A shorter model theory
Closure properties of constraints
Journal of the ACM (JACM)
Closure Functions and Width 1 Problems
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Constraint Processing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Constraint Satisfaction with Countable Homogeneous Templates
Journal of Logic and Computation
The complexity of temporal constraint satisfaction problems
Journal of the ACM (JACM)
A fast algorithm and datalog inexpressibility for temporal reasoning
ACM Transactions on Computational Logic (TOCL)
New Conditions for Taylor Varieties and CSP
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
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A famous result by Jeavons, Cohen, and Gyssens shows that every Constraint Satisfaction Problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the so-called universal algebraic approach to a systematic theory of tractability and hardness in finite domain constraint satisfaction. Not surprisingly, the theorem of Jeavons et al. fails for arbitrary infinite domain CSPs. Many CSPs of practical interest, though, and in particular those CSPs that are motivated by qualitative reasoning calculi from artificial intelligence, can be formulated with constraint languages that are rather well-behaved from a model-theoretic point of view. In particular, the automorphism group of these constraint languages tends to be large in the sense that the number of orbits of n-subsets of the automorphism group is bounded by some function in n. In this article we present a generalization of the theorem by Jeavons et al. to infinite domain CSPs where the number of orbits of n-subsets grows subexponentially in n, and prove that preservation under a semi-lattice operation for such CSPs implies polynomial-time tractability. Unlike the result of Jeavons et al., this includes CSPs that cannot be solved by Datalog.