A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.
- ORNL
Consider an event alphabet $$\Sigma$$. The Supervisory Control Theory of Ramadge and Wonham asks the question, given a plant model $$G$$ with language $$\LanM(G) \subseteq \Sigma^{*}$$ and another language $$K \subseteq \LanM(G)$$, is there a supervisor $$\varphi$$ such that $$\LanM(\varphi/G)=K$$? Ramadge and Wonham showed that a necessary condition for this to be true is the so called \textit{controllability} of $$K$$ with respect to $$\LanM(G)$$. They showed that when $$G$$ is a finite state automaton and $$K$$ is a regular language (also generated by a finite state automaton), then there is a regular \textit{supremal controllable sublanguage} $$\supC(K) \subseteq K$ that is is effectively constructable from generators of $$K$$ and $$G$$. In this paper, we show: (i) There is an algorithm to compute the supremal controllable sublanguage of a prefix closed $$K$$ accepted by a deterministic pushdown automaton when the plant language is also prefix closed and accepted by a finite state automaton. (ii) In this case, we show this supremal controllable sublanguage is also accepted by a DPDA.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- ORNL other overhead
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 939933
- Journal Information:
- IEEE Transactions on Automatic Control, Vol. 53, Issue 3
- Country of Publication:
- United States
- Language:
- English
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