Verification and Enforcement of (?, )-Differential Privacy over Finite Steps in Discrete Event Systems

In the realm of data protection strategies, differential privacy ensures that unauthorized entities cannot reconstruct original data from system outputs. This study explores discrete event systems, specifically through probabilistic automata. Central is the protection of state data, particularly the initial state privacy of multiple starting states. We introduce an evaluation criterion to safeguard initial states. Using advanced algorithms, the proposed method counters the probabilistic identification of any state within this collection by adversaries from observed data points. The efficacy is confirmed when the probability distributions of data observations tied to these states converge. If a system's architecture does not meet state differential privacy demands, we propose an enhanced supervisory control mechanism. This control upholds state differential privacy across all initial states, maintaining operational flexibility within the probabilistic automaton framework. Concluding, a numerical analysis validates the approach's strength in probabilistic automata and discrete event systems.