Open Systems in Reactive Environments: Control and Synthesis

We study the problems of synthesizing open systems as well as controllers for them. The key aspect of our model is that it caters to reactive environments, which can disable different sets of responses when reacting with the system. We deal with specifications given as formulas in CTL* and its sub-logic CTL. We show that both these problems, with specifications in CTL (CTL*), are 2EXPTIME-complete (resp. 3EXPTIME-complete). Thus, in a sense, reactive environments constitute a provably harder setting for the synthesis of open systems and controllers for them.