Article

Efficient clause learning for quantified boolean formulas via QBF pseudo unit propagation

Authors:

Florian Lonsing,

Allen Van GelderAuthors Info & Claims

SAT'13: Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing

Pages 100 - 115

https://doi.org/10.1007/978-3-642-39071-5_9

Published: 08 July 2013 Publication History

Abstract

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.

References

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Cited By

Beyersdorff OBlinkhorn JMahajan MPeitl T(2023)Hardness Characterisations and Size-width Lower Bounds for QBF ResolutionACM Transactions on Computational Logic10.1145/356528624:2(1-30)Online publication date: 27-Jan-2023
https://dl.acm.org/doi/10.1145/3565286
Beyersdorff OBlinkhorn JMahajan MHermanns HZhang LKobayashi NMiller D(2020)Hardness Characterisations and Size-Width Lower Bounds for QBF ResolutionProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394793(209-223)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394793
Peitl TSlivovsky FSzeider S(2019)Dependency learning for QBFJournal of Artificial Intelligence Research10.1613/jair.1.1152965:1(181-208)Online publication date: 1-May-2019
https://dl.acm.org/doi/10.1613/jair.1.11529
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Efficient clause learning for quantified boolean formulas via QBF pseudo unit propagation
1. Theory of computation
  1. Logic

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Published In

cover image Guide Proceedings

SAT'13: Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing

July 2013

436 pages

ISBN:9783642390708

Editors:
Matti Järvisalo
HIIT and Department of Computer Science, University of Helsinki, Gustaf Hällströmin katu 2 b, Helsinki, Finland
,
Allen Van Gelder
Computer Science Department, University of California at Santa Cruz, 1156 High Street, SOE-3, Santa Cruz, CA, Finland

Sponsors

University of Helsinki
Federation of Finnish Learned Societies
IBMR: IBM Research
SAT Association: SAT Association
AI Journal: AI Journal

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 08 July 2013

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Cited By

Beyersdorff OBlinkhorn JMahajan MPeitl T(2023)Hardness Characterisations and Size-width Lower Bounds for QBF ResolutionACM Transactions on Computational Logic10.1145/356528624:2(1-30)Online publication date: 27-Jan-2023
https://dl.acm.org/doi/10.1145/3565286
Beyersdorff OBlinkhorn JMahajan MHermanns HZhang LKobayashi NMiller D(2020)Hardness Characterisations and Size-Width Lower Bounds for QBF ResolutionProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394793(209-223)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394793
Peitl TSlivovsky FSzeider S(2019)Dependency learning for QBFJournal of Artificial Intelligence Research10.1613/jair.1.1152965:1(181-208)Online publication date: 1-May-2019
https://dl.acm.org/doi/10.1613/jair.1.11529
Beyersdorff OChew LJanota M(2019)New Resolution-Based QBF Calculi and Their Proof ComplexityACM Transactions on Computation Theory10.1145/335215511:4(1-42)Online publication date: 12-Sep-2019
https://dl.acm.org/doi/10.1145/3352155
Peitl TSlivovsky FSzeider S(2019)Long-Distance Q-Resolution with Dependency SchemesJournal of Automated Reasoning10.1007/s10817-018-9467-363:1(127-155)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s10817-018-9467-3
Hallen MParamonov SJanssens GDenecker M(2019)Knowledge representation analysis of graph miningAnnals of Mathematics and Artificial Intelligence10.1007/s10472-019-09624-y86:1-3(21-60)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s10472-019-09624-y
Egly UKronegger MLonsing FPfandler A(2017)Conformant planning as a case study of incremental QBF solvingAnnals of Mathematics and Artificial Intelligence10.1007/s10472-016-9501-280:1(21-45)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s10472-016-9501-2
Lonsing FSeidl MVan Gelder A(2016)The QBF GalleryArtificial Intelligence10.1016/j.artint.2016.04.002237:C(92-114)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1016/j.artint.2016.04.002

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