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A Note on the Properties of the Supremal Controllable Sublanguage in Pushdown Systems

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1 Author(s)
Griffin, C. ; Oak Ridge Nat. Lab., Oak Ridge

Consider an event alphabet Sigma. The supervisory control theory of Ramadge and Wonham asks the question: given a plant model G with language LM (G) sube Sigma* and another language K sube LM (G), is there a supervisor phi such that LM (phi/G) = K? Ramadge and Wonham showed that a necessary condition for this to be true is the so-called controllability of K with respect to LM (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 supremal controllable sublanguage supC (K) sube K that is effectively constructable from generators of K and G. In this paper, we show: 1) there is an algorithm to compute the supremal controllable sublanguage of a prefix closed K accepted by a deterministic pushdown automaton (DPDA) when the plant language is also prefix closed and accepted by a finite state automaton and 2) in this case, we show that this supremal controllable sublanguage is also accepted by a DPDA.

Published in:

Automatic Control, IEEE Transactions on  (Volume:53 ,  Issue: 3 )