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 certain operator ??. 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 {Kj} given by Kj+1 = ??(Kj), K0 = L. An effective computational algorithm is developed, and three examples are provided for illustration.