Resolution for quantified Boolean formulas
Information and Computation
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
Collapsibility and consistency in quantified constraint satisfaction
AAAI'04 Proceedings of the 19th national 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
A symbolic search based approach for quantified boolean formulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A solver for quantified Boolean and linear constraints
Proceedings of the 2007 ACM symposium on Applied computing
Solving quantified constraint satisfaction problems
Artificial Intelligence
Quantified Constraint Optimization
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
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)
Quantified constraint satisfaction problems: from relaxations to explanations
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Solution directed backjumping for QCSP
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Reusing CSP propagators for QCSPs
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
Realtime online solving of quantified CSPs
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Algorithms for stochastic CSPs
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Relaxations and explanations for quantified constraint satisfaction problems
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Consistencies for ultra-weak solutions in minimax weighted CSPs using the duality principle
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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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 simple, classical notion of solution inappropriate. As a consequence, even such essential CSP properties as consistency or substitutability are not completely understood in the quantified case. In this paper, we show that most of the properties which are used by solvers for CSP can be generalized to Quantified CSP. 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 generalise the approach used in CSP and propose weakenings of these notions based on locality, which allow for a tractable, albeit incomplete detecting of these properties.