On the homology language of HDA models of transition systems

TL;DR

This paper introduces a method to construct smaller, non-symmetric higher-dimensional automata (HDA) that preserve the homology language of transition systems with independence relations, reducing complexity while maintaining essential properties.

Contribution

It presents a novel approach to simplify HDA models by using acyclic relations to produce smaller automata with equivalent homology language, improving efficiency in modeling transition systems.

Findings

Smaller non-symmetric HDA can preserve the homology language of transition systems.

Acyclic relations can replace symmetric independence relations in HDA construction.

The method reduces automaton size without losing topological properties.

Abstract

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.