Beyond NP: Arc-Consistency for Quantified Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Solving QBF with combined conjunctive and disjunctive normal form
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
CSP properties for quantified constraints: definitions and complexity
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Scenario-based stochastic constraint programming
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
QCSP-solve: a solver for quantified constraint satisfaction problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Variable Dependencies of Quantified CSPs
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Generalizing consistency and other constraint properties to quantified constraints
ACM Transactions on Computational Logic (TOCL)
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We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constraints. From a theoretical perspective, we clarify the problem of the treatment of universal quantifiers by proposing a "symmetric" version of the notion of quantified consistency. This notion imposes to maintain two constraint stores, which will be used to reason on universal and existential variables, respectively. We then describe a branch & bound algorithm that integrates both forms of propagation. Its implementation is, to the best of our knowledge, the first CP solver for this class of quantified constraints.