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On Deadlock Analysis and Characterization of Labeled Petri Nets with Undistinguishable and Unobservable Transitions

Author

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  • Amal Zaghdoud

    (Macau Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau SAR, China
    These authors contributed equally to this work.)

  • Zhiwu Li

    (Macau Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau SAR, China
    These authors contributed equally to this work.)

Abstract

This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization in such a way that deadlock control and synthesis are technically and methodologically possible. To this end, we introduce the notion of dangerous implicit vectors (DIVs), which implicitly threaten the system deadlock-freedom. The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs). An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system. Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions for identifying the existence of blocking markings in an LPN. Finally, an algorithm is developed to construct an observed graph that is a compendious presentation of the reachability graph of a net system, with respect to the existence of dead reaches. At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented.

Suggested Citation

  • Amal Zaghdoud & Zhiwu Li, 2024. "On Deadlock Analysis and Characterization of Labeled Petri Nets with Undistinguishable and Unobservable Transitions," Mathematics, MDPI, vol. 12(22), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3523-:d:1518758
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    References listed on IDEAS

    as
    1. Ye Liang & Gaiyun Liu & Ahmed M. El-Sherbeeny, 2023. "Polynomial-Time Verification of Decentralized Fault Pattern Diagnosability for Discrete-Event Systems," Mathematics, MDPI, vol. 11(18), pages 1-12, September.
    2. Yongyao Li & Yufeng Chen & Rui Zhou, 2024. "A Set Covering Approach to Design Maximally Permissive Supervisors for Flexible Manufacturing Systems," Mathematics, MDPI, vol. 12(11), pages 1-20, May.
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