On bounded specifications

Orna Kupferman, Moshe Y. Vardi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

22 Scopus citations

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 Σω 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 languageAmerican English
Title of host publicationLogic for Programming, Artificial Intelligence, and Reasoning - 8th International Conference, LPAR 2001, Proceedings
EditorsRobert Nieuwenhuis, Andrei Voronkov
PublisherSpringer Verlag
Pages24-38
Number of pages15
ISBN (Electronic)9783540429579
DOIs
StatePublished - 2001
Event8th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2001 - Havana, Cuba
Duration: 3 Dec 20017 Dec 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2250
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2001
Country/TerritoryCuba
CityHavana
Period3/12/017/12/01

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

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