# Deciding some Maltsev conditions in finite idempotent algebras

## TL;DR

This paper studies the computational complexity of determining whether finite idempotent algebras satisfy certain Maltsev conditions, showing that for path-based conditions, this testing can be done efficiently in polynomial time.

## Contribution

The paper proves that deciding fixed path-based Maltsev conditions in finite idempotent algebras is polynomial-time solvable.

## Key findings

- Polynomial-time decision algorithms for path-based Maltsev conditions
- Applicability to conditions like Maltsev, majority, and Jónsson terms
- Enhanced understanding of the complexity landscape for algebraic property testing

## Abstract

In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a fixed (strong) Maltsev condition $\Sigma$. Our goal in this paper is to show that $\Sigma$-testing can be accomplished in polynomial time when the algebras tested are idempotent and the Maltsev condition $\Sigma$ can be described using paths. Examples of such path conditions are having a Maltsev term, having a majority operation, and having a chain of J\'onsson (or Gumm) terms of fixed length.