A Class of Zielonka Automata with a Decidable Controller Synthesis Problem
Hugo Gimbert · arXiv (Cornell University) · 2016
The decidability of the distributed version of the Ramadge and Wonham control problem (Ramadge and Wonham 1989), where both the plant and the controllers are modelled as Zielonka au-tomata (Zielonka 1987; Diekert and Rozenberg 1995) is a challenging open problem (Muscholl et al. 2008). There exists three classes of plants for which the existence of a correct controller has been shown decidable in the distributed setting: 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 generalize these three results by showing that a larger class of plants, called broadcast plants, has a decidable controller synthesis problem. We give new examples of plants for which controller synthesis is decidable.