Combinatorics of labelling in higher-dimensional automata

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 ncube, 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 nonfunctorial 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...

• Type: Journal
• Year: 2010
• Where: TCS
• Authors: Philippe Gaucher
• Keywords: Labelled Coskeleton, Labelled Coskeleton Functor, Precubical Set, TCS 2010, Theoretical Computer Science