Article 6220
Title of the article |
ON THE PROBLEM OF LOGIC-AUTOMATIC FORMULAS PERFORMABILITY |
Authors |
Marchenkov Sergey Serafimovich, Doctor of physical and mathematical sciences, professor, sub-department of mathematical cybernetics, Moscow State University (1 Leninskiye Gory, Moscow, Russia), E-mail: ssmarchen@yandex.ru |
Index UDK |
519.712.2 |
DOI |
10.21685/2072-3040-2020-2-6 |
Abstract |
Background. In the theory of finite automata, there are a number of ways to define finite automata (finitely automatic functions). There are systems of canonical equations among them, Moore diagrams, information trees, schemes of automatic elements, and finite-automaton operations. Each of these methods has certain advantages and finds application in suitable research areas. Quite often finite automata are studied by algebraic and logical means. For example, the results of J. Büchi on the connection of finite automata with second-order logic are well known, as well as the results of S. V. Aleshin on the use of groups of finitely automatic permutations in solving the weakened Burnside problem. One of the promising directions in the theory of finite automata is the study of automaton equations of various types. In addition to the well-known canonical equations, there may be functional equations in which variables are finite automata, and connections between them are made using algebraic and logical means. The most natural option is the option when automatic terms are determined based on the given automata and functional variables for (multi-input) automata, then equality of terms (elementary formulas) and finally from elementary formulas using logical connectives-arbitrary logic automaton formulas. For such formulas, the “classic” feasibility problem is posed. Its peculiarity is that we consider the existence of finite automata that perform this formula, i.e. giving the true value of the formula for any values of subject variables (their values are arbitrary superwords in the alphabet {0,1}). The goal of this work is to prove the algorithmic solvability of this problem, while the resolving algorithm is defined in automata terms and ultimately based on a directed iteration of partial nondeterministic automata. |
Key words |
logic automaton formulas formulas, performability problem |
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References |
1. Brauer V. Vvedenie v teoriyu konechnykh avtomatov [Introduction to the theory of finite state automaton]. Moscow: Radio i svyaz', 1987, 392 p. [In Russian] |
Дата обновления: 16.09.2020 13:51