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Reachability Analysis of (Timed) Petri Nets Using Real Arithmetic

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CONCUR’99 Concurrency Theory (CONCUR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1664))

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Abstract

In this paper, we address the issue of reachability analysis for Petri nets, viewed as automata with counters. We show that exact reachability analysis can be achieved by treating Petri nets integer variables (counters) as real-valued variables, and using Fourier-Motzkin procedure instead of Presburger elimination procedure. As a consequence, one can safely analyse Petri nets with performant tools, e.g. HyTech, originally designed for analysing automata with real-valued variables (clocks). We also investigate the use of meta-transitions (iterative application of a transition in a single step) and give sufficient conditions ensuring an exact computation in this case. Experimental results with HyTech show an impressive speed-up with respect to previous experiences performed with a Presburger arithmetic solver. The method extends for analysing Petri nets with inhibitors and with timing constraints, but difficulties arise for the treatment of meta-transitions in the latter case.

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Authors and Affiliations

  1. LSV — ENS de Cachan/CNRS, 61 av. Pdt. Wilson, 94235, Cachan, France

    Béatrice Bérard & Laurent Fribourg

Authors
  1. Béatrice Bérard
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  2. Laurent Fribourg
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Editors and Affiliations

  1. Department of Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten  & Sjouke Mauw  & 

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Bérard, B., Fribourg, L. (1999). Reachability Analysis of (Timed) Petri Nets Using Real Arithmetic. In: Baeten, J.C.M., Mauw, S. (eds) CONCUR’99 Concurrency Theory. CONCUR 1999. Lecture Notes in Computer Science, vol 1664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48320-9_14

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  • DOI: https://doi.org/10.1007/3-540-48320-9_14

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  • Print ISBN: 978-3-540-66425-3

  • Online ISBN: 978-3-540-48320-5

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