Resolution for quantified Boolean formulas
Information and Computation
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Conflict driven learning in a quantified Boolean Satisfiability solver
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Variable Dependencies of Quantified CSPs
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
A Compact Representation for Syntactic Dependencies in QBFs
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
Generalized conflict-clause strengthening for satisfiability solvers
SAT'11 Proceedings of the 14th international conference on Theory and application 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
Unified QBF certification and its applications
Formal Methods in System Design
Resolution-based certificate extraction for QBF
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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
Producing and verifying extremely large propositional refutations
Annals of Mathematics and Artificial Intelligence
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Recent solvers for quantified boolean formulas (QBF) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. Recently, an exponential worst case for this procedure has been shown by Van Gelder (CP 2012). That paper introduced QBF Pseudo Unit Propagation (QPUP) for non-tautological clause learning in a limited setting and showed that its worst case is theoretically polynomial, although it might be impractical in a high-performance QBF solver, due to excessive time and space consumption. No implementation was reported. We describe an enhanced version of QPUP learning that is practical to incorporate into high-performance QBF solvers, being compatible with pure-literal rules and dependency schemes. It can be used for proving in a concise format that a QBF formula is either unsatisfiable or satisfiable (working on both proofs in tandem). A lazy version of QPUP permits non-tautological clauses to be learned without actually carrying out resolutions, but this version is unable to produce proofs. Experimental results show that QPUP is somewhat faster than the previous non-tautological clause learning procedure on benchmarks from QBFEVAL-12-SR.