A necessary and sufficient condition for the existence of finite state supervisors in discrete-event systems

A supervisor realized by finite automaton is called a finite state supervisor. It is clear that a finite state supervisor exists for every regular controllable language. However, an example of a finite state supervisor for a nonregular one has been reported. A necessary and sufficient condition is proved here, for the existence of a finite state supervisor, and an example of a simple manufacturing system that has a finite state supervisor for a nonregular controllable language is given