Protect Your Knowledge: Epistemic Property Enforcement of Discrete-Event Systems With Asymmetric Information

Many property verification and enforcement problems of partially observed discrete event systems (DES) are typically addressed solely from the outside observer’s perspective. However, systems may be monitored not only by a designated observer but also by a potentially malicious intruder when deployed in complex and open environments. The observer infers the information of the system based on its observation, which is referred to as knowledge. In addition, the intruder not only eavesdrops on the system’s behaviors but also attempts to infer the observer’s knowledge from its own observation. Notably, the information flow from the system to the observer and the intruder is asymmetric, resulting in incomparable observable events for each agent. Such an inference scenario has recently been formalized as the epistemic property. This paper addresses the enforcement of the epistemic property in a partially observed DES through supervisory control. Specifically, we propose a game-theoretic framework involving the observer/supervisor, the intruder, and the environment. A bipartite structure named all-protect structure is constructed as the game area, from which we solve the game and synthesize maximally permissive controllable and observable supervisors to enforce the epistemic properties.