### Abstract

Language | Undefined |
---|---|

Title of host publication | First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012) |

Editors | A.J. Wijs, D. Bošnački, S. Edelkamp |

Publisher | EPTCS |

Pages | 50-65 |

Number of pages | 16 |

DOIs | |

State | Published - Apr 2012 |

### Publication series

Name | Electronic Proceedings in Theoretical Computer Science |
---|---|

Publisher | EPTCS |

Volume | 99 |

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

*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

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

AU - Kant,Gijs

AU - van de Pol,Jan Cornelis

N1 - eemcs-eprint-22278

PY - 2012/4

Y1 - 2012/4

N2 - 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.

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.

KW - FMT-MC: MODEL CHECKING

KW - EWI-22278

KW - Instantiation

KW - METIS-293172

KW - Parity Games

KW - Parameterised Boolean Equation Systems

KW - LTSMIN

KW - IR-83359

U2 - 10.4204/EPTCS.99.7

DO - 10.4204/EPTCS.99.7

M3 - Conference contribution

T3 - Electronic Proceedings in Theoretical Computer Science

SP - 50

EP - 65

BT - First Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2012)

PB - EPTCS

ER -