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Resolution for quantified Boolean formulas
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Experimental Analysis of the Computational Cost of Evaluating Quantified Boolean Formulae
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Algorithms for quantified Boolean formulas
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Logical Cryptanalysis as a SAT Problem
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An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation
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SAT-Based Decision Procedures for Classical Modal Logics
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Beyond NP: Arc-Consistency for Quantified Constraints
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Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems
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Backjumping for quantified Boolean logic satisfiability
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Expressing default abduction problems as quantified Boolean formulas
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A new general method to generate random modal formulae for testing decision procedures
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Backjumping for quantified Boolean logic satisfiability
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A branching heuristics for quantified renamable horn formulas
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Representing paraconsistent reasoning via quantified propositional logic
Inconsistency Tolerance
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The high computational complexity of advanced reasoning tasks such as belief revision and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., reasoning about knowledge, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the Davis-Putnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting Evaluate, we discuss all the abstract properties of QBFs that we singled out to make the algorithm more efficient. We also briefly mention the main results of the experimental analysis, which is reported elsewhere.