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Bisimulation Minimisations for Boolean Equation Systems

  • Jeroen J. A. Keiren
  • Tim A. C. Willemse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6405)

Abstract

Boolean equation systems (BESs) have been used to encode several complex verification problems, including model checking and equivalence checking. We introduce the concepts of strong bisimulation and idempotence-identifying bisimulation for BESs, and we prove that these can be used for minimising BESs prior to solving these. Our results show that large reductions of the BESs may be obtained efficiently. Minimisation is rewarding for BESs with non-trivial alternations: the time required for solving the original BES mostly exceeds the time required for quotienting plus the time for solving the quotient. Furthermore, we provide a verification example that demonstrates that bisimulation minimisation of a process prior to encoding the verification problem on that process as a BES can be arbitrarily less effective than minimising the BES that encodes the verification problem.

Keywords

Model Check Equation System Proposition Variable Label Transition System Proposition Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jeroen J. A. Keiren
    • 1
  • Tim A. C. Willemse
    • 1
  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands

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