Labeled homology of higher-dimensional automata

We construct labeling homomorphisms on the cubical homology of higher-dimensional automata and show that they are natural with respect to cubical dimaps and compatible with the tensor product of HDAs. We also indicate two possible applications of labeled homology in concurrency theory.info:eu-repo/semantics/publishedVersio

On the homology language of HDA models of transition systems

Given a transition system with an independence relation on the alphabet of labels, one can associate with it a usually very large symmetric higher-dimensional automaton. The purpose of this paper is to show that by choosing an acyclic relation whose symmetric closure is the given independence relation, it is possible to construct a much smaller nonsymmetric HDA with the same homology language.Comment: 17 page

Weak equivalence of higher-dimensional automata

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes

Weak equivalence of higher-dimensional automata

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes.This research was partially supported by FCT (Fundacao para a Ciencia e a Tecnologia, Portugal) through project UID/MAT/00013/2013

Homology and cohomology of cubical sets with coefficients in systems of objects

This paper continues the research of the author on the homology of cubical and semi-cubical sets with coefficients in systems. The main result is the theorem that the homology of cubical sets with coefficients in contravariant systems in an Abelian category with exact coproducts is isomorphic to the left satellites of a colimit functor. It allowed proving a number of new assertions presented in this paper about homology and cohomology of cubical sets with coefficients in systems, including homology and cohomology with coefficients in local systems.Comment: 62 page