Homology of spaces of directed paths in Euclidean pattern spaces

TL;DR

This paper investigates the topological structure of the space of directed paths in Euclidean pattern spaces, providing insights into concurrency models and their homological properties.

Contribution

It computes the homology of trace spaces in PV-programs with instantaneous resource access and release, advancing understanding of their topological features.

Findings

Homology of trace spaces can be explicitly computed for certain PV-programs.

Provides a topological framework for analyzing concurrency in parallel computations.

Enhances the mathematical understanding of Euclidean pattern spaces in concurrency theory.

Abstract

The paper addresses certain topological aspects of Dijkstra's PV-model for parallel computations in concurrency theory. The main result is a computation of the homology of the trace space associated with PV-programs in which access and release of every resource happen without time delay.