Abstract
Reactive synthesis (RS) and supervisory control theory (SCT) both provide a design methodology for digital systems. RS takes a computer science perspective and seeks to synthesise a system that interacts with its environment in computation cycles and which, doing so, satisfies a prescribed specification. SCT takes a control theoretic perspective and seeks to synthesise a controller that - in closed-loop configuration with a plant - enforces a prescribed specification, where all dynamics are driven by discrete events. While both synthesis techniques seem superficially very similar, their technical details differ significantly. We provide a formal comparison allowing us to identify conditions under which one can solve one synthesis problem via the other one and we discuss how the resulting solutions compare. To facilitate this comparison, we give a unified introduction to RS and SCT and derive formal problem statements and a characterisation of their solutions in terms of ω-languages. As recent contributions to the two fields focus on different aspects of the respective problem, our translational theorems can be used to guide the application of algorithmic techniques from one field in the other.
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