Self-Assembly as Graph Grammar as Distributed System

TL;DR

This paper explores the connection between graph grammars used in self-assembly and distributed systems, providing new theoretical insights and methods for simulation of distributed computing models using self-assembly systems.

Contribution

It establishes a duality between graph grammars for self-assembly and graph rewriting in distributed systems, and introduces a method to simulate distributed models with self-assembly.

Findings

Proves a generalized version of Soloveichik and Winfree's theorem on local determinism.

Presents a canonical simulation method for distributed computing models using self-assembly.

Highlights the duality between graph grammars and graph rewriting in distributed systems.

Abstract

In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. It turns out that these graph grammars are a "dual notion" of a graph rewriting characterization of distributed systems that was proposed by Degano and Montanari over twenty years ago. By applying techniques obtained from this observation, we prove a generalized version of Soloveichik and Winfree's theorem on local determinism, and we also present a canonical method to simulate asynchronous constant-size-message-passing models of distributed computing with systems of self-assembly.