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Time-Bounded Resilience

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Rewriting Logic and Its Applications (WRLA 2024)

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Abstract

Most research on system design has focused on optimizing efficiency. However, insufficient attention has been given to the design of systems optimizing resilience, the ability of systems to adapt to unexpected changes or adversarial disruptions. In our prior work, we formalized the intuitive notion of resilience as a property of cyber-physical systems by using a multiset rewriting language with explicit time. In the present paper, we study the computational complexity of a formalization of time-bounded resilience problems for the class of \(\eta \)-simple progressing planning scenarios, where, intuitively, it is simple to check that a system configuration is critical, and only a bounded number of rules can be applied in a single time step. We show that, in the time-bounded model with n (adversarially-chosen) disruptions, the corresponding time-bounded resilience problem for this class of systems is complete for the \(\Sigma ^\textsf {P}_{2n+1}\) class of the polynomial hierarchy, PH. To support the formal models and complexity results, we perform automated experiments for time-bounded verification using the rewriting logic tool Maude.

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Notes

  1. 1.

    For a discussion of various conditions in the model that may affect complexity, see [23, 24].

  2. 2.

    Execution terminates if a critical state is reached, so paths to goal states are always compliant.

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Acknowledgment

We thank Vivek Nigam for many insightful discussions during the early part of this work. Kanovich was partially supported by EPSRC Programme Grant EP/R006865/1: “Interface Reasoning for Interacting Systems (IRIS)”. Scedrov was partially supported by the U. S. Office of Naval Research under award number N00014-20-1-2635 during the early part of this work. Talcott was partially supported by the U. S. Office of Naval Research under award numbers N00014-15-1-2202 and N00014-20-1-2644, and NRL grant N0017317-1-G002.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Rijeka, Rijeka, Croatia

    Tajana Ban Kirigin

  2. University of Pennsylvania, Philadelphia, PA, USA

    Jesse Comer & Andre Scedrov

  3. University College, London, UK

    Max Kanovich

  4. SRI International, Menlo Park, CA, USA

    Carolyn Talcott

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  1. Tajana Ban Kirigin
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  2. Jesse Comer
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  4. Andre Scedrov
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  5. Carolyn Talcott
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Corresponding author

Correspondence to Jesse Comer .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Kazuhiro Ogata

  2. Universidad Complutense de Madrid, Madrid, Spain

    Narciso Martí-Oliet

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Ban Kirigin, T., Comer, J., Kanovich, M., Scedrov, A., Talcott, C. (2024). Time-Bounded Resilience. In: Ogata, K., Martí-Oliet, N. (eds) Rewriting Logic and Its Applications. WRLA 2024. Lecture Notes in Computer Science, vol 14953. Springer, Cham. https://doi.org/10.1007/978-3-031-65941-6_2

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  • DOI: https://doi.org/10.1007/978-3-031-65941-6_2

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