On maximal permissiveness in partially-observed discrete event systems: Verification and synthesis

The notion of maximal permissiveness plays an important role in synthesis problems in the supervisory control framework. It is well known that the supervisor synthesis problem has a unique supremal solution when all the events are observable. However, under the partial observation setting, no supremal solution exists in general and there may exist several locally maximal solutions. In this paper, we tackle the supervisory control problem under partial observation from a new angle. First, we propose an approach to verify whether a given supervisor is maximal or not. If a supervisor is not maximal, then we provide an algorithm that synthesizes a new supervisor that is strictly more permissive than the given one. To the best of our knowledge, both the verification of maximality and the synthesis of a larger solution were previously open problems; our algorithms are the first ones of their kind.