Preprints
Warning: the ArXiv version of these preprints may
differ from the versions of this page. Only this page contains the
most up-to-date version.
Philippe Gaucher. Homotopical equivalence of combinatorial and categorical semantics of process
algebra (PS,PDF), ArXiv
(UNDER REVISION with a future improved redaction: this version is
correct as far as I know).
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.
Philippe Gaucher. T-homotopy
and
refinement of observation (V) : Strom model structure for branching and
merging homologies (PS,PDF), ArXiv.
(We check that there exists a model
structure on
the
category of
flows whose weak equivalences are the S-homotopy equivalences. As an
application, we prove that the generalized T-homotopy equivalences
preserve the branching and merging homology theories of a flow. The
method of proof is completely different from the one of the third part
of this series of papers). UNDER REVISION. The main result (the
Cole-Strom model structure) is correct, not the link with the
application: Theorem 8.17 is false. The revised paper will provide a
new application which
will be used in a future paper. The title will be also changed.
Chapter of a book
Philippe Gaucher. Abstract
homotopical methods for theoretical computer science (PS,PDF), ArXiv.
The purpose of this paper is to collect the
homotopical methods used in the development of the theory of flows
initialized by author's paper ``A model category for the homotopy
theory of concurrency''. It is presented generalizations of the
classical Whitehead theorem inverting weak homotopy equivalences
between CW-complexes using weak factorization systems. It is also
presented methods of calculation of homotopy limits and homotopy
colimits using Quillen adjunctions and Reedy categories.
Non-publié/Unpublished
Philippe Gaucher. Déformation
des Flots de Chemins Continus : Théorie et
Applications (PS,PDF).
Mémoire d'habilitation. 2001. And the associated research
program (PS,PDF).
My habilitation thesis, in French. A survey of my
research
activities. But it's getting old.
Philippe Gaucher.
Closed symmetric monoidal
structure and flow (PS,PDF),
ArXiv.
The category of flows is not cartesian closed. We
construct a
closed symmetric monoidal structure which has moreover a satisfactory
behavior from the computer scientific viewpoint.
Philippe Gaucher. Timed
Event Structure and
Confidentiality by
Causality (PS).
The first attempt to write something about
causality using a modified version of the notion of event structure
using a timed version of event structures.
Philippe
Gaucher. Entrée et
sortie d'automates en
algèbre homologique 1997 (PS)
(French).
I
am trying to model the notion of flow of information using homological
algebra (French). Very old write-up.
Philippe Gaucher. étude
homologique
des chemins de
dimension 1 dans un automate (French). 1997 (PS)
(French).
I am trying to model the
notion of $1$-dimensional execution path (so without concurrency at
all) using homological algebra (French). Very old write-up.