## Abstract

Bounded model checkingmethodologies check the correctnessofasystem with respect to a given specification by examining computations of a bounded length. Results from set-theoretic topology imply that sets in Σ^{ω} that are both open and closed (clopen sets) are precisely bounded sets: membership of a word in a clopen set can be determined by examining a bounded prefix of it. Clopen sets correspond to specifications that are both safety and co-safety. In this paper we study bounded specifications from this perspective. We consider both the linear and the branching frameworks. In the linear framework, we show that when clopen specifications are given by word automata or temporal logic formulas, we can identify a bound and translate the specification to bounded formalisms such as cycle-free automata and bounded LTL. In the branching framework, we show that while clopen sets of trees with infinite branching degrees may not be bounded, we can extend the results from the linear framework to clopen specifications given by tree automata or temporal logic formulas, even for trees with infinite branching degrees. There, we can identify a bound and translate clopen specifications to cycle-free automata and modal logic. Finally, we show how our results imply that the bottom levels of the μ-calculus hierarchy coalesce.

Original language | American English |
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Title of host publication | Logic for Programming, Artificial Intelligence, and Reasoning - 8th International Conference, LPAR 2001, Proceedings |

Editors | Robert Nieuwenhuis, Andrei Voronkov |

Publisher | Springer Verlag |

Pages | 24-38 |

Number of pages | 15 |

ISBN (Electronic) | 9783540429579 |

DOIs | |

State | Published - 2001 |

Event | 8th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2001 - Havana, Cuba Duration: 3 Dec 2001 → 7 Dec 2001 |

### 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 | 2250 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 8th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2001 |
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Country/Territory | Cuba |

City | Havana |

Period | 3/12/01 → 7/12/01 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2001.