Reaction and Control I. Mixing Additive and Multiplicative Network Algebras

This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding Multi-Agent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomial-like calculus for representing flowgraphs and their behaviours. An ‘additive’ interpretation of the calculus was intensively developed to study control flowcharts and finite automata. For instance, regular algebra and iteration theories are included in a unified presentation. On the other hand, a ‘multiplicative’ interpretation of the calculus of flownomials was developed to study dataflow networks. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras will contribute to the understanding of distributed computation. The rôle of this first paper is to present a few motivating examples1.