# Labeled homology of higher-dimensional automata

## TL;DR

This paper introduces labeled homology for higher-dimensional automata, providing a new algebraic tool that respects automata transformations and has potential applications in concurrency theory.

## Contribution

It constructs labeling homomorphisms on cubical homology of HDAs, demonstrating their naturality and compatibility, and suggests applications in concurrency analysis.

## Key findings

- Labeled homology is compatible with cubical dimaps.
- Homology respects tensor product of HDAs.
- Potential applications in concurrency theory.

## Abstract

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.