Polynomial-time Tests for Difference Terms in Idempotent Varieties

TL;DR

This paper presents an efficient method to determine whether a finite algebra in an idempotent variety has a difference term, along with algorithms for constructing such operations, advancing the understanding of algebraic structures.

Contribution

It provides the first polynomial-time decision procedure for the existence of difference terms in finite idempotent algebras and algorithms for their construction.

Findings

Decided the existence of difference terms in polynomial time for idempotent varieties.

Developed algorithms for constructing difference term operations.

Extended the understanding of algebraic properties in finite idempotent varieties.

Abstract

We consider the following practical question: given a finite algebra A in a finite language, can we efficiently decide whether the variety generated by A has a difference term? We answer this question (positively) in the idempotent case and then describe algorithms for constructing difference term operations.