Abstract
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 μ-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 μ-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 μ-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 “conic”.
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Briand, X. Dynamic Control with Indistinguishable Events. Discrete Event Dyn Syst 16, 353–384 (2006). https://doi.org/10.1007/s10626-006-9327-x
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DOI: https://doi.org/10.1007/s10626-006-9327-x