A Compact and Uniform Approach for Synthesizing State-Based Property-Enforcing Supervisors for Discrete-Event Systems

In this article, we are interested in the problem of synthesizing a partial observation supervisor for a discrete-event system such that it enforces a desired property. We introduce a compact and uniform approach to the problem of synthesizing state-based property-enforcing supervisors. A state-based property is a property that only depends on the current estimate of the past behavior of the system and does not depend on its future behavior. Previous work has introduced a uniform methodology to solve this problem through the construction of a finite structure called the all enforcement structure (AES), which captures a game between the supervisor and the environment. Although the AES is a powerful structure that includes all possible property-enforcing supervisors, its construction is computationally challenging since the number of states grows exponentially in the number of states and the number of events of the system. Our contribution is the definition of a compact AES that is equivalent to but computationally more efficient than the original AES. Specifically, the compact AES enjoys the same properties as the original AES with respect to synthesizing maximally permissive supervisors under the assumption of incomparable sets of controllable and observable events. We also provide experimental results to show the benefits of the compact AES over the original AES.