Topological abstraction of higher-dimensional automata

Higher-dimensional automata constitute a very expressive model for concurrent systems. In this paper, we discuss " topological abstraction " of higher-dimensional automata, i.e., the replacement of HDAs by smaller ones that can be considered equivalent from both a computer scientific and a topo-logical point of view. By definition, topological abstraction preserves the ho-motopy type, the trace category, and the homology graph of an HDA. We establish conditions under which cube collapses yield topological abstractions of HDAs.