Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.
LanguageUndefined
Title of host publicationFirst Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012)
EditorsA.J. Wijs, D. Bošnački, S. Edelkamp
PublisherEPTCS
Pages50-65
Number of pages16
DOIs
StatePublished - Apr 2012

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherEPTCS
Volume99
ISSN (Print)2075-2180
ISSN (Electronic)2075-2180

Keywords

  • FMT-MC: MODEL CHECKING
  • EWI-22278
  • Instantiation
  • METIS-293172
  • Parity Games
  • Parameterised Boolean Equation Systems
  • LTSMIN
  • IR-83359

Cite this

Kant, G., & van de Pol, J. C. (2012). Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games. In A. J. Wijs, D. Bošnački, & S. Edelkamp (Eds.), First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012) (pp. 50-65). (Electronic Proceedings in Theoretical Computer Science; Vol. 99). EPTCS. DOI: 10.4204/EPTCS.99.7
Kant, Gijs ; van de Pol, Jan Cornelis. / Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games. First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012). editor / A.J. Wijs ; D. Bošnački ; S. Edelkamp. EPTCS, 2012. pp. 50-65 (Electronic Proceedings in Theoretical Computer Science).
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abstract = "Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.",
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doi = "10.4204/EPTCS.99.7",
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series = "Electronic Proceedings in Theoretical Computer Science",
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Kant, G & van de Pol, JC 2012, Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games. in AJ Wijs, D Bošnački & S Edelkamp (eds), First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012). Electronic Proceedings in Theoretical Computer Science, vol. 99, EPTCS, pp. 50-65. DOI: 10.4204/EPTCS.99.7

Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games. / Kant, Gijs; van de Pol, Jan Cornelis.

First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012). ed. / A.J. Wijs; D. Bošnački; S. Edelkamp. EPTCS, 2012. p. 50-65 (Electronic Proceedings in Theoretical Computer Science; Vol. 99).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.

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Kant G, van de Pol JC. Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games. In Wijs AJ, Bošnački D, Edelkamp S, editors, First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012). EPTCS. 2012. p. 50-65. (Electronic Proceedings in Theoretical Computer Science). Available from, DOI: 10.4204/EPTCS.99.7