On the Computation of Supremal Sublanguages Relevant to Supervisory Control

Given a specification language, this paper discusses an iterative procedure for the computation of the supremal sublanguage, that possesses a conjunction of certain closed-loop properties, including controllability, normality and completeness. The iteration is stated in terms of (i) supremal sublanguage operators for each individual property, (ii) prefix-closures, and, (iii) language intersections. Within the iteration, the individual supremal sublanguage operators are only applied on prefix-closed languages, while the overall specification is not required to be prefix-closed. Our main result establishes finite convergence, provided that all parameters are regular.