On Singleton Arc Consistency for CSPs Defined by Monotone Patterns
This work addresses a theoretical classification problem in constraint satisfaction for researchers in computational complexity and AI, representing incremental progress.
The paper tackled the problem of characterizing constraint satisfaction problems (CSPs) defined by forbidden patterns that are solvable by singleton arc consistency, identifying five new patterns and making progress toward a complete classification.
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.