On the Control of Asynchronous Automata

The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem [12], where both the plant and the controllers are modelled as Zielonka automata [13,1] and the controllers have causal memory is a challenging open problem [8,9]. There exists 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 provide a unified proof of these three results, and design a class of plants, called broadcast games, with a decidable controller synthesis problem. This leads to new examples of decidable architectures.