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Resilience and Home-Space for WSTS

  • Conference paper
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Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14499))

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Abstract

Resilience of unperfect systems is a key property for improving safety by insuring that if a system could go into a bad state in \(\textsf {Bad}\) then it can also leave this bad state and reach a safe state in \(\textsf {Safe}\). We consider six types of resilience (one of them is the home-space property) defined by an upward-closed set or a downward-closed set \(\textsf {Safe}\), and by the existence of a bound on the length of minimal runs starting from a set \(\textsf {Bad}\) and reaching \(\textsf {Safe}\) (\(\textsf {Bad}\) is generally the complementary of \(\textsf {Safe}\)).

We first show that all resilience problems are undecidable for effective Well Structured Transition Systems (WSTS) with strong compatibility. We then show that resilience is decidable for Well Behaved Transition Systems (WBTS) and for WSTS with adapted effectiveness hypotheses. Most of the resilience properties are shown decidable for other classes like WSTS with the downward compatibility, VASS, lossy counter machines, reset-VASS, integer VASS and continuous VASS.

This work was partly done while the authors were supported by the Agence Nationale de la Recherche grant BraVAS (ANR-17-CE40-0028).

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Acknowledgements

We express our thanks to the reviewers of the VMCAI 2024 Conference for their numerous and relevant comments and improvement suggestions.

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Authors and Affiliations

  1. Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France

    Alain Finkel & Mathieu Hilaire

  2. Institut Universitaire de France, Paris, France

    Alain Finkel

Authors
  1. Alain Finkel
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  2. Mathieu Hilaire
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Correspondence to Mathieu Hilaire .

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Editors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

  3. New York University, New York, NY, USA

    Sebastian Wolff

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Finkel, A., Hilaire, M. (2024). Resilience and Home-Space for WSTS. In: Dimitrova, R., Lahav, O., Wolff, S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2024. Lecture Notes in Computer Science, vol 14499. Springer, Cham. https://doi.org/10.1007/978-3-031-50524-9_7

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  • DOI: https://doi.org/10.1007/978-3-031-50524-9_7

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