A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
Resolution for quantified Boolean formulas
Information and Computation
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
On the lengths of proofs in the propositional calculus (Preliminary Version)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A solver for QBFs in negation normal form
Constraints
A first step towards a unified proof checker for QBF
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Resolution proofs and Skolem functions in QBF evaluation and applications
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Contributions to the theory of practical quantified boolean formula solving
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
On propositional QBF expansions and q-resolution
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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Quantified Boolean formulas generalize propositional formulas by admitting quantifications over propositional variables. We compare proof systems with different quantifier handling paradigms for quantified Boolean formulas (QBFs) with respect to their ability to allow succinct proofs. We analyze cut-free sequent systems extended by different quantifier rules and show that some rules are better than some others. Q-resolution is an elegant extension of propositional resolution to QBFs and is applicable to formulas in prenex conjunctive normal form. In Q-resolution, there is no explicit handling of quantifiers by specific rules. Instead the forall reduction rule which operates on single clauses inspects the global quantifier prefix. We show that there are classes of formulas for which there are short cut-free tree proofs in a sequent system, but any Q-resolution refutation of the negation of the formula is exponential.