On the Control of Asynchronous Automata
Résumé
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 automata
and the controllers have causal memory
is 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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