The conjugacy problem in semigroups and monoids

TL;DR

This paper introduces an algorithmic method using rewriting systems to solve conjugacy problems in certain classes of monoids and semigroups, including free monoids and completely simple semigroups.

Contribution

It provides a new solution to the conjugacy problem for monoids and semigroups presented by complete rewriting systems under specific conditions.

Findings

Algorithmic approach to conjugacy problems

Equivalence of transposition and conjugacy in certain classes

Solution for monoids and semigroups with complete rewriting systems

Abstract

We present an algorithmic approach to the conjugacy problems in monoids and semigroups, using rewriting systems. There is a class of monoids and semigroups that satisfy the condition that the transposi- tion problem and the left and right conjugacy problem are equivalent. The free monoid and the completely simple semigroups belong to this class. We give a solution to the conjugacy problem for monoids and semigroups in this class that are presented by a complete rewriting system that satisfies some additional conditions.