## Abstract

In the automata-theoretic approach to verification, we model programs and specifications by automata on infinite words. Correctness of a program with respect to a specification can then be reduced to the language-containment problem. In a concurrent setting, the program is typically a parallel composition of many coordinating processes, and the language-containment problem that corresponds to verification is (formula presented), where P_{1}, P_{2}, … P_{n} are automata that model the underlying coordinating processes, and T is the task they should perform. In 1994, Kurshan suggested the heuristic of Reduction Hierarchies for circumventing the exponential blow-up introduced by conventional methods that solve the problem (†). In the reduction hierarchy heuristic, we solve the problem (†) by solving a sequence of easier problems, which involve only automata of tractable sizes. Complexity-theoretic conjectures (NP ≠ PSPACE) imply that there are settings in which the heuristic cannot circumvent the exponential blow-up. In this paper, we demonstrate the strength of the heuristic, study its properties, characterize settings in which it performs effectively, and suggest a method for searching for reduction hierarchies. In particular, we prove, independently of the NP ≠ PSPACE question, that reduction hierarchies of tractable sizes do not always exist.

Original language | American English |
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Title of host publication | Computer Science Logic - 11th International Workshop, CSL 1997 Annual Conference of the EACSL, Selected Papers |

Editors | Mogens Nielsen, Wolfgang Thomas |

Publisher | Springer Verlag |

Pages | 327-340 |

Number of pages | 14 |

ISBN (Print) | 3540645705, 9783540645702 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | 11th International Workshop on Computer Science Logic, CSL 1997, Annual Conference of the European Association for Computer Science, EACSL 1997 - Aarhus, Denmark Duration: 23 Aug 1997 → 29 Aug 1997 |

### 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 | 1414 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th International Workshop on Computer Science Logic, CSL 1997, Annual Conference of the European Association for Computer Science, EACSL 1997 |
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Country/Territory | Denmark |

City | Aarhus |

Period | 23/08/97 → 29/08/97 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1997.