A Formula for the Supremal Controllable and Opaque Sublanguage Arising in Supervisory Control
Shigemasa Takai, Yusuke Oka · SICE Journal of Control Measurement and System Integration · 2008
In this paper, we study a property of opacity in the language-based framework of discrete event systems. The problem of synthesizing a supervisor that enforces opacity in a maximally permissive way is addressed. A maximally permissive opacity-enforcing supervisor is realized by an automaton that generates the supremal closed controllable and opaque sublanguage of the generated language of the system. This motivates the study on computability of the supremal sublanguage. We present a formula for computing the supremal sublanguage under some assumption on uncontrollable events. Whenever the languages under consideration are regular, the supremal sublanguage is effectively computed using the presented formula.