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 noncanonical 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1330
 Bibcode:
 2007arXiv0711.1330G
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 55U35;
 18G55;
 68Q85
 EPrint:
 23 pages, 1 figure, LaTeX2e