A system model is developed where the criterion to partition the world into a system and a rest is based on the functional relation between its states. This approach implies that the gestalt of systems becomes very dynamic. Especially interactions between systems may create temporary super systems "on the fly". The reference to the function notion establishes the link to computation. Based on the distinction between the intended determinism versus nondeterminism of the interaction, two classes of system interactions are distinguished: composition and cooperation. Composition means that by interaction super systems are created and the interacting systems become subsystems. Cooperation means that systems sensibly interact loosely without creating any identifiable super system function and therefore without super system creation from the perspective of the interacting systems. Cooperative system interactions are described with the help of the protocol notion based on shared states, interpreted as the stateful exchange of characters via Shannon channels between roles - the projection of systems onto the interaction channels. It is shown that roles can be internally coordinated by a set of rules, leading to a very flexible process notion which unfolds its full potential only in a new type of execution environment capable of executing spontaneous transitions. The system model has immediate implications for componentization which can be viewed as an attempt to either hide functional recursion and provide only functionality whose composition behavior is easy to understand, or to provide loosely coupled interactions via protocols. To be complete, component models should therefore at least support three general classes of components: one for loose coupling, one for hierarchical composition, and one for pipes.
In his excellent book ''Principles of Cyber-Physical Systems'' @cite_33 Rajeev Alur distinguishes between functional and reactive components in the tradition of David Harel and Amir Pnueli.
@cite_33
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A cyber-physical system consists of a collection of computing devices communicating with one another and interacting with the physical world via sensors and actuators in a feedback loop. Increasingly, such systems are everywhere, from smart buildings to medical devices to automobiles. This textbook offers a rigorous and comprehensive introduction to the principles of design, specification, modeling, and analysis of cyber-physical systems. The book draws on a diverse set of subdisciplines, including model-based design, concurrency theory, distributed algorithms, formal methods of specification and verification, control theory, real-time systems, and hybrid systems, explaining the core ideas from each that are relevant to system design and analysis.The book explains how formal models provide mathematical abstractions to manage the complexity of a system design. It covers both synchronous and asynchronous models for concurrent computation, continuous-time models for dynamical systems, and hybrid systems for integrating discrete and continuous evolution. The role of correctness requirements in the design of reliable systems is illustrated with a range of specification formalisms and the associated techniques for formal verification. The topics include safety and liveness requirements, temporal logic, model checking, deductive verification, stability analysis of linear systems, and real-time scheduling algorithms. Principles of modeling, specification, and analysis are illustrated by constructing solutions to representative design problems from distributed algorithms, network protocols, control design, and robotics.This book provides the rapidly expanding field of cyber-physical systems wit