The complexity of maximal constraint languages

Bulatov, A.; Krokhin, A.; Jeavons, P.

Abstract

Many combinatorial search problems can be expressed as “constraint satisfaction problems” using an appropriate “constraint language”, that is, a set of relations over some fixed finite set of values. It is well-known that there is a trade-off between the expressive power of a constraint language and the complexity of the problems it can express. In the present paper we systematically study the complexity of all maximal constraint languages, that is, languages whose expressive power is just weaker than that of the language of all constraints. Using the algebraic invariance properties of constraints, we exhibit a strong necessary condition for tractability of such a constraint language. Moreover, we show that, at least for small sets of values, this condition is also sufficient.

Citation

Bulatov, A., Krokhin, A., & Jeavons, P. (2001, December). The complexity of maximal constraint languages. Presented at 33rd ACM Symposium on the Theory of Computing(STOC), Crete, Greece

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 33rd ACM Symposium on the Theory of Computing(STOC)
• Publication Date: Jan 1, 2001
• Deposit Date: Mar 29, 2010
• Publisher: Association for Computing Machinery (ACM)
• Pages: 667-674
• Series Title: Annual ACM symposium on theory of computing
• Series Number: STOC '01
• Book Title: Proceedings of the 33rd annual ACM symposium on theory of computing.
• DOI: https://doi.org/10.1145/380752.380868
• Public URL: https://durham-repository.worktribe.com/output/1162327
• Additional Information: July 6-8, 2001