# Span(Graph): A categorical algebra of transition systems

## Abstract

We have shown that a natural algebraic structure on **Span(Graph)** allows the compositional specification of concurrent systems. Hoare's parallel operation appears as a derived operation in this algebra. The simpler basic operations of our algebra are possible because we do not insist on interleaving semantics: interleaving prevents consideration of the identity span, as well as other natural constants such as the diagonal. We have given some examples of transforming systems using the equations of the algebra. Associated to the algebra there is a geometry which expresses the distributed nature of a concurrent system. This relation between algebra and geometry makes precise the relation between process algebras and circuit diagrams as used, for example, in Ebergen [E87].

## Keywords

Label Transition System Process Algebra Concurrent System Initial Vertex Distributive Category## Preview

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