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.Comment: 33 pages ; LaTeX2e ; 1 eps figure ; package semantics included ; v2
HDA paradigm clearly stated and simplification in a homotopical argument ; v3
"bug" fixed in notion of non-twisted shell + several redactional improvements
; v4 minor correction : the set of labels must not be ordered ; published at
http://intlpress.com/HHA/v10/n1/a16