On the controller synthesis problem for distributed systems with causal memory
Résumé
The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem
where both the plant and the controllers are modelled as Zielonka automata
and the controllers have causal memory
is a challenging open problem.
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.
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