Edit Mechanism Synthesis for Opacity Enforcement Under Uncertain Observations

This letter addresses the problem of opacity enforcement by using edit functions in discrete event systems modeled as deterministic finite automata under partial observation. The edit function is an output interface of the system that manipulates actual observations to confuse a malicious intruder. We assume that the edit function simply knows whether the intruder observes a larger or smaller set of events than itself, but does not know the exact set of events observed by the intruder. In this uncertain observation setting, the edit function aims to confuse the intruder while relying on its own set of observable events, which requires the edit function to be $u$ -enforcing. The opacity enforcement problem is then transformed to a two-player game between the system and the edit function under partial information. A so-called edit mechanism is proposed in a game scheme to enumerate all possible edited operations following the system behavior. We show that an edit function synthesized from the edit mechanism (if any) can be used to enforce opacity in the system under the uncertain observation setting.