On the composition of processes

We describe a model of net-connected processes that amounts to a reformulation of a model derived by Brock and Ackerman from the Kahn-McQueen model of processes as relations on streams of data. The reformulation leads directly to a straightforward definition of process composition. Our notion of processes and their composition constitutes a natural generalization of the notion of functions and their composition. We apply this definition of process composition to the development of an algebra of processes, which we propose as supplying a formal semantics for a language whose domain of discourse includes nets of interconnected processes. This in turn leads us to logics of such nets, about which we raise three open and fundamental problems: existence of a finite basis for the operations of the language, finite axiomatizability of the equational theory, and decidability of this theory. A natural generalization of the model deals with the time complexity of computations.

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