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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, Volume 17, Issue 1, Pages 85–95
DOI: https://doi.org/10.18500/1816-9791-2017-17-1-85-95
(Mi isu706)
 

Scientific Part
Computer Sciences

The algorithm for checking transitivity of mappings associated with the finite state machines from the groups $AS_p$

M. V. Karandashov

Saratov State University, 83, Astrakhanskaya str., 410012, Saratov, Russia
References:
Abstract: The paper deals with a question of determining the property of transitivity for mappings defined by finite automata. A criterion of transitivity for mappings defined by finite automata on the words of finite length in terms of finite automata and trees of deterministic functions is presented. It is shown that for finite automata from groups $AS_p$ an algorithm can be constructed for checking transitivity. To prove this fact some properties of Abelian groups of permutations are used. Based on these results a matrix algorithm is constructed for checking transitivity of mappings associated with initial automata from groups $AS_p$. The special feature of this algorithm is its independence from lengths of the considered words. Results of numerical experiments and the upper bound of complexity of the algorithm are presented.
Key words: finite state machine, transitivity, automata mapping, $AS_p$ groups.
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: M. V. Karandashov, “The algorithm for checking transitivity of mappings associated with the finite state machines from the groups $AS_p$”, Izv. Saratov Univ. Math. Mech. Inform., 17:1 (2017), 85–95
Citation in format AMSBIB
\Bibitem{Kar17}
\by M.~V.~Karandashov
\paper The algorithm for checking transitivity of mappings associated with the finite state machines from the groups~$AS_p$
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2017
\vol 17
\issue 1
\pages 85--95
\mathnet{http://mi.mathnet.ru/isu706}
\crossref{https://doi.org/10.18500/1816-9791-2017-17-1-85-95}
\elib{https://elibrary.ru/item.asp?id=29112759}
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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