  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.
