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Weak Kripke Structures and LTL

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6901))

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Abstract

We revisit the complexity of the model checking problem for formulas of linear-time temporal logic (LTL). We show that the classic PSPACE-hardness result is actually limited to a subclass of the Kripke frames, which is characterized by a simple structural condition: the model checking problem is only PSPACE-hard if there exists a strongly connected component with two distinct cycles. If no such component exists, the problem is in coNP. If, additionally, the model checking problem can be decomposed into a polynomial number of finite path checking problems, for example if the frame is a tree or a directed graph with constant depth, or the frame has an SCC graph of constant depth, then the complexity reduces further to NC.

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Author information

Authors and Affiliations

  1. Microsoft Redmond, USA

    Lars Kuhtz

  2. Saarland University, Germany

    Bernd Finkbeiner

Authors
  1. Lars Kuhtz
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  2. Bernd Finkbeiner
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Editor information

Editors and Affiliations

  1. Software Modeling and Verification, RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Joost-Pieter Katoen

  2. Fakultät für Ingenieurwesen, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen,, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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Kuhtz, L., Finkbeiner, B. (2011). Weak Kripke Structures and LTL. In: Katoen, JP., König, B. (eds) CONCUR 2011 – Concurrency Theory. CONCUR 2011. Lecture Notes in Computer Science, vol 6901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23217-6_28

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  • DOI: https://doi.org/10.1007/978-3-642-23217-6_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23216-9

  • Online ISBN: 978-3-642-23217-6

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