Open AccessOn generic complexity of the problem of searching of isomorphism for finite semigroups
Author(s) -
Alexander Rybalov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1901/1/012045
Subject(s) - mathematics , isomorphism (crystallography) , bijection , semigroup , finite set , permutation (music) , krohn–rhodes theory , special classes of semigroups , discrete mathematics , combinatorics , algebra over a field , pure mathematics , mathematical analysis , chemistry , physics , acoustics , crystal structure , crystallography
This article is devoted to the investigation of generic complexity of the problem of searching of isomorphism for finite semigroups. That problem can be formulated as follows. For any pair of isomorphic finite semigroup Si and S 2 with elements {1, 2,…, n}, represented by its multiplication tables, we need to find a bijection (permutation) of the set {1, 2,…, n}, which implements an isomorphism between S 1 and S 2 . As for the classical isomorphism problem, any polynomial (even probabilistic) algorithms are unknown for the problem of searching of isomorphism for finite semigroups. We construct natural subproblems of this problem, for which there is no polynomial generic algorithm, provided that this problem is hard in the classical case. The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0004).