From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4435 Path: news.gmane.org!not-for-mail From: Gaucher Philippe Newsgroups: gmane.science.mathematics.categories Subject: Preprint : Combinatorics of labelling in higher dimensional automata Date: Tue, 1 Jul 2008 14:49:24 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019945 13290 80.91.229.2 (29 Apr 2009 15:45:45 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:45 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jul 1 12:35:00 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jul 2008 12:35:00 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KDhpJ-0002Hs-HP for categories-list@mta.ca; Tue, 01 Jul 2008 12:31:29 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 2 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:4435 Archived-At: Dear all, Here is a new preprint. Sincerely yours, pg. Title: Combinatorics of labelling in higher dimensional automata Abstract: The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled n-cube, in exactly one way. The main ingredient is the non-functorial construction called labelled directed coskeleton. It is defined as a subobject of the labelled coskeleton, the latter coinciding in the unlabelled case with the right adjoint to the truncation functor. This non-functorial construction is necessary since the labelled coskeleton functor of the category of labelled precubical sets does not fulfil the above requirement. We prove in this paper that it is possible to force the labelled coskeleton functor to be well-behaved by working with labelled transverse symmetric precubical sets. Moreover, we prove that this solution is the only one. A transverse symmetric precubical set is a precubical set equipped with symmetry maps and with a new kind of degeneracy map called transverse degeneracy. Finally, we also prove that the two settings are equivalent from a directed algebraic topological viewpoint. To illustrate, a new semantics of CCS, equivalent to the old one, is given. Url: http://www.pps.jussieu.fr/~gaucher/symcub.ps http://www.pps.jussieu.fr/~gaucher/symcub.pdf Comments: 40 pages, comments welcome