We consider the problem of synthesizing controllers for dicrete event systems with indistinguishable events. The specification for the supervised system as well as the constraints for the controllers are defined by an extension of the logic of the 2-calculus that generalize the framework introduced by Ramadge and Wonham. More precisely, in order to express that some events are indistinguishable, one can specify with this extension that, from a node of a graph, two edges reach the same node. As for the 2-calculus, the model cheking problem and also the emptiness problem for this extension amount to computing winning strategies in parity games. We show that the centralized control problem with indistinguishable events is decidable by reducing it to the satisfiability problem of a formula of this extension of the 2-calculus. We prove also that, unfortunately, the decentralized control problem is undecidable by a reduction of the halting problem of a Turing machine. Moreover, we exhibit a decidable case of decentralized control by restricting the specifications to those which we called here Bconic^.
In this paper, we present extensions of the framework of the µ-calculus which allow us to handle in a very generic and extensible way many control problems. The fundamental new tool is a division operator, and two new modalities are given as examples which allow us to handle observability and distinguishability. Furthermore, all this gives rise to a method for the synthesis of controllers which is implemented in a tool presented here.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.