## Abstract

Mechanical theorem proving and model checking are the two main methods of formal verification, each with its own strengths and weaknesses. While mechanical theorem proving is more general, it requires intensive human guidance, model checking is automatic, but is applicable to a more restricted class of problems. It is appealing to combine these two methods in order to take advantage of their different strengths. Prior research in this direction has focused on how to decompose a verification problem into parts each of which is manageable by one of the two methods. In this paper we explore another possibility: we use mechanical theorem proving to formally verify a meta-theory of model checking. As a case study, we use the mechanical theorem prover HOL to verify the correctness of a partial-order reduction technique for cutting down the amount of state search performed by model checkers. We choose this example for two reasons. First, this reduction technique has been implemented in the protocol analysis tool SPIN to significantly speed up the analysis of many practical protocols; hence its correctness has important practical consequences. Second, the correctness arguments involve nontrivial mathematics, the formalization of which we hope will become the basis of a formal meta-theory of many model checking algorithms and techniques. Our formalization led to a nontrivial generalization of the original informal theory. We also discuss the lessons, both encouraging and discouraging, learned from this exercise.

Original language | English |
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Title of host publication | Tools and Algorithms for the Construction and Analysis of Systems - 2nd International Workshop, TACAS 1996, Proceedings |

Editors | Tiziana Margaria, Bernhard Steffen |

Publisher | Springer Verlag |

Pages | 241-257 |

Number of pages | 17 |

ISBN (Print) | 3540610421, 9783540610427 |

DOIs | |

State | Published - 1996 |

Externally published | Yes |

Event | 2nd International Workshop on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 1996 - Passau, Germany Duration: 27 Mar 1996 → 29 Mar 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1055 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 2nd International Workshop on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 1996 |
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Country/Territory | Germany |

City | Passau |

Period | 27/03/96 → 29/03/96 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1996.