On the cardinality computation problem for regular languages over symmetric groups. (English. Russian original) Zbl 07881447
Mosc. Univ. Comput. Math. Cybern. 48, No. 2, 130-136 (2024); translation from Vestn. Mosk. Univ., Ser. XV 2024, No. 2, 73-79 (2024).
Summary: Representations of regular languages over symmetric groups in the form of finite automata and regular expressions are considered. The NP-hardness of deciding the cardinality of a language for such representations is proven.
References:
| [1] | Eilenberg, S., Automata, Languages, and Machines, 1974, New York: Academic Press, New York · Zbl 0317.94045 |
| [2] | Sakarovitch, J., Elements of Automata Theory, 2009, Cambridge: Cambridge Univ. Press, Cambridge · Zbl 1188.68177 · doi:10.1017/CBO9781139195218 |
| [3] | A. I. Kostrikin, Introduction to Algebra, Part I: Fundamentals of Algebra (MTsNMO, Moscow, 2020) [in Russian]. |
| [4] | Eder, E., Properties of substitutions and unifications, J. Symbolic Comput., 1, 31-46, 1985 · Zbl 0589.68063 · doi:10.1016/S0747-7171(85)80027-4 |
| [5] | G. Metakides and A. Nerode, Principles of Logic and Logic Programming (North-Holland, Amsterdam, 1996; Factorial, Moscow, 1998). · Zbl 0862.68013 |
| [6] | A. A. Letichevskii, ‘‘Equivalence of automata with respect to semigroups,’’ Teor. Kibern., No. 6 (Kiev, 1970), pp. 3-71. |
| [7] | Letichevskii, A. A., Probl. Kibern., No. 27, 1973, Moscow: Nauka, Moscow |
| [8] | Letichevskii, A. A.; Smikun, L. B., On a class of groups with solvable problem of automata equivalence, Sov. Math. Dokl., 17, 341-344, 1976 · Zbl 0359.02034 |
| [9] | R. I. Podlovchenko, ‘‘Semigroup program models,’’ Programmirovanie, No. 4, 3-13 (1981) [Program. Comput. Software 7 (4), 181-189 (1981)]. · Zbl 0482.68016 |
| [10] | Zakharov, V. A.; Zhailauova, Sh. R., On the minimization problem for sequential programs, Model. Anal. Inf. Sist., 24, 415-433, 2017 · doi:10.18255/1818-1015-2017-4-415-433 |
| [11] | Khashaev, A. A., On the membership problem for finite automata over symmetric groups, Discrete Math. Appl., 32, 383-389, 2022 · Zbl 1506.68047 · doi:10.1515/dma-2022-0033 |
| [12] | Thompson, K., Programming Techniques: Regular expression search algorithm, Commun. ACM, 11, 419-422, 1968 · Zbl 0164.46205 · doi:10.1145/363347.363387 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
