Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
A shorter model theory
Closure properties of constraints
Journal of the ACM (JACM)
A unifying approach to temporal constraint reasoning
Artificial Intelligence
Building tractable disjunctive constraints
Journal of the ACM (JACM)
Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
The complexity of temporal constraint satisfaction problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Constraint Satisfaction Problems with Infinite Templates
Complexity of Constraints
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We study logical techniques for deciding the computational complexity of infinite-domain constraint satisfaction problems (CSPs). For the fundamental algebraic structure $\Gamma=(\mathbb R; L_1,L_2,\dots)$ where $\mathbb R$ are the real numbers and L 1 ,L 2 ,... is an enumeration of all linear relations with rational coefficients, we prove that a semilinear relation R (i.e., a relation that is first-order definable with linear inequalities) either has a quantifier-free Horn definition in Γ or the CSP for $(\mathbb R; R,L_1,L_2,\dots)$ is NP-hard. The result implies a complexity dichotomy for all constraint languages that are first-order expansions of Γ : the corresponding CSPs are either in P or are NP-complete depending on the choice of allowed relations. We apply this result to two concrete examples (generalised linear programming and metric temporal reasoning) and obtain full complexity dichotomies in both cases.