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Randomized First-Order Monitoring with Hashing

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Book cover Runtime Verification (RV 2022)

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Abstract

Online monitors for first-order specifications may need to store many domain values in their state, requiring significant memory. We propose an approach that compresses the monitor’s state using randomized hash functions. Unlike input sampling, our approach does not require the knowledge of distributions over traces to achieve low error probability. We develop algorithms that insert hash functions into temporal–relational algebra specifications and compute upper bounds on the resulting error probability. We employ a special hashing scheme that allows us to merge values across attributes, which further reduces memory usage. We evaluated our implementation and achieved memory reductions up to \(33\%\) when monitoring traces with large domain values, with error probability less than two in a million.

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Notes

  1. 1.

    The meta-variable I will later be used for both types of intervals.

  2. 2.

    The support of a discrete probability distribution is the set of values with nonzero probability.

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Acknowledgement

The author thanks David Basin, Srđan Krstić, Dmitriy Traytel, and the anonymous reviewers for their helpful comments and suggestions. This research was supported by the US Air Force grant “Monitoring at Any Cost” (FA9550-17-1-0306).

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  1. Institute of Information Security, Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Joshua Schneider

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  1. CNRS/Verimag, Saint Martin d’Hères, France

    Thao Dang

  2. Høgskulen på Vestlandet, Bergen, Norway

    Volker Stolz

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Schneider, J. (2022). Randomized First-Order Monitoring with Hashing. In: Dang, T., Stolz, V. (eds) Runtime Verification. RV 2022. Lecture Notes in Computer Science, vol 13498. Springer, Cham. https://doi.org/10.1007/978-3-031-17196-3_1

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  • DOI: https://doi.org/10.1007/978-3-031-17196-3_1

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