preprint : Towards an homotopy theory of process algebra

[Philippe Gaucher <gaucher@pps.jussieu.fr>]

Author : Philippe Gaucher

Title : Towards an homotopy theory of process algebra

Abstract : 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: 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 an 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.

URL : my web page or arxiv math.AT/0701552.