On generic complexity of the problem of searching of isomorphism for finite semigroups

Abstract

Abstract 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 S2 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 S1 and S2. 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).