Almost k -Step Opacity Enforcement in Stochastic Discrete-Event Systems via Differential Privacy

Rong Zhao, Murat Uzam and Zhiwu Li ()
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Rong Zhao: Institute of Systems Engineering, Macau University of Science and Technology, Macau SAR, China
Murat Uzam: Department of Electrical and Electronics Engineering, Faculty of Engineering and Architecture, Yozgat Bozok University, 66900 Yozgat, Turkiye
Zhiwu Li: Institute of Systems Engineering, Macau University of Science and Technology, Macau SAR, China

Mathematics, 2025, vol. 13, issue 8, 1-24

Abstract: This paper delves into current-state opacity enforcement in partially observed discrete event systems through an innovative application of differential privacy, which is fundamental for security-critical cyber–physical systems. An opaque system implies that an external agent cannot infer the predefined system secret via its observational output, such that the important system information flow cannot be leaked out. Differential privacy emerges as a robust framework that is pivotal for the protection of individual data integrity within these systems. Motivated by the differential privacy mechanism for information protection, this research proposes the secret string adjacency relation as a novel concept, assessing the similarity between potentially compromised strings and system-generated alternatives, thereby shielding the system’s confidential data from external observation. The development of secret string differential privacy is achieved by substituting sensitive strings. These substitution strings are generated by a modified Levenshtein automaton, following exponentially distributed generation probabilities. The verification and illustrative examples of the proposed mechanism are provided.

Keywords: discrete event system; finite state automaton; k-step opacity; differential privacy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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