Embedding Memoization to the Semantic Tree Search for Deciding QBFs
Identifieur interne : 001570 ( Istex/Corpus ); précédent : 001569; suivant : 001571Embedding Memoization to the Semantic Tree Search for Deciding QBFs
Auteurs : Mohammad Ghasemzadeh ; Volker Klotz ; Christoph MeinelSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2005.
Abstract
Abstract: Quantified Boolean formulas (QBFs) play an important role in artificial intelligence subjects, specially in planning, knowledge representation and reasoning [20]. In this paper we present ZQSAT (sibling of our FZQSAT [15]), which is an algorithm for evaluating quantified Boolean formulas. QBF is a language that extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. ZQSAT is based on ZDD, which is a variant of BDD, and an adopted version of the DPLL algorithm. The program has been implemented in C using the CUDD package. The capability of ZDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with few overheads. This idea along some other techniques, enabled ZQSAT to solve some standard QBF benchmark problems faster than the best existing QSAT solvers.
Url:
DOI: 10.1007/978-3-540-30549-1_59
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<front><div type="abstract" xml:lang="en">Abstract: Quantified Boolean formulas (QBFs) play an important role in artificial intelligence subjects, specially in planning, knowledge representation and reasoning [20]. In this paper we present ZQSAT (sibling of our FZQSAT [15]), which is an algorithm for evaluating quantified Boolean formulas. QBF is a language that extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. ZQSAT is based on ZDD, which is a variant of BDD, and an adopted version of the DPLL algorithm. The program has been implemented in C using the CUDD package. The capability of ZDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with few overheads. This idea along some other techniques, enabled ZQSAT to solve some standard QBF benchmark problems faster than the best existing QSAT solvers.</div>
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<editor><persName><forename type="first">Xinghuo</forename>
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<editor><persName><forename type="first">Takeo</forename>
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<editor><persName><forename type="first">Josef</forename>
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<editor><persName><forename type="first">Jon</forename>
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<surname>Kleinberg</surname>
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<editor><persName><forename type="first">Friedemann</forename>
<surname>Mattern</surname>
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<editor><persName><forename type="first">John</forename>
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<editor><persName><forename type="first">Moni</forename>
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<affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation>
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<editor><persName><forename type="first">Oscar</forename>
<surname>Nierstrasz</surname>
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<affiliation>University of Bern, Switzerland</affiliation>
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<editor><persName><forename type="first">C.</forename>
<surname>Pandu Rangan</surname>
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<affiliation>Indian Institute of Technology, Madras, India</affiliation>
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<editor><persName><forename type="first">Bernhard</forename>
<surname>Steffen</surname>
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<affiliation>University of Dortmund, Germany</affiliation>
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<editor><persName><forename type="first">Madhu</forename>
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<affiliation>Massachusetts Institute of Technology, MA, USA</affiliation>
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<editor><persName><forename type="first">Demetri</forename>
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<affiliation>New York University, NY, USA</affiliation>
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<editor><persName><forename type="first">Dough</forename>
<surname>Tygar</surname>
</persName>
<affiliation>University of California, Berkeley, CA, USA</affiliation>
</editor>
<editor><persName><forename type="first">Moshe</forename>
<forename type="first">Y.</forename>
<surname>Vardi</surname>
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<affiliation>Rice University, Houston, TX, USA</affiliation>
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<editor><persName><forename type="first">Gerhard</forename>
<surname>Weikum</surname>
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<affiliation>Max-Planck Institute of Computer Science, Saarbruecken, Germany</affiliation>
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<affiliation>Lancaster University, UK</affiliation>
</editor>
<editor><persName><forename type="first">Takeo</forename>
<surname>Kanade</surname>
</persName>
<affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation>
</editor>
<editor><persName><forename type="first">Josef</forename>
<surname>Kittler</surname>
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<affiliation>University of Surrey, Guildford, UK</affiliation>
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<editor><persName><forename type="first">Jon</forename>
<forename type="first">M.</forename>
<surname>Kleinberg</surname>
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<affiliation>Cornell University, Ithaca, NY, USA</affiliation>
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<editor><persName><forename type="first">Friedemann</forename>
<surname>Mattern</surname>
</persName>
<affiliation>ETH Zurich, Switzerland</affiliation>
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<editor><persName><forename type="first">John</forename>
<forename type="first">C.</forename>
<surname>Mitchell</surname>
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<affiliation>Stanford University, CA, USA</affiliation>
