Computing congruences of finite inverse semigroups

TL;DR

This paper introduces a new algorithm for efficiently computing congruences in finite inverse semigroups using techniques from group theory, automata, and inverse semigroup theory, significantly outperforming previous methods.

Contribution

The paper presents a novel, highly efficient algorithm for computing congruences in finite inverse semigroups, integrating multiple theoretical techniques.

Findings

Algorithm outperforms existing implementations by several orders of magnitude

Uses techniques from group theory, automata, and inverse semigroup theory

Provides an initial implementation demonstrating superior performance

Abstract

In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups. An initial implementation of this algorithm outperforms existing implementations by several orders of magnitude.