Towards a homotopy theory of process algebra

Philippe Gaucher (1)

1 PPS - Preuves, Programmes et Systèmes

This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebra with any synchronization algebra using a notion of labelled flow. This interpretation of process algebra satisfies the paradigm of higher dimensional automata (HDA): one non-degenerate full n-dimensional cube (no more no less) in the underlying space of the time flow corresponding to the concurrent execution of n actions. This result will enable us in future papers to develop a homotopical approach of process algebras. Indeed, several homological constructions related to the causal structure of time flow are possible only in the framework of flows.

Mots clés: homotopy; model category; precubical set; concurrency; process algebra

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]

Philippe Gaucher. Towards a homotopy theory of process algebra. Homology, Homotopy and Applications, 2008, 10 (1), pp.353-388. ⟨hal-00338471⟩