IDENTIFICATION OF ALGEBRAIC OBJECTS WITH A BASED ON BAER METRIZATION OF OBJECTS CLASS

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I.I. Maksimenko
Federal State Educational Institution of Higher Education «Donetsk State University», Donetsk, University
Research interests: automata theory, graph theory, category theory, topology, artificial intelligence systems.

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UDC 519.713.4
DOI 10.34757/2413-7383.2023.30.3.006
Language:Russian

Annotation: The article discusses the problem of identifying objects of a class with a standard on the basis of various mathematical structures (finite automata, unstructured sets, lattices, closed semirings) based on the introduction of the concept of representation and the Baire metric of a special type. A criterion for the existence of representations in terms of the properties of limit objects of a class has been found, which generalizes the previously found criterion for Mealy automata. For a finite definition of classes the criterion is constructive. This criterion indicates the presence of a deep connection between the process of identification with the standard and the properties of the limiting points of the metric space of a class of objects.

Keywords: identification, representation, metric, fragment, cofragment, limits objects.

References:
1. Trakhtenbrot B.A., Barzdin Ya.M. Finite state machines (behavior and synthesis). M.: 1970. 400 p.
2. Kudryavtsev A.B., Aleshin S.V., Podkolzin A.S. Introduction to automata theory. M.: Nauka, 1985. 320 s.
3. Grunsky I.S., Kozlovsky V.A., Ponomarenko G.G. Representations of finite state machines by fragments of behavior. Kyiv: Nauk. Dumka, 1990. 232 p.
4. Grunsky I. S., Kozlovsky V. A. Synthesis and identification of automata. Kyiv: Naukova Dumka, 2004. 246 p.
5. Representations of automata and analysis of attacks on cryptosystems [Text]/I.S. Grunsky, V.A. Kozlovsky, O.M. Kopytova // Artificial intelligence. 2004. No. 4. P. 764–775.
6. Testing of fuzzy linear automata/D. V. Speransky//Izv. Sarat. un-ta. New ser. Ser.: Mathematics. Mechanics. Informatics.-2019.-No. 19(2), pp. 233–240.
7. Experiments with non-stationary bilinear automata /D. V. Speransky // Automation and telemechanics. - 2015. - No. 9. – P.161–174.
8. Properties of systems of defining relations for automata /I. S. Grunsky, A. S. Senchenko // Discrete Mathematics.-2004.-No. 16(4). -WITH. 79–87.
9. Control of deterministic graphs / S.V. Sapunov // Proceedings of IPMM NASU.-2003. t. 8. P. 106−110.
10. About one algorithmic model of relativity/ A.N. Kurgansky// Problems of artificial intelligence. 2018. No. 4(11). P. 16-27.
11. On the directed movement of a group of automata without a compass on a one-dimensional integer lattice / A. N. Kurgansky, S. V. Sapunov // Izv. Sarat. un-ta. New ser. Ser.: Mathematics. Mechanics. Informatics. 2016. No. 16(3). pp. 356–365
12. Experiments in the class of implementations of non-deterministic automata/I.I. Maksimenko//Reports of the National Academy of Sciences of Ukraine. 1999. No. 7. P.95–99.
13. Maksimenko I.I. On experiments with automata in the absence of an upper bound for the number of states [Text] / I.S. Grunsky, I.I. Maksimenko//Cybernetics and systems analysis. 1999. No. 4. P. 59–71.
14. Maksimenko I.I. Experiments in finitely defined metric spaces of automata: Abstract of Ph.D. physics and mathematics sciences; 01.01.09 / SSU - Saratov, 2000. - 16 p.
15. Polyintervals and their application in modeling systems / V. I. Levin // Problems of artificial intelligence. 2016. No. 2 (3). pp. 39–47.
16. Interval equations and their solutions / V. I. Levin, E. A. Nemkova // Problems of artificial intelligence. 2017. No. 3 (6). P.12-21.
17. Maksimenko I.I. Finite representations of unstructured objects / I.I. Maksimenko // Proceedings of the Institute of Applied Mathematics and Mechanics. 2009. No. 19.-P.162—167.
18. Maksimenko I.I. Finite representations in algebraic systems / I.S. Grunsky, I.I. Maksimenko // Proceedings of the Institute of Applied Mathematics and Mechanics. 2011. No. 21.P.80-91.
19. Maksimenko I. I. Recognition in Kleene algebras on idempotent semirings / I. I. Maksimenko, V. N. Kotenko // Bulletin of the Donetsk National University. Series G: Technical Sciences. 2023. No. 3. P. 24-32.
20. Maksimenko I.I. Coalgebraic elements of the theory of experiments with automata / A.N. Kurgansky, I.I. Maksimenko // Donetsk readings 2016. Education, science and challenges of our time: Proceedings of the I International Scientific Conference (Donetsk, May 16-18, 2016) - Volume 1 .- Rostov-on-Don: Southern Federal University Publishing House, 2016. P.240-243.

Issues: 3(30)'2023
Section: Math modeling
Cite: Maksimenko, I.I. IDENTIFICATION OF ALGEBRAIC OBJECTS WITH A BASED ON BAER METRIZATION OF OBJECTS CLASS // I.I. Maksimenko // Проблемы искусственного интеллекта. - 2023. № 3 (30). - http://search.rads-doi.org/project/13749/object/201188 doi: 10.34757/2413-7383.2023.30.3.006

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