Preprint : Combinatorics of labelling in higher dimensional automata

Preprint : Combinatorics of labelling in higher dimensional automata

[Gaucher Philippe]

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