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Predictive Run-Time Verification of Discrete-Time Reachability Properties in Black-Box Systems Using Trace-Level Abstraction and Statistical Learning

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Runtime Verification (RV 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11237))

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Abstract

Run-time Verification (RV) has become a crucial aspect of monitoring black-box systems. Recently, we introduced \(\mathcal {P}{} \textit{revent} \), a predictive RV framework, in which the monitor is able to predict the future extensions of an execution, using a model inferred from the random sample executions of the system. The monitor maintains a table of the states of the prediction model, with the probability of the extensions from each state that satisfy a safety property.

The size of the prediction model directly influences the monitor’s memory usage and computational performance, due to the filtering techniques used for run-time state estimation, that depends on the size of the model. Hence, achieving a small prediction model is key in predictive RV.

In this paper, we use symmetry reduction to apply abstraction, that, in the absence of a model in black-box systems, is performed on the observation space. The symmetry relation is inferred based on k-gapped pair model, that lumps symbols with similar empirical probability to reach a set of target labels on a set of samples. The obtained equivalence classes on the observation space are used to abstract traces that are used in training the prediction model.

We demonstrate the soundness of the abstraction, in the case that the generating abstract model is a deterministic Discrete-Time Markov Chain (DTMC). We use Hidden Markov Models (HMMs) to handle the abstraction-induced non-determinism by learning the distribution of a hidden state variable. We implemented our approach in our tool, \(\mathcal {P}{} \textit{revent} \), to empirically evaluate our approach on the Herman’s randomised self-stabilising algorithm. Our results show that the inferred abstraction significantly reduces the size of the model and the training time, without a meaningful impact on the prediction accuracy, with better results from the HMM models.

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Notes

  1. 1.

    Available at https://bitbucket.org/rbabaeecar/prevent/.

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Authors and Affiliations

  1. Electrical and Computer Engineering, University of Waterloo, Waterloo, Canada

    Reza Babaee, Arie Gurfinkel & Sebastian Fischmeister

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  1. Reza Babaee
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  2. Arie Gurfinkel
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  3. Sebastian Fischmeister
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Correspondence to Reza Babaee .

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Editors and Affiliations

  1. University of Malta, Msida, Malta

    Christian Colombo

  2. University of LĂĽbeck, LĂĽbeck, Germany

    Martin Leucker

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Babaee, R., Gurfinkel, A., Fischmeister, S. (2018). Predictive Run-Time Verification of Discrete-Time Reachability Properties in Black-Box Systems Using Trace-Level Abstraction and Statistical Learning. In: Colombo, C., Leucker, M. (eds) Runtime Verification. RV 2018. Lecture Notes in Computer Science(), vol 11237. Springer, Cham. https://doi.org/10.1007/978-3-030-03769-7_11

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  • DOI: https://doi.org/10.1007/978-3-030-03769-7_11

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