The homology graph of a higher dimensional automaton

TL;DR

This paper introduces the homology graph of higher dimensional automata, a directed graph capturing homology classes, and proves its invariance under certain homeomorphic transformations, aiding in the analysis of concurrent systems.

Contribution

It defines the homology graph for HDAs and demonstrates its invariance under homeomorphic abstractions, providing a new tool for analyzing concurrent systems.

Findings

Homology graph is well-defined for higher dimensional automata.

Homology graph remains invariant under homeomorphic abstractions.

Provides a new topological invariant for concurrent system models.

Abstract

Higher dimensional automata, i.e. labelled precubical sets, model concurrent systems. We introduce the homology graph of an HDA, which is a directed graph whose nodes are the homology classes of the HDA. We show that the homology graph is invariant under homeomorphic abstraction, i.e. under weak morphisms that are homeomorphisms.