A note on deciding the controllability of a language K with respect to a language L

It has been shown by P.J. Ramadge and W.M. Wonham (1987) if G is a plant automaton and K contained in L(G) is a prefix-closed language, there exists a supervisor Theta that is complete with respect to G so that L( Theta /G)=K intersection L(G)=K if and only if K is controllable with respect to the plant language L(D). It is shown that if L(G) and K are represented as free-labeled Petri nets, then the controllability of K with respect to L(G) is detectable. This result is a direct consequence of the decidability of the Petri net and reachability problem. In effect, a modeling framework capable of finitely representing a class of infinite-state systems is identified, and controllability is decidable within this framework.<
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