The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem,where both the plant and the controllers are modeled as asynchronous automataand the controllers have causal memoryis a challenging open problem.There exist three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when the dependency graph of actions is series-parallel, when the processes are connectedly communicating and when the dependency graph of processes is a tree. We design a class of plants, called decomposable games, with a decidable controller synthesis problem.This provides a unified proof of the three existing decidability results as well as new examples of decidable plants.
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