# On Singleton Arc Consistency for CSPs Defined by Monotone Patterns

## TL;DR

This paper characterizes classes of CSPs defined by forbidden patterns that are solvable by singleton arc consistency, identifying new maximal patterns and extending understanding of their solving power.

## Contribution

It introduces five new forbidden patterns ensuring singleton arc consistency solves the CSPs, advancing towards a complete classification.

## Key findings

- Identified five new forbidden patterns for singleton arc consistency
- Four patterns are provably maximal
- Three patterns generalize 2-SAT problems

## Abstract

Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification.