On tractability and congruence distributivity

TL;DR

This paper proves that constraint languages invariant under a short sequence of Jonsson terms are tractable, expanding understanding of the algebraic conditions that ensure computational efficiency in constraint satisfaction problems.

Contribution

It establishes that relations invariant under a short sequence of Jonsson terms have bounded relational width, demonstrating tractability for a significant class of congruence distributive algebras.

Findings

Relations invariant under short Jonsson term sequences are tractable.

Such relations have bounded relational width.

This advances the algebraic understanding of constraint satisfaction problems.

Abstract

Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence distributive varieties and included among this class are lattices, and more generally, those algebras that have near-unanimity term operations. An algebra will generate a congruence distributive variety if and only if it has a sequence of ternary term operations, called Jonsson terms, that satisfy certain equations. We prove that constraint languages consisting of relations that are invariant under a short sequence of Jonsson terms are tractable by showing that such languages have bounded relational width.