On the membership problem for finite automata over symmetric groups

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-12-01 DOI:10.1515/dma-2022-0033

Arthur A. Khashaev

引用次数: 1

Abstract

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.

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对称群上有限自动机的隶属性问题

摘要:我们考虑的自动机中的转换被标记为任意排列。这种自动机的语言由所有可能允许的计算路径的排列组合组成。有限自动机在对称群上的隶属性问题是一个决策问题:给定的排列是否属于给定自动机的语言?我们证明了这个问题是np完全的。对于强连接自动机，我们也提出了一种有效的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.