Unraveling simplicity in elementary cellular automata

TL;DR

This paper systematically classifies elementary cellular automata based on their computational complexity, revealing that many are computationally simple, and introduces a method applicable to various natural systems.

Contribution

It provides the first formal classification of elementary cellular automata by computational complexity using communication complexity theory.

Findings

Many elementary cellular automata are computationally simple.

The classification method is generalizable to neural and gene regulatory networks.

First systematic complexity-based classification of cellular automata.

Abstract

We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the generality of communication complexity, the perspectives of our method include its application to other natural systems such as neural networks and gene regulatory networks.