A total ordering on languages with a bipartite alphabet

We consider the Ramadge-Wonham framework for discrete event (dynamical) systems. Therein arise situations when the supervisory marking problem or the supervisory control problem is not solvable and hence, a unique minimally restrictive language does not exist. In such cases, a basis is needed for language comparison to select an appropriate alternative. We consider the case of prefix-closed regular languages containing “illegal” strings. Languages are naturally partially ordered by inclusion. The aim here is to define a measure for these languages based upon the nature of “illegal:” strings they contain. The measure should impose a total ordering on such languages and thus enable selection of better controllers