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 $\{ {K_j } \}$ given by $K_{j + 1} = \Omega (K_j )$, $K_0 = L$. An effective computational algorithm is developed, and three examples are provided for illustration.