What are the fundamental structures of concurrency? We still don't know!

TL;DR

This paper explores the foundational structures of concurrency, highlighting the lack of a unifying fundamental theory and examining insights from process algebra, Petri Nets, physics, and geometry.

Contribution

It critically analyzes current approaches and seeks to identify core principles underlying concurrency, proposing new directions for foundational research.

Findings

Limited understanding of concurrency's fundamental structures

Insights from Petri Nets, physics, and geometry offer potential avenues

Current theories lack a unifying fundamental framework

Abstract

Process algebra has been successful in many ways; but we don't yet see the lineaments of a fundamental theory. Some fleeting glimpses are sought from Petri Nets, physics and geometry.