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On the minimality and global consistency of row-convex constraint networks
Journal of the ACM (JACM)
Tractable constraints on ordered domains
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Closure properties of constraints
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Constraints, consistency and closure
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A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Closure Functions and Width 1 Problems
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
A Unifying Framework for Tractable Constraints
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LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
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New Tractable Classes from Old
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In this paper we consider constraint satisfaction problems where the set of constraint relations is fixed. Feder and Vardi (1998) identified three families of constraint satisfaction problems containing all known polynomially solvable problems. We introduce a new class of problems called para-primal problems, incomparable with the families identified by Feder and Vardi (1998) and we prove that any constraint problem in this class is decidable in polynomial time. As an application of this result we prove a complete classification for the complexity of constraint satisfaction problems under the assumption that the basis contains all the permutation relations. In the proofs, we make an intensive use of algebraic results from clone theory about the structure of para-primal and homogeneous algebras.