A supervisory controller controls and coordinates the behavior of different components of a complex machine by observing their discrete behaviour. Supervisory control theory studies automated synthesis of controller models, known as supervisors, based on formal models of the machine components and a formalization of the requirements. Subsequently, code generation can be used to implement this supervisor in software, on a PLC, or embedded microprocessor. In this article, we take a closer look at the control loop that couples the supervisory controller and the machine. We model both event-based and state-based observations using process algebra and bisimulation-based semantics. The main application area of supervisory control that we consider is coordination, referred to as supervisory coordination, and we give an academic and an industrial example, discussing the process-theoretic concepts employed

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edges to the Cartesian product G H such that a minimal dominating set D of size γ(G)γ(H) emerges. We hypothesize that D is also a minimum dominating set for the resulting graph and show that this implies Vizing's conjecture.

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Grabmayer and Fokkink recently presented a finite and complete axiomatization for 1-free process terms over the binary Kleene star under bismilarity equivalence (proceedings of LICS 2020, preprint available). A different and considerably simpler proof is detailed in this paper. This result, albeit still somewhat technical, only relies on induction and normal forms and is therefore also much closer to a potential rewriting algorithm. In addition, a complete verification in the Coq proof assistant of all results in this work is provided, but correctness does not depend upon any computer-assisted methodology.