## Abstract

We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems. We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.

Original language | American English |
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Title of host publication | Computer Aided Verification - 14th International Conference, CAV 2002, Proceedings |

Editors | Ed Brinksma, Kim Guldstrand Larsen |

Publisher | Springer Verlag |

Pages | 371-385 |

Number of pages | 15 |

ISBN (Electronic) | 9783540439974 |

DOIs | |

State | Published - 2002 |

Event | 14th International Conference on Computer Aided Verification, CAV 2002 - Copenhagen, Denmark Duration: 27 Jul 2002 → 31 Jul 2002 |

### 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 | 2404 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Conference on Computer Aided Verification, CAV 2002 |
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Country/Territory | Denmark |

City | Copenhagen |

Period | 27/07/02 → 31/07/02 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2002.