Arc Consistency and Friends

TL;DR

This paper analyzes arc consistency and its extensions within the framework of constraint languages, providing new polynomial-time results for singleton arc consistency and comparing their effectiveness across different languages.

Contribution

It offers a comprehensive comparison of arc consistency methods based on constraint languages and introduces new polynomial-time tractability results for singleton arc consistency.

Findings

Singleton arc consistency is polynomial-time tractable.

Different arc consistency methods solve different classes of constraint languages.

The study clarifies the relationships between various arc consistency extensions.

Abstract

A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc consistency, a heavily investigated inference method, and three extensions thereof from the perspective of constraint languages. We conduct a comparison of the studied methods on the basis of which constraint languages they solve, and we present new polynomial-time tractability results for singleton arc consistency, the most powerful method studied.