Homology and Bisimulation of Asynchronous Transition Systems and Petri Nets

TL;DR

This paper introduces homology groups for asynchronous transition systems and Petri nets, demonstrating their invariance under bisimulation and providing a method to construct Petri nets with specified homology groups.

Contribution

It establishes a novel homology theory for asynchronous systems and Petri nets, linking homology groups to bisimulation equivalence and construction methods.

Findings

Homology groups are computable for labelled asynchronous transition systems and Petri nets.

Bisimulation equivalent systems have isomorphic homology groups.

A method to construct Petri nets with prescribed homology groups is developed.

Abstract

Homology groups of labelled asynchronous transition systems and Petri nets are introduced. Examples of computing the homology groups are given. It is proved that if labelled asynchronous transition systems are bisimulation equivalent, then they have isomorphic homology groups. A method of constructing a Petri net with given homology groups is found.