Supremal and maximal sublanguages arising in supervisor synthesis problems with partial observations

Abstract

The paper studies in a unified manner both the class of closed, (Σu,N)-invariant, and (M, N)-recognizable sublanguages and the class of closed, (Σu,N)-invariant, and (M, Σc,N)-controllable sublanguages of a given languageL that arise in supervisor synthesis problems of discrete event dynamical systems with partial observations. The supremal element of the former class is often too restrictive, and it is natural to study maximal elements of the latter class. A procedure which computes such a maximal element as a limit of a decreasing sequence of sublanguages ofL is presented. Each term of the sequence is shown to be regular if a slightly modified procedure is used.