Preprint: Homotopical equivalence of combinatorial and categorical semantics of process algebra

Preprint: Homotopical equivalence of combinatorial and categorical semantics of process algebra

[Gaucher Philippe]

Dear All,

Here is a new preprint. Sincerely yours. pg.

Author: P. Gaucher

Title:
Homotopical equivalence of combinatorial and categorical semantics of process
algebra

Abstract:
It is possible to translate a modified version of K. Worytkiewicz's
combinatorial semantics of CCS (Milner's Calculus of Communicating Systems)
in terms of labelled precubical sets into a categorical semantics of CCS in
terms of labelled flows using a geometric realization functor. It turns out
that a satisfactory semantics in terms of flows requires to work directly in
their homotopy category since such a semantics requires non-canonical choices
for constructing cofibrant replacements, homotopy limits and homotopy
colimits. No geometric information is lost since two precubical sets are
isomorphic if and only if the associated flows are weakly equivalent. The
interest of the categorical semantics is that combinatorics totally
disappears.  Last but not least, a part of the categorical semantics of CCS
goes down to a pure homotopical semantics of CCS using A. Heller's privileged
weak limits and colimits. These results can be easily adapted to any other
process algebra for any synchronization algebra.

URL:
http://www.pps.jussieu.fr/~gaucher/cubeflow.pdf
http://www.pps.jussieu.fr/~gaucher/cubeflow.ps

Comments: 23 pages