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<editor><persName><forename type="first">Moni</forename>
<surname>Naor</surname>
</persName>
<affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation>
</editor>
<editor><persName><forename type="first">Oscar</forename>
<surname>Nierstrasz</surname>
</persName>
<affiliation>University of Bern, Switzerland</affiliation>
</editor>
<editor><persName><forename type="first">C.</forename>
<surname>Pandu Rangan</surname>
</persName>
<affiliation>Indian Institute of Technology, Madras, India</affiliation>
</editor>
<editor><persName><forename type="first">Bernhard</forename>
<surname>Steffen</surname>
</persName>
<affiliation>University of Dortmund, Germany</affiliation>
</editor>
<editor><persName><forename type="first">Madhu</forename>
<surname>Sudan</surname>
</persName>
<affiliation>Massachusetts Institute of Technology, MA, USA</affiliation>
</editor>
<editor><persName><forename type="first">Demetri</forename>
<surname>Terzopoulos</surname>
</persName>
<affiliation>New York University, NY, USA</affiliation>
</editor>
<editor><persName><forename type="first">Dough</forename>
<surname>Tygar</surname>
</persName>
<affiliation>University of California, Berkeley, CA, USA</affiliation>
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<editor><persName><forename type="first">Moshe</forename>
<forename type="first">Y.</forename>
<surname>Vardi</surname>
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<affiliation>Rice University, Houston, TX, USA</affiliation>
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<editor><persName><forename type="first">Gerhard</forename>
<surname>Weikum</surname>
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<affiliation>Max-Planck Institute of Computer Science, Saarbruecken, Germany</affiliation>
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<editor><persName><forename type="first">Jaime</forename>
<forename type="first">G.</forename>
<surname>Carbonell</surname>
</persName>
<affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation>
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<editor><persName><forename type="first">Jörg</forename>
<surname>Siekmann</surname>
</persName>
<affiliation>University of Saarland, Saarbrücken, Germany</affiliation>
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<editor><persName><forename type="first">Geoffrey</forename>
<forename type="first">I.</forename>
<surname>Webb</surname>
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<email>Geoff.Webb@infotech.monash.edu.au</email>
<affiliation>Faculty of Information Technology, Monash University, VIC 3800, Australia</affiliation>
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<editor><persName><forename type="first">Xinghuo</forename>
<surname>Yu</surname>
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<email>x.yu@rmit.edu.au</email>
<affiliation>Science, Engineering and Technology Portfolio, Royal Melbourne Institute of Technology, VIC 3001, Melbourne, Australia</affiliation>
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<abstract xml:lang="en"><p>Abstract: Quantified Boolean formulas (QBFs) play an important role in artificial intelligence subjects, specially in planning, knowledge representation and reasoning [20]. In this paper we present ZQSAT (sibling of our FZQSAT [15]), which is an algorithm for evaluating quantified Boolean formulas. QBF is a language that extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. ZQSAT is based on ZDD, which is a variant of BDD, and an adopted version of the DPLL algorithm. The program has been implemented in C using the CUDD package. The capability of ZDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with few overheads. This idea along some other techniques, enabled ZQSAT to solve some standard QBF benchmark problems faster than the best existing QSAT solvers.</p>
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<ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Mohammad</GivenName>
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<Affiliation ID="Aff20"><OrgDivision>FB-IV Informatik</OrgDivision>
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<City>Trier</City>
<Country>Germany</Country>
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<Para>Quantified Boolean formulas (QBFs) play an important role in artificial intelligence subjects, specially in planning, knowledge representation and reasoning [20]. In this paper we present ZQSAT (sibling of our FZQSAT [15]), which is an algorithm for evaluating quantified Boolean formulas. QBF is a language that extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. ZQSAT is based on ZDD, which is a variant of BDD, and an adopted version of the DPLL algorithm. The program has been implemented in C using the CUDD package. The capability of ZDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with few overheads. This idea along some other techniques, enabled ZQSAT to solve some standard QBF benchmark problems faster than the best existing QSAT solvers.</Para>
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<Keyword>DPLL</Keyword>
<Keyword>Zero-Suppressed Binary Decision Diagram (ZDD)</Keyword>
<Keyword>Quantified Boolean Formula (QBF)</Keyword>
<Keyword>Satisfiability</Keyword>
<Keyword>QSAT</Keyword>
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<abstract lang="en">Abstract: Quantified Boolean formulas (QBFs) play an important role in artificial intelligence subjects, specially in planning, knowledge representation and reasoning [20]. In this paper we present ZQSAT (sibling of our FZQSAT [15]), which is an algorithm for evaluating quantified Boolean formulas. QBF is a language that extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. ZQSAT is based on ZDD, which is a variant of BDD, and an adopted version of the DPLL algorithm. The program has been implemented in C using the CUDD package. The capability of ZDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with few overheads. This idea along some other techniques, enabled ZQSAT to solve some standard QBF benchmark problems faster than the best existing QSAT solvers.</abstract>
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