The Cubical Homology of Trace Monoids

TL;DR

This paper explores the cubical homology of trace monoids, linking algebraic topology with computer science, and provides algorithms for computing homology groups of various asynchronous systems.

Contribution

It introduces a novel connection between cubical homology of generalized tori and partial trace monoid actions, along with algorithms for practical computation.

Findings

Established the relationship between cubical homology groups and monoid actions.

Developed algorithms for computing homology of asynchronous systems.

Applied methods to Petri nets and Mazurkiewicz trace languages.

Abstract

This article contains an overview of the results of the author in a field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid actions is described. Algorithms for computing the homology groups of asynchronous systems, Petri nets, and Mazurkiewicz trace languages are shown.