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Clairvoyant Monitoring for Signal Temporal Logic

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Formal Modeling and Analysis of Timed Systems (FORMATS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12288))

Abstract

In this paper, we consider the problem of monitoring temporal patterns expressed in Signal Temporal Logic (STL) over time-series data in a clairvoyant fashion. Existing offline or online monitoring algorithms can only compute the satisfaction of a given STL formula on the time-series data that is available. We use off-the-shelf statistical time-series analysis techniques to fit available data to a model and use this model to forecast future signal values. We derive the joint probability distribution of predicted signal values and use this to compute the satisfaction probability of a given signal pattern over the prediction horizon. There are numerous potential applications of such prescient detection of temporal patterns. We demonstrate practicality of our approach on case studies in automated insulin delivery, unmanned aerial vehicles, and household power consumption data.

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Notes

  1. 1.

    We can easily extend clairvoyant monitoring of unbounded horizon STL formulas over entire traces by considering the notion of nominal robustness [10]. This would also require us to track the robustness over the signal prefix.

  2. 2.

    When signals are evaluated w.r.t. Signal Temporal Logic formulas, we assume that the signal is defined at each time point in the interval \([0,t_N]\). We can do this using piecewise constant interpolation, i.e. \(\forall i \in [0,N-1]: (t_i \le t < t_{i+1}) \implies x(t) = x(t_i)\).

  3. 3.

    Our implementation was done in Matlab, and Matlab has a certain precision when computing probabilities, and the number 1 is actually \(1 -\delta \), where \(\delta \) is smaller than the machine precision. This indicates that the probability is so high that it is practically 1.

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Acknowledgments

We thank the anonymous reviewers for their careful reading of the paper and the constructive feedback. We gratefully acknowledge the support by the National Science Foundation under grant no. CCF/SHF-1910088, and a grant from Toyota Motors R&D North America. We thank Yue Wu and Weixin Cai for fruitful discussions that helped shape the proofs for Theorem 1.

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  1. University of Southern California, Los Angeles, USA

    Xin Qin & Jyotirmoy V. Deshmukh

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  1. Xin Qin
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Correspondence to Xin Qin or Jyotirmoy V. Deshmukh .

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  1. Inria, Université de Rennes, Rennes, France

    Nathalie Bertrand

  2. Radboud University, Nijmegen, The Netherlands

    Nils Jansen

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Qin, X., Deshmukh, J.V. (2020). Clairvoyant Monitoring for Signal Temporal Logic. In: Bertrand, N., Jansen, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2020. Lecture Notes in Computer Science(), vol 12288. Springer, Cham. https://doi.org/10.1007/978-3-030-57628-8_11

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