## Abstract

Model checking is a method for the verification of systems with respect to their specifications. Symbolic model-checking, which enables the verification of large systems, proceeds by calculating fixed-point expressions over the system's set of states. The μ-calculus is a branching-Time temporal logic with fixed-point operators. As such, it is a convenient logic for symbolic model-checking tools. In particular, the alternation-free fragment of μ-calculus has a restricted syntax, making the symbolic evaluation of its formulas computationally easy. Formally, it takes time that is linear in the size of the system. On the other hand, specifiers find the μ-calculus inconvenient. In addition, specifiers often prefer to use Linear-Time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free CL-calculus, and their symbolic evaluation involves nesting of fixed-points, resulting in time complexity that is quadratic in the size of the system. In this paper we characterize linear-Time properties that can be specified in the alternation-free μ-calculus. We show that a linear-Time property can be specified in the alternation-free μ-calculus if it can be recognized by a deterministic Buchi automation. We study the problem of deciding whether a linear-Time property, specified by either an automaton or an LTL formula, can be translated to an alternation-free μ-calculus formula, and describe the translation, when exists.

Original language | American English |
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Title of host publication | Proceedings - 13th Annual IEEE Symposium on Logic in Computer Science, LICS 1998 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 81-92 |

Number of pages | 12 |

ISBN (Electronic) | 0818685069 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | 13th Annual IEEE Symposium on Logic in Computer Science, LICS 1998 - Indianapolis, United States Duration: 21 Jun 1998 → 24 Jun 1998 |

### Publication series

Name | Proceedings - Symposium on Logic in Computer Science |
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Volume | 1998-June |

ISSN (Print) | 1043-6871 |

### Conference

Conference | 13th Annual IEEE Symposium on Logic in Computer Science, LICS 1998 |
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Country/Territory | United States |

City | Indianapolis |

Period | 21/06/98 → 24/06/98 |

### Bibliographical note

Publisher Copyright:© 1998 IEEE.