Abstract
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.