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Symbolic model checking for probabilistic processes

  • Session 10: Logic and Verification
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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Abstract

We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems by Multi-Terminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [14]. Our procedure, based on the algorithm used by Hansson and Jonsson [24], uses BDDs to represent formulas and MTBDDs to represent Markov chains, and is efficient because it avoids explicit state space construction. A PCTL model checker is being implemented in Verus [9].

This research was sponsored in part by the National Science Foundation under grant no. CCR-8722633, by the Semiconductor Research Corporation under contract 92-DJ-294, and by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, the Advanced Research Projects Agency (ARPA) under grant F33615-93-1-1330.

This research was sponsored in part by the European Union ESPRIT projects ASPIRE and FIREworks, British Telecom, and the Nuffield Foundation.

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Authors and Affiliations

  1. Fakultät für Mathematik & Informatik, Universität Mannheim, 68131, Mannheim, Germany

    Christel Baier

  2. Department of Computer Science, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Edmund M. Clarke & Vasiliki Hartonas-Garmhausen

  3. School of Computer Science, University of Birmingham, B152TT, Birmingham, UK

    Marta Kwiatkowska & Mark Ryan

Authors
  1. Christel Baier
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  2. Edmund M. Clarke
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  3. Vasiliki Hartonas-Garmhausen
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  4. Marta Kwiatkowska
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  5. Mark Ryan
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Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Baier, C., Clarke, E.M., Hartonas-Garmhausen, V., Kwiatkowska, M., Ryan, M. (1997). Symbolic model checking for probabilistic processes. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_199

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  • DOI: https://doi.org/10.1007/3-540-63165-8_199

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  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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