Resolution for quantified Boolean formulas
Information and Computation
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Journal of the ACM (JACM)
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Conflict driven learning in a quantified Boolean Satisfiability solver
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Learning for quantified boolean logic satisfiability
Eighteenth national conference on Artificial intelligence
Improved Conflict-Clause Minimization Leads to Improved Propositional Proof Traces
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
A Compact Representation for Syntactic Dependencies in QBFs
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Beyond CNF: A Circuit-Based QBF Solver
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Clause/term resolution and learning in the evaluation of quantified Boolean formulas
Journal of Artificial Intelligence Research
Evaluating and certifying QBFs: A comparison of state-of-the-art tools
AI Communications
Bounded universal expansion for preprocessing QBF
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Failed literal detection for QBF
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Generalized conflict-clause strengthening for satisfiability solvers
SAT'11 Proceedings of the 14th international conference on Theory and application 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
Variable independence and resolution paths for quantified boolean formulas
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
A non-prenex, non-clausal QBF solver with game-state learning
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Integrating dependency schemes in search-based QBF solvers
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
A uniform approach for generating proofs and strategies for both true and false QBF formulas
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Extended failed-literal preprocessing for quantified boolean formulas
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
On sequent systems and resolution for QBFs
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Producing and verifying extremely large propositional refutations
Annals of Mathematics and Artificial Intelligence
Recovering and utilizing partial duality in QBF
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Efficient clause learning for quantified boolean formulas via QBF pseudo unit propagation
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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Recent solvers for quantified boolean formulas (QBFs) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. The underlying proof system is Q-resolution. This paper shows an exponential worst case for the clause-learning procedure. This finding confirms empirical observations that some formulas take mysteriously long times to solve, compared to other apparently similar formulas. Q-resolution is known to be refutation complete for QBF, but not all logically implied clauses can be derived with it. A stronger proof system called QU-resolution is introduced, and shown to be complete in this stronger sense. A new procedure called QPUP for clause learning without tautologies is also described. A generalization of pure literals is introduced, called effectively depth-monotonic literals. In general, the variable-elimination resolution operation, as used by Quantor, sQueezeBF, and Bloqqer is unsound if the existential variable being eliminated is not at innermost scope. It is shown that variable-elimination resolution is sound for effectively depth-monotonic literals even when they are not at innermost scope.