, G., Chen, W. Evacuation Simulation of Multi-story Buildings during Earthquakes Based on Improved Cellular Automata Model // Journal of Asian Architecture and Building Engineering. – 2022. – Vol. 22, iss. 2. – P. 1007–1027.
- Горбатов В.А. Фундаментальные основы дискретной математики. Информационная математика. – М.: Наука. Физматлит, 2000. – 544 с. [Gorbatov, V.A. Fundamental'nye osnovy diskretnoj matematiki. Informacionnaya matematika. – M.: Nauka. Fizmatlit, 2000. – 544 s. (In Russian)]
- Teren, V., Villa, T., Cortadella, J. Decomposition of Transition Systems into Sets of Synchronizing State Machines // Proceedings of 24th Euromicro Conference on Digital System Design (DSD 2021). – Palermo, 2021. – P. 77–81.
- Мелихов А.Н. Ориентированные графы и конечные автоматы. – М.: «Наука», 1971. – 416 с. [Melihov, A.N. Orientirovannye grafy i konechnye avtomaty. – M.: «Nauka», 1971. – 416 s. (In Russian)]
- Алгебраическая теория автоматов, языков и полугрупп / Под ред. A.M. Арбиба. – М.: Статистика, 1975. – 335 c. [Algebraic Theory of Machines, Languages and Semigroups / Ed. by A.M. Arbib. – New York and London: Academic Press, 1968. – 359 p.]
- Салий В.Н. Универсальная алгебра и автоматы: Учебное пособие для студентов механико-математического факультета. – Саратов: Саратовский национальный исследовательский государственный университет имени Н.Г. Чернышевского, 1988. – 73 с. [Salij, V.N. Universal'naya algebra i avtomaty: Uchebnoe posobie dlya studentov mekhaniko-matematicheskogo fakul'teta. – Saratov: Saratovskij nacional'nyj issledovatel'skij gosudarstvennyj universitet imeni N.G. Chernyshevskogo, 1988. – 73 s. (In Russian)
- Алешин С.В. Алгебраические системы автоматов. – М.: ООО «МАКС Пресс», 2016. – 192 с. [Aleshin, S.V. Algebraicheskie sistemy avtomatov. – Moscow: OOO «MAKS Press», 2016. – 192 s. (In Russian)]
- Кожухов И.Б., Михалев А.В. Об алгебраической теории автоматов // Интеллектуальные системы. Теория и приложения. – 2021. – Т. 25, № 4. – С. 45–51. [Kozhuhov, I.B., Mihalev, A.V. On Algebraic Automata // Intelligent Systems. Theory and Applications. – 2021. – Vol. 25, no. 4. – P. 45–51. (In Russian)]
Supplementary files
