Supervisory control and the gateway problem

The underlying model for a discrete event system is taken to be a finite graph (finite state system) with edges labeled by external or internal events and nodes labeled by attributes that facilitate useful definitions of process operators. An attributed finite transition system is a quadruple of the (finite) set of states of a finite external event alphabet set, the transition relation and a function that maps the set of states into the state attribute set. The author discusses control and languages relating to this model, and presents theorems relating thereto