Topological abstraction of higher-dimensional automata

TL;DR

This paper introduces a method for simplifying higher-dimensional automata through topological abstraction, preserving key properties like homotopy type and homology, facilitating more efficient analysis of concurrent systems.

Contribution

It defines topological abstraction for HDAs, establishing conditions for cube collapses that preserve essential topological and computational properties.

Findings

Topological abstraction preserves homotopy type, trace category, and homology graph.

Cube collapses can produce topological abstractions under certain conditions.

Method enables simplified yet equivalent models of concurrent systems.

Abstract

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 topological point of view. By definition, topological abstraction preserves the homotopy type, the trace category, and the homology graph of an HDA. We establish conditions under which cube collapses yield topological abstractions of HDAs.