Abstract
A temporal constraint language is a set of relations that has a first-order definition in(Q;<), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint languages, then the CSP can be solved in polynomial time; otherwise, the CSP is NP-complete. Our proof combines model-theoretic concepts with techniques from universal algebra, and also applies the so-called product Ramsey theorem, which we believe will useful in similar contexts of constraint satisfaction complexity classification. An extended abstract of this article appeared in the proceedings of STOC'08.
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