Traced communication complexity of cellular automata

TL;DR

This paper introduces a new communication complexity framework for cellular automata, analyzing how minimal communication enables players to predict the evolution of the central cell, linking it to classical dynamical properties.

Contribution

It defines a novel communication complexity problem for cellular automata and computes the asymptotic complexity for most elementary cases, connecting it to dynamical concepts.

Findings

Asymptotic communication complexity characterized for elementary cellular automata

Links established between communication complexity and dynamical properties like entropy

Most elementary cellular automata have explicitly determined communication complexity

Abstract

We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by communicating as little as possible between each other. We present some links with classical dynamical concepts, especially equicontinuity, expansiveness, entropy and give the asymptotic communication complexity of most elementary cellular automata.