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Using SMT for Solving Fragments of Parameterised Boolean Equation Systems

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Automated Technology for Verification and Analysis (ATVA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9364))

Abstract

Fixpoint logics such as parameterised Boolean equation systems (PBESs) provide a unifying framework in which a number of practical decision problems can be encoded. Efficient evaluation methods (solving methods in the terminology of PBESs) are needed to solve the encoded decision problems. We present a sound pseudo-decision procedure that uses SMT solvers for solving conjunctive and disjunctive PBESs. These are important fragments, allowing to encode typical verification problems and planning problems. Our experiments, conducted with a prototype implementation, show that the new solving procedure is complementary to existing techniques for solving PBESs.

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Notes

  1. 1.

    In LTL one would write \(G (A \ge 0 \wedge B \ge 0)\).

  2. 2.

    In LTL one would write \(G(A \ge 0 \wedge B \ge 0 \wedge F(\text {loc} = C))\).

  3. 3.

    These can be found online via http://mcrl2.org.

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Acknowledgement

We thank Jan Friso Groote (TU/e) for helpful discussions and feedback on our ideas, and the referees for their constructive feedback.

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Authors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Ruud P. J. Koolen, Tim A. C. Willemse & Hans Zantema

Authors
  1. Ruud P. J. Koolen
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  2. Tim A. C. Willemse
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  3. Hans Zantema
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Corresponding author

Correspondence to Tim A. C. Willemse .

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Editors and Affiliations

  1. Universität des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

  2. East China Normal University, Shanghai, China

    Geguang Pu

  3. Chinese Academy of Sciences, Beijing, China

    Lijun Zhang

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Koolen, R.P.J., Willemse, T.A.C., Zantema, H. (2015). Using SMT for Solving Fragments of Parameterised Boolean Equation Systems. In: Finkbeiner, B., Pu, G., Zhang, L. (eds) Automated Technology for Verification and Analysis. ATVA 2015. Lecture Notes in Computer Science(), vol 9364. Springer, Cham. https://doi.org/10.1007/978-3-319-24953-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-24953-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24952-0

  • Online ISBN: 978-3-319-24953-7

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