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An Automata-Theoretic Approach to Infinite-State Systems

  • Chapter
Time for Verification

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6200))

Abstract

In this paper we develop an automata-theoretic framework for reasoning about 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 a system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. We show how this framework can be used to solve the model-checking problem for μ-calculus and LTL specifications with respect to pushdown and prefix-recognizable systems. In order to handle model checking of linear-time specifications, we introduce and study 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.

As has been the case with finite-state systems, the automata-theoretic framework is quite versatile. We demonstrate it by solving the realizability and synthesis problems for μ-calculus specifications with respect to prefix-recognizable environments, and extending our framework to handle systems with regular labeling regular fairness constraints and μ-calculus with backward modalities.

The paper is based on the papers [KV00a,KPV02].

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Author information

Authors and Affiliations

  1. School of Engineering and Computer Science, Hebrew University, Jerusalem, 91904, Israel

    Orna Kupferman

  2. Department of Computing, Imperial College London, London, SW7 2AZ, UK

    Nir Piterman

  3. Department of Computer Science, Rice University, Houston, TX, 77251-1892, U.S.A.

    Moshe Y. Vardi

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  1. Orna Kupferman
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  2. Nir Piterman
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  3. Moshe Y. Vardi
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Editors and Affiliations

  1. Computer Science Department, Stanford University, 94305, Stanford, CA, USA

    Zohar Manna

  2. Department of Computer Science, Bar Ilan University, 52900, Ramat Gan, Israel

    Doron A. Peled

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Kupferman, O., Piterman, N., Vardi, M.Y. (2010). An Automata-Theoretic Approach to Infinite-State Systems. In: Manna, Z., Peled, D.A. (eds) Time for Verification. Lecture Notes in Computer Science, vol 6200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13754-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-13754-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13753-2

  • Online ISBN: 978-3-642-13754-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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