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Gaussian Process-Based Confidence Estimation for Hybrid System Falsification

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Formal Methods (FM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 13047))

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Abstract

Cyber-Physical Systems (CPSs) are widely adopted in safety-critical domains, raising great demands on their quality assurance. However, the application of formal verification is limited due to the continuous dynamics of CPSs. Instead, simulation-based falsification, which aims at finding a counterexample to refute the system specification, is a more feasible and hence actively pursued approach. Falsification adopts an optimization approach, treating robustness, given by the quantitative semantics of the specification language (usually Signal Temporal Logic (STL)), as the objective function. However, similarly to traditional testing, in the absence of found counterexamples, falsification does not give any guarantee on the system safety. To fill this gap, in this paper, we propose a confidence measure that estimates the probability that a formal specification is indeed not falsifiable, by relying on the information encapsulated in the simulation data collected during falsification. Methodologically, we approximate the robustness domain by feeding simulation data into a Gaussian Process (GP) Regression process; we then do a minimization sampling on the trained GP, and then estimate the probability that all the robustness values inferred from these sampled points are positive; we take this probability as the confidence measure. We experimentally study the properties of monotonicity and soundness of the proposed confidence measure. We also apply the measure to several state-of-the-art falsification algorithms to assess the maximum confidence they provide when they do not find a falsifying input, and the stability of such confidence across different repetitions.

Zhenya Zhang is supported by JSPS KAKENHI Grant No.20H04168, 19K24348, 19H04086, and JST-Mirai Program Grant No. JPMJMI18BB, Japan. Paolo Arcaini is supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST.

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Notes

  1. 1.

    Note that we assume that the confidence measure is computed starting from non-falsifying inputs only. The measure does not make sense if at least one falsifying input is used for its computation; in that case, there is no need of the confidence measure, as we know that the specification is falsifiable.

  2. 2.

    Since computing the confidence measure can take up to 30 s, we have computed it only for some sizes of |T|.

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Authors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Zhenya Zhang

  2. National Institute of Informatics, Tokyo, Japan

    Paolo Arcaini

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  1. Zhenya Zhang
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  1. University of Twente, Enschede, The Netherlands

    Marieke Huisman

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Corina Păsăreanu

  3. Institute of Software, Chinese Academy of Sciences, Beijing, China

    Naijun Zhan

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Zhang, Z., Arcaini, P. (2021). Gaussian Process-Based Confidence Estimation for Hybrid System Falsification. In: Huisman, M., Păsăreanu, C., Zhan, N. (eds) Formal Methods. FM 2021. Lecture Notes in Computer Science(), vol 13047. Springer, Cham. https://doi.org/10.1007/978-3-030-90870-6_18

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