Compositional construction of most general controllers

Given a system $${\fancyscript{A}}$$A and an objective $$\varPhi $$Φ, the task of controller synthesis is to design a decision making policy that ensures $$\varPhi $$Φ to be satisfied. This article deals with transition system-like system models and controllers that base their decisions on the observables of the actions performed so far. We present a framework for the compositional construction of controllers for conjunctive sequences of linear-time objectives in an online manner. For this approach, it is crucial that the controllers enforce the objectives in a most general manner, being as permissive as possible. We then present game-based algorithms for the construction of such most general controllers for invariance, reachability and $$\omega $$ω-regular objectives.

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