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Software for Quantifier Elimination in Propositional Logic

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Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

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Abstract

We consider the following problem of Quantifier Elimination (QE). Given a Boolean CNF formula F where some variables are existentially quantified, find a logically equivalent CNF formula that is free of quantifiers. Solving this problem comes down to finding a set of clauses depending only on free variables that has the following property: adding the clauses of this set to F makes all the clauses of F with quantified variables redundant. To solve the QE problem we developed a tool meant for handling a more general problem called partial QE. This tool builds a set of clauses adding which to F renders a specified subset of clauses with quantified variables redundant. In particular, if the specified subset contains all the clauses with quantified variables, our tool performs QE.

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References

  1. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)

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  2. Goldberg, E., Manolios, P.: Quantifier elimination via clause redundancy. In: FMCAD 2013, pp. 85–92 (2013)

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  3. Goldberg, E., Manolios, P.: Partial quantifier elimination, submitted to a conference (2014)

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  4. McMillan, K.L.: Interpolation and SAT-based model checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)

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Author information

Authors and Affiliations

  1. Northeastern University, USA

    Eugene Goldberg & Panagiotis Manolios

Authors
  1. Eugene Goldberg
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  2. Panagiotis Manolios
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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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Goldberg, E., Manolios, P. (2014). Software for Quantifier Elimination in Propositional Logic. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_45

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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