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NASA Formal Methods Symposium

NFM 2022: NASA Formal Methods pp 451–469Cite as

Zone Extrapolations in Parametric Timed Automata

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13260))

Abstract

Timed automata (TAs) are an efficient formalism to model and verify systems with hard timing constraints, and concurrency. While TAs assume exact timing constants with infinite precision, parametric TAs (PTAs) leverage this limitation and increase their expressiveness, at the cost of undecidability. A practical explanation for the efficiency of TAs is zone extrapolation, where clock valuations beyond a given constant are considered equivalent. This concept cannot be easily extended to PTAs, due to the fact that parameters can be unbounded or can take arbitrary rational values. In this work, we propose several definitions of extrapolation for PTAs based on the \({{M}}\)-extrapolation, and we study their correctness. Our experiments show an overall decrease of the computation time and, most importantly, allow termination of some previously unsolvable benchmarks.

This work is partially supported by the ANR-NRF French-Singaporean research program ProMiS (ANR-19-CE25-0015).

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Notes

  1. 1.

    While “L/U” means in both cases “lower-upper (bound)”, L/U-PTAs are a completely different concept from LU-extrapolation for (P)TAs.

  2. 2.

    The proofs of all our results are in a technical report [10].

  3. 3.

    Source, benchmarks, raw results and full table are available at doi.org/10.5281/zenodo.5824264. We used a fork of IMITATOR 3.1 “Cheese Artichoke” extended with extrapolation functions (exact version: v3.1.0+extrapolation).

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Acknowledgements

The authors would like to thank the reviewers for their comments, and Dylan Marinho for his help in providing the models and automation tools that were used for the benchmarking presented in this paper.

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Authors and Affiliations

  1. Université de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France

    Johan Arcile & Étienne André

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  1. Johan Arcile
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  2. Étienne André
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Correspondence to Johan Arcile .

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Editors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Jyotirmoy V. Deshmukh

  2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    Klaus Havelund

  3. National Institute of Aerospace, Hampton, VA, USA

    Ivan Perez

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Arcile, J., André, É. (2022). Zone Extrapolations in Parametric Timed Automata. In: Deshmukh, J.V., Havelund, K., Perez, I. (eds) NASA Formal Methods. NFM 2022. Lecture Notes in Computer Science, vol 13260. Springer, Cham. https://doi.org/10.1007/978-3-031-06773-0_24

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  • DOI: https://doi.org/10.1007/978-3-031-06773-0_24

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