article

A satisfiability procedure for quantified boolean formulae

Authors:

David A. Plaisted,

Yunshan ZhuAuthors Info & Claims

Discrete Applied Mathematics, Volume 130, Issue 2

Pages 291 - 328

https://doi.org/10.1016/S0166-218X(02)00409-2

Published: 15 August 2003 Publication History

Abstract

We present a satisfiability tester QSAT for quantified Boolean formulae and a restriction QSAT_CNF of QSAT to unquantified conjunctive normal form formulae. QSAT makes use of procedures which replace subformulae of a formula by equivalent formulae. By a sequence of such replacements, the original formula can be simplified to true or false. It may also be necessary to transform the original formula to generate a subformula to replace. QSAT_CNF eliminates collections of variables from an unquantified clause form formula until all variables have been eliminated. QSAT and QSAT_CNF can be applied to hardware verification and symbolic model checking. Results of an implementation of QSAT_CNF are described, as well as some complexity results for QSAT and QSAT_CNF. QSAT runs in linear time on a class of quantified Boolean formulae related to symbolic model checking. We present the class of "long and thin" unquantified formulae and give evidence that this class is common in applications. We also give theoretical and empirical evidence that QSAT_CNF is often faster than Davis and Putnam-type satisfiability checkers and ordered binary decision diagrams (OBDDs) on this class of formulae. We give an example where QSAT_CNF is exponentially faster than BDDs.

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Goldberg EManolios P(2014)Quantifier elimination by dependency sequentsFormal Methods in System Design10.1007/s10703-014-0214-z45:2(111-143)Online publication date: 1-Oct-2014
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Janota MMarques-Silva J(2011)Abstraction-based algorithm for 2QBFProceedings of the 14th international conference on Theory and application of satisfiability testing10.5555/2023474.2023500(230-244)Online publication date: 19-Jun-2011
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Zinovik IKroening DChebiryak Y(2007)An algebraic algorithm for the identification of glass networks with periodic orbits along cyclic attractorsProceedings of the 2nd international conference on Algebraic biology10.5555/1769026.1769037(140-154)Online publication date: 2-Jul-2007
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A satisfiability procedure for quantified boolean formulae

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Published In

cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 130, Issue 2

The renesse issue on satisfiability

15 August 2003

278 pages

ISSN:0166-218X

Issue’s Table of Contents

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 15 August 2003

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Cited By

Goldberg EManolios P(2014)Quantifier elimination by dependency sequentsFormal Methods in System Design10.1007/s10703-014-0214-z45:2(111-143)Online publication date: 1-Oct-2014
https://dl.acm.org/doi/10.1007/s10703-014-0214-z
Janota MMarques-Silva J(2011)Abstraction-based algorithm for 2QBFProceedings of the 14th international conference on Theory and application of satisfiability testing10.5555/2023474.2023500(230-244)Online publication date: 19-Jun-2011
https://dl.acm.org/doi/10.5555/2023474.2023500
Zinovik IKroening DChebiryak Y(2007)An algebraic algorithm for the identification of glass networks with periodic orbits along cyclic attractorsProceedings of the 2nd international conference on Algebraic biology10.5555/1769026.1769037(140-154)Online publication date: 2-Jul-2007
https://dl.acm.org/doi/10.5555/1769026.1769037
Jussila TBiere ASinz CKröning DWintersteiger C(2007)A first step towards a unified proof checker for QBFProceedings of the 10th international conference on Theory and applications of satisfiability testing10.5555/1768142.1768163(201-214)Online publication date: 28-May-2007
https://dl.acm.org/doi/10.5555/1768142.1768163
Stéphan I(2006)Boolean Propagation Based on Literals for Quantified Boolean FormulaeProceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy10.5555/1567016.1567115(452-456)Online publication date: 22-May-2006
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Sinz CBiere A(2006)Extended resolution proofs for conjoining BDDsProceedings of the First international computer science conference on Theory and Applications10.1007/11753728_60(600-611)Online publication date: 8-Jun-2006
https://dl.acm.org/doi/10.1007/11753728_60
Hristov NRemshagen AGuimaraes M(2005)Local search for quantified Boolean formulasProceedings of the 43rd annual ACM Southeast Conference - Volume 110.1145/1167350.1167390(116-120)Online publication date: 18-Mar-2005
https://dl.acm.org/doi/10.1145/1167350.1167390
Yu YMalik STang T(2005)Validating the result of a Quantified Boolean Formula (QBF) solverProceedings of the 2005 Asia and South Pacific Design Automation Conference10.1145/1120725.1120821(1047-1051)Online publication date: 18-Jan-2005
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Remshagen ATruemper K(2005)An Effective Algorithm for the Futile Questioning ProblemJournal of Automated Reasoning10.1007/s10817-005-0981-834:1(31-47)Online publication date: 1-Jan-2005
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Prasad MBiere AGupta A(2005)A survey of recent advances in SAT-based formal verificationInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-004-0183-47:2(156-173)Online publication date: 1-Apr-2005
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