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NASA Formal Methods Symposium

NFM 2017: NASA Formal Methods pp 35–51Cite as

Parametric Model Checking Timed Automata Under Non-Zenoness Assumption

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10227))

Abstract

Real-time systems often involve hard timing constraints and concurrency, and are notoriously hard to design or verify. Given a model of a real-time system and a property, parametric model-checking aims at synthesizing timing valuations such that the model satisfies the property. However, the counter-example returned by such a procedure may be Zeno (an infinite number of discrete actions occurring in a finite time), which is unrealistic. We show here that synthesizing parameter valuations such that at least one counterexample run is non-Zeno is undecidable for parametric timed automata (PTAs). Still, we propose a semi-algorithm based on a transformation of PTAs into Clock Upper Bound PTAs to derive all valuations whenever it terminates, and some of them otherwise.

This work is partially supported by the ANR national research program PACS (ANR-14-CE28-0002).

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Notes

  1. 1.

    Note that if a clock has more than a single upper bound in a guard, then the minimum can be encoded as a disjunction of constraints, and our results would still apply with non-convex constraints (that can be implemented using a finite list of convex constraints).

  2. 2.

    This model assumes that, after the change of a signal in the input of a gate, the output changes after a delay which is modeled using a parametric closed interval.

  3. 3.

    A purely parametric constraint (e. g. \(p_1 > p_2 \wedge p_3 = 3\)) is generally not allowed by the PTA syntax, but can be simulated using appropriate clocks (e. g. \(p_1> x> p_2 \wedge p_3 = x' = 3\)). Such parametric constraints are allowed in the input syntax of IMITATOR.

  4. 4.

    Following a well-known result for PTAs, all symbolic states belonging to a same cycle in a parametric zone graph have the same parameter constraint.

  5. 5.

    For experimental data including source and binary, see http://imitator.fr/static/NFM17.

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Authors and Affiliations

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

    Étienne André, Hoang Gia Nguyen & Laure Petrucci

  2. ISTD, Singapore University of Technology and Design, Singapore, Singapore

    Jun Sun

Authors
  1. Étienne André
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  2. Hoang Gia Nguyen
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  3. Laure Petrucci
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  4. Jun Sun
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Corresponding author

Correspondence to Hoang Gia Nguyen .

Editor information

Editors and Affiliations

  1. Stanford University, Palo Alto, California, USA

    Clark Barrett

  2. NASA Ames Research Center, Moffett Field, California, USA

    Misty Davies

  3. NASA Ames Research Center, Moffett Field, California, USA

    Temesghen Kahsai

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André, É., Nguyen, H.G., Petrucci, L., Sun, J. (2017). Parametric Model Checking Timed Automata Under Non-Zenoness Assumption. In: Barrett, C., Davies, M., Kahsai, T. (eds) NASA Formal Methods. NFM 2017. Lecture Notes in Computer Science(), vol 10227. Springer, Cham. https://doi.org/10.1007/978-3-319-57288-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-57288-8_3

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