CD(4) has bounded width

TL;DR

This paper proves that certain algebraic constraint languages invariant under specific Jónsson terms have bounded width, indicating their tractability and supporting the Larose-Zadori conjecture in the congruence-distributive case.

Contribution

It establishes bounded width for constraint languages invariant under a short sequence of Jónsson terms, improving previous results and providing evidence for the Larose-Zadori conjecture.

Findings

Constraint languages with specific Jónsson invariance are tractable.

Bounded width is proven for these languages.

Supports the Larose-Zadori conjecture in the congruence-distributive case.

Abstract

We prove that the constraint languages invariant under a short sequence of J\'onsson terms (containing at most three non-trivial ternary terms) are tractable by showing that they have bounded width. This improves the previous result by Kiss and Valeriote and presents some evidence that the Larose-Zadori conjecture holds in the congruence-distributive case.