Knuth-Bendix algorithm and the conjugacy problems in monoids

TL;DR

This paper introduces an algorithmic method for solving conjugacy problems in monoids by extending the Knuth-Bendix rewriting system to incorporate cyclic conjugates, advancing the theoretical framework for these algebraic structures.

Contribution

It extends the classical Knuth-Bendix rewriting theory to handle cyclic conjugates, providing a new approach for conjugacy problems in monoids.

Findings

Developed a new rewriting algorithm for conjugacy in monoids

Extended classical rewriting theory to cyclic conjugates

Provides a framework for algorithmic conjugacy decision in monoids

Abstract

We present an algorithmic approach to the conjugacy problems in monoids, using rewriting systems. We extend the classical theory of rewriting developed by Knuth and Bendix to a rewriting that takes into account the cyclic conjugates.