Composition, Cooperation, and Coordination of Computational Systems

In this paper I elaborated on the idea of David Harel and Amir Pnueli to distinguish systems according to their compositional behavior. The basic idea is to assume a functional relation between state functions as the system-constituting property, allowing to partition the world into a system and a rest. The obvious idea to base the composition of systems on the concept of computable functions and their compositional behavior leads to supersystem formation by composing simple and recursive systems. But this approach does not allow to account adequately for systems that interact with many other systems in a stateful and nondeterministic way which is why I introduce the concept of interactivity and cooperation. In order to describe interactive systems satisfactorily, a balance is needed between the representation of their relationship to all the other systems and what happens within the systems. I thus introduce the complementary descriptions of external interactions and internal coordination, both based on a role concept in the sense of a projection of a system onto its interactions. Beside the interesting distinction between composition, cooperation and coordination, the presented approach also fits well with other rather well known concepts. First the concept of components and interfaces. Components become systems with a well defined compositional behavior were the interface concept captures both, the transformational and the compositional behavior of a system in its interactions. Another tightly related concept is that of decisions and games. I introduce the concept of decisions as an additional internal input alphabet in order to determine nondeterministic interactions and thus fictitiously assume a system function where we actually do not have the knowledge to do so. Thus, the close relationship between protocols and games becomes obvious.