Generic complexity of solving of equations in finite groups, semigroups and fields

Abstract

The paper is devoted by investigation of generic complexity of the algorithmic problem of solving of systems of equations in finite groups, finite semigroups and finite fields. We show that if this problem is intractable in the worst case and P = BPP, then there is no polynomial strongly generic algorithm, which solves it. The first author is supported by Russian Science Foundation, grant 19-11-00209. The second author is supported by Russian Science Foundation, grant 18-71-10028.