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Article

Verification of Opacity Under a K-Delay Orwellian Observation Mechanism

1
Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau SAR 999078, China
2
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
3
College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin 300457, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(10), 1568; https://doi.org/10.3390/math13101568
Submission received: 30 March 2025 / Revised: 29 April 2025 / Accepted: 8 May 2025 / Published: 9 May 2025
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)

Abstract

Opacity, an important property of the information flow in discrete-event systems (DESs), characterizes whether the secret information in a system is ambiguous to a passive observer (called an intruder). Observation models play a critical role in the analysis of opacity. In this paper, instead of adopting a fully static observation model or a fully dynamic observation model, we use a novel Orwellian-type observation model to study the verification of the current-state opacity (CSO), where the observability of an unobservable event can be re-interpreted once certain/several specific conditions are met. First, a K-delay Orwellian observation mechanism (KOOM) is proposed as a novel Orwellian-type observation mechanism for extending the existing Orwellian projection. The main characteristics of the KOOM are delaying the inevitable information release and narrowing the release range for historical information to protect the secrets in a system to a greater extent than with the existing Orwellian projection. Second, we formulate the definitions of standard and strong CSO under the KOOM. Finally, we address the verification problem for these two types of opacity by constructing two novel information structures called a standard K-delay verifier and a strong K-delay verifier, respectively. An analysis of the computational complexity and illustrative examples are also presented for the proposed results. Overall, the proposed notions of standard and strong CSO under the KOOM capture the security privacy requirements regarding a delayed release in applications, such as intelligent transportation systems, etc.
Keywords: discrete-event system; opacity; information release; K-delay Orwellian observation; verifier discrete-event system; opacity; information release; K-delay Orwellian observation; verifier

Share and Cite

MDPI and ACS Style

Zhang, J.; Zhang, K.; Han, X.; Li, Z. Verification of Opacity Under a K-Delay Orwellian Observation Mechanism. Mathematics 2025, 13, 1568. https://doi.org/10.3390/math13101568

AMA Style

Zhang J, Zhang K, Han X, Li Z. Verification of Opacity Under a K-Delay Orwellian Observation Mechanism. Mathematics. 2025; 13(10):1568. https://doi.org/10.3390/math13101568

Chicago/Turabian Style

Zhang, Jiahui, Kuize Zhang, Xiaoguang Han, and Zhiwu Li. 2025. "Verification of Opacity Under a K-Delay Orwellian Observation Mechanism" Mathematics 13, no. 10: 1568. https://doi.org/10.3390/math13101568

APA Style

Zhang, J., Zhang, K., Han, X., & Li, Z. (2025). Verification of Opacity Under a K-Delay Orwellian Observation Mechanism. Mathematics, 13(10), 1568. https://doi.org/10.3390/math13101568

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