A sequential solution to the density classification task using an intermediate alphabet

TL;DR

This paper introduces a sequential cellular automaton with an intermediate alphabet that effectively solves the density classification task, converging to a fixed