The essence of constraint propagation
Theoretical Computer Science
Beyond NP: Arc-Consistency for Quantified Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
CSP properties for quantified constraints: definitions and complexity
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
QCSP-solve: a solver for quantified constraint satisfaction problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Solving quantified constraint satisfaction problems
Artificial Intelligence
Value ordering for quantified CSPs
Constraints
QCSP made practical by virtue of restricted quantification
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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Quantified Constraint Satisfaction Problems are considerably more difficult to solve than classical CSP and the pruning obtained by local consistency is of crucial importance. In this paper, instead of designing specific consistency operators for constraints w.r.t each possible quantification pattern, we propose to build them by relying on classical existential propagators and a few analysis of some mathematical properties of the constraints. It allows to reuse a large set of constraints already carefully implemented in existing solvers. Moreover, multiple levels of consistency for quantified constraint can be defined by choosing which analysis to use. This can be used to control the complexity of the pruning effort. We also introduce QeCode, a full-featured publicly available quantified constraint solver, built on top of Gecode.