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Probabilistic Hyperproperties with Rewards

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NASA Formal Methods (NFM 2022)

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

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Abstract

Probabilistic hyperproperties describe system properties that are concerned with the probability relation between different system executions. Likewise, it is desirable to relate performance metrics (e.g., energy, execution time, etc.) between multiple runs. This paper introduces the notion of rewards to the temporal logic HyperPCTL by extending the syntax and semantics of the logic to express the accumulated reward relation among different computations. We demonstrate the application of the extended logic in expressing side-channel timing countermeasures, efficiency in probabilistic conformance, path planning in robotics applications, and recovery time in distributed self-stabilizing systems. We also propose a model checking algorithm for verifying Markov Decision Processes against HyperPCTL with rewards and report experimental results.

This research was partially supported by the United States NSF SaTC Award 2100989, WWTF ICT19-018 grant ProbInG and the DFG Research and Training Group UnRAVeL.

O. Dobe and L. Wilke—First co-authors.

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Notes

  1. 1.

    Instead of syntactical substitutions, we could also use binding functions to map scheduler variables to schedulers and state variables to indices in the state sequence in the context.

  2. 2.

    For n scheduler quantifiers, we would simply need to include such a scheduler encoding for each of the schedulers \(\sigma _1,\ldots ,\sigma _n\), and in the rest of the encoding, refer to the respective schedulers \(\sigma _i\) instead of \(\sigma \).

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Authors and Affiliations

  1. Michigan State University, East Lansing, MI, USA

    Oyendrila Dobe & Borzoo Bonakdarpour

  2. RWTH Aachen University, Aachen, Germany

    Lukas Wilke & Erika Ábrahám

  3. Technische Universität Wien, Vienna, Austria

    Ezio Bartocci

Authors
  1. Oyendrila Dobe
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  2. Lukas Wilke
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  3. Erika Ábrahám
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  4. Ezio Bartocci
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  5. Borzoo Bonakdarpour
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Correspondence to Borzoo Bonakdarpour .

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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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Dobe, O., Wilke, L., Ábrahám, E., Bartocci, E., Bonakdarpour, B. (2022). Probabilistic Hyperproperties with Rewards. 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_35

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  • DOI: https://doi.org/10.1007/978-3-031-06773-0_35

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