Synchrony vs. Causality in Asynchronous Petri Nets

TL;DR

This paper investigates whether synchronous systems can be implemented asynchronously without altering their behavior, demonstrating through counterexamples that such an implementation often requires infinite resources or changes in causality.

Contribution

It provides a formal analysis showing the limitations of asynchronous implementation of synchronous systems and highlights the necessity of altering causal structures or accepting infinite implementations.

Findings

Synchronous systems cannot always be implemented asynchronously without modifications.

Counterexamples demonstrate the need for infinite resources or causal changes.

Asynchronous implementations may alter system behavior or require infinite steps.

Abstract

Given a synchronous system, we study the question whether the behaviour of that system can be exhibited by a (non-trivially) distributed and hence asynchronous implementation. In this paper we show, by counterexample, that synchronous systems cannot in general be implemented in an asynchronous fashion without either introducing an infinite implementation or changing the causal structure of the system behaviour.