Parameterised Boolean Equation Systems

  • Jan Friso Groote
  • Tim Willemse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3170)


Boolean equation system are a useful tool for verifying formulas from modal mu-calculus on transition systems (see [9] for an excellent treatment). We are interested in an extension of boolean equation systems with data. This allows to formulate and prove a substantially wider range of properties on much larger and even infinite state systems. In previous works [4,6] it has been outlined how to transform a modal formula and a process, both containing data, to a so-called parameterised boolean equation system, or equation system for short. In this article we focus on techniques to solve such equation systems.

We introduce a new equivalence between equation systems, because existing equivalences are not compositional. We present techniques similar to Gauß elimination as outlined in [9] that allow to solve each equation system provided a single equation can be solved. We give several techniques for solving single equations, such as approximation (known), patterns (new) and invariants (new). Finally, we provide several small but illustrative examples of verifications of modal mu-calculus formulas on concrete processes to show the use of the techniques.


Model Check Equation System Input Stream Modal Formula Predicate Variable 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jan Friso Groote
    • 1
  • Tim Willemse
    • 1
    • 2
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Faculty of Science, Mathematics and Computing ScienceUniversity of NijmegenNijmegenThe Netherlands

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