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Matrix Approach for Verification of Opacity of Partially Observed Discrete Event Systems

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Abstract

Opacity is a confidential property characterizing whether the secret of a system can be inferred or not by an outside observer (also called an intruder). This paper focuses on presenting a matrix-based approach for verification of opacity of nondeterministic discrete event systems (DESs). Firstly, the given system is modeled as a finite-state automaton. Further, based on Boolean semi-tensor product (BSTP) of matrices, the algebraic expression of the observable dynamic of the system can be obtained. We, respectively, investigate current-state opacity and K-step opacity owing to the equivalence between a few opacity properties. Finally, necessary and sufficient conditions are presented to verify whether the secret is opaque for a given system, and the proposed methodology is tested effectively by examples. The matrix-based characterization of opacity proposed in this paper may provide a helpful angel for understanding the structure of this property.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61573102 and 61877033, the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20170019, Natural Science Foundation of Shandong Province under Grant No. ZR2019MF021, “333 Engineering” Foundation of Jiangsu Province of China under Grant BRA2019260, and the Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant KYCX19_0112.

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Authors and Affiliations

  1. School of Cyber Science and Engineering, Southeast University, Nanjing, 210096, People’s Republic of China

    Liujuan Mei & Rongjian Liu

  2. School of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Jianquan Lu

  3. Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong (Linyi University), School of Automation and Electrical Engineering, Linyi University, Linyi, 276005, People’s Republic of China

    Jianlong Qiu

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  1. Liujuan Mei
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Correspondence to Jianquan Lu or Jianlong Qiu.

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Mei, L., Liu, R., Lu, J. et al. Matrix Approach for Verification of Opacity of Partially Observed Discrete Event Systems. Circuits Syst Signal Process 40, 70–87 (2021). https://doi.org/10.1007/s00034-020-01462-2

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