Synchronous Machines: a Traced Category

Synchronous programming languages have been extensively used in the area of critical embedded systems. Synchronous machines, a specific class of labelled transition systems, are often used to give denotational semantics of these languages. In this work, we study the categorical structure of the aforementioned machines. We first show that the category S of synchronous machines can be given a traced symmetric monoidal structure with diagonals. Then, we apply a standard variant of the Int construction to S and relate the composition in the resulting category with the synchronous product, the operation used to model parallel composition of synchronous programs. We also show how properties of synchronous machines like determinism and reactivity relate to the way they compose with diagonal morphisms of S.