Mathematics – Algebraic Topology
Scientific paper
2008-08-12
Theoretical Computer Science vol 411 (11-13), pp 1452-1483, 2010
Mathematics
Algebraic Topology
47 pages, LaTeX2e, no figures
Scientific paper
10.1016/j.tcs.2009.11.013
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.
No associations
LandOfFree
Combinatorics of labelling in higher dimensional automata does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Combinatorics of labelling in higher dimensional automata, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Combinatorics of labelling in higher dimensional automata will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-202949