Resolution for quantified Boolean formulas
Information and Computation
An algorithm to evaluate quantified Boolean formulae
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation
Journal of Automated Reasoning
Improvements to the Evaluation of Quantified Boolean Formulae
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Beyond NP: Arc-Consistency for Quantified Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
A solver for quantified Boolean and linear constraints
Proceedings of the 2007 ACM symposium on Applied computing
Collapsibility and consistency in quantified constraint satisfaction
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
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
QCSP made practical by virtue of restricted quantification
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Quantified constraint satisfaction problems: from relaxations to explanations
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Symmetry breaking in quantified boolean formulae
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
QCSP-solve: a solver for quantified constraint satisfaction problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Solution directed backjumping for QCSP
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
BlockSolve: a bottom-up approach for solving quantified CSPs
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Binary clause reasoning in QBF
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A unifying framework for structural properties of CSPs: definitions, complexity, tractabilit
Journal of Artificial Intelligence Research
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Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic properties of Constraint Satisfaction Problems (CSPs), such as consistency or substitutability, are not completely understood in the quantified case. These properties are important because they are the basis of most of the reasoning methods used to solve classical (existentially quantified) constraints, and it is desirable to benefit from similar reasoning methods in the resolution of quantified constraints. In this article, we show that most of the properties that are used by solvers for CSP can be generalized to quantified CSP. This requires a rethinking of a number of basic concepts; in particular, we propose a notion of outcome that generalizes the classical notion of solution and on which all definitions are based. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalize the approach used in CSP and propose weaker, easier to check notions based on locality, which allow to detect these properties incompletely but in polynomial time.