Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
Tractable constraints on ordered domains
Artificial Intelligence
Closure properties of constraints
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Constraints, consistency and closure
Artificial Intelligence
Building tractable disjunctive constraints
Journal of the ACM (JACM)
New tractable constraint classes from old
Exploring artificial intelligence in the new millennium
Towards a Dichotomy Theorem for the Counting Constraint Satisfaction Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Domain permutation reduction for constraint satisfaction problems
Artificial Intelligence
Structural Tractability of Propagated Constraints
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Enumerating all solutions for constraint satisfaction problems
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Structural tractability of enumerating CSP solutions
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Enumerating all solutions of a boolean CSP by non-decreasing weight
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Approximability of integer programming with generalised constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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A constraint satisfaction problem (CSP) instance has a set of variables, each of which can take values in some domain. It also has a set of constraints, each of which restricts the variables in its scope to take values limited by its constraint relation.The language of a constraint satisfaction problem instance is the set of different constraint relations used in its specification. For a given set of relations Γ over some domain we define the problem CSP (Γ) to the set of CSP instances whose language is contained in Γ.The decision problem for a set of CSP instances is, given an instance in the class, to decide whether a solution exists. The search problem is to find such a solution. Here we address the connection between the tractability of the decision and search problems. We prove that given a constraint language Γ over a finite domain for which the decision problem for CSP (Γ) is tractable, the search problem is always tractable.We define a surjective language over a finite domain in a standard way. We also show that we can determine in polynomial time whether an instance over a surjective language with a tractable decision problem has fewer than k solutions, and that we can generate all of its solutions with polynomial delay.