Finite state supervisors in discrete event systems under partial observations

We consider a discrete event system under partial observations, and its behavior is described by a formal language. The concept of an augmented language of a control specification is very useful for design of a finite state supervisor. We study the relationship between the (M, Σ_c, L(G))-controllability of a control specification and the (M, Σ_c, Σ*)-controllability of its corresponding augmented language. And we derive necessary and sufficient conditions for the existence of finite state supervisors under partial observations using augmented languages. Moreover, we deal with the relationship between blocking and finiteness of supervisors