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International Workshop on Reachability Problems

RP 2015: Reachability Problems pp 7–19Cite as

Integer-Complete Synthesis for Bounded Parametric Timed Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9328))

Abstract

Ensuring the correctness of critical real-time systems, involving concurrent behaviors and timing requirements, is crucial. Parameter synthesis aims at computing dense sets of valuations for the timing requirements, guaranteeing a good behavior. However, in most cases, the emptiness problem for reachability (i.e., whether there exists at least one parameter valuation for which some state is reachable) is undecidable and, as a consequence, synthesis procedures do not terminate in general, even for bounded parameters. In this paper, we introduce a parametric extrapolation, that allows us to derive an underapproximation in the form of linear constraints containing all the integer points ensuring reachability or unavoidability, and all the (non-necessarily integer) convex combinations of these integer points, for general PTA with a bounded parameter domain. Our algorithms terminate and can output constraints arbitrarily close to the complete result.

This work is partially supported by the ANR national research program “PACS” (ANR-2014).

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Author information

Authors and Affiliations

  1. LIPN, CNRS, UMR 7030, Université Paris 13, Sorbonne Paris Cité, Villetaneuse, France

    Étienne André

  2. IRCCyN, CNRS, UMR 6597, École Centrale de Nantes, Nantes, France

    Didier Lime & Olivier H. Roux

Authors
  1. Étienne André
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  2. Didier Lime
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  3. Olivier H. Roux
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Corresponding author

Correspondence to Étienne André .

Editor information

Editors and Affiliations

  1. The Institute of Informatics, University of Warsaw, Warsaw, Poland

    Mikolai Bojanczyk

  2. The Institute of Informatics, University of Warsaw, Warsaw, Poland

    Slawomir Lasota

  3. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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© 2015 Springer International Publishing Switzerland

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André, É., Lime, D., Roux, O.H. (2015). Integer-Complete Synthesis for Bounded Parametric Timed Automata. In: Bojanczyk, M., Lasota, S., Potapov, I. (eds) Reachability Problems. RP 2015. Lecture Notes in Computer Science(), vol 9328. Springer, Cham. https://doi.org/10.1007/978-3-319-24537-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-24537-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24536-2

  • Online ISBN: 978-3-319-24537-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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