ON THE SUPREMAL CONTROLLABLE SUBLANGUAGE OF A GIVEN LANGUAGE.

The concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes. In this paper the supremal controllable sublanguage S of a given language L is characterized as the largest fixpoint of a monotone operator OMEGA . In the case where the languages involved are regular it is shown that the fixpoint S can be computed as the limit of the (finite) sequence left brace K//j right brace given by K//j// plus //1 equals OMEGA (K//j), K//0 equals L. An effective computational algorithm is developed, and three examples are provided for illustration.