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Diskretnaya Matematika, 2021, Volume 33, Issue 1, Pages 82–90
DOI: https://doi.org/10.4213/dm1633 (Mi dm1633) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the membership problem for finite automata over symmetric groups

A. A. Khashaev

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/dm1633
Abstract: We consider automata in which transitions are labelled with arbitrary permutations. The language of such an automaton consists of compositions of permutations for all possible admissible computation paths. The membership problem for finite automata over symmetric groups is the following decision problem: does a given permutation belong to the language of a given automaton? We show that this problem is NP-complete. We also propose an efficient algorithm for the case of strongly connected automata.
Keywords: finite automata, groups, permutations, computational complexity.
Received: 19.01.2021
English version:
Discrete Mathematics and Applications, 2022, Volume 32, Issue 6, Pages 383–389
DOI: https://doi.org/10.1515/dma-2022-0033
Document Type: Article
UDC: 519.713
Language: Russian
Citation: A. A. Khashaev, “On the membership problem for finite automata over symmetric groups”, Diskr. Mat., 33:1 (2021), 82–90; Discrete Math. Appl., 32:6 (2022), 383–389
Citation in format AMSBIB
\Bibitem{Kha21}
\by A.~A.~Khashaev
\paper On the membership problem for~finite automata over~symmetric groups
\jour Diskr. Mat.
\yr 2021
\vol 33
\issue 1
\pages 82--90
\mathnet{http://mi.mathnet.ru/dm1633}
\crossref{https://doi.org/10.4213/dm1633}
\transl
\jour Discrete Math. Appl.
\yr 2022
\vol 32
\issue 6
\pages 383--389
\crossref{https://doi.org/10.1515/dma-2022-0033}
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    • This publication is cited in the following 1 articles:
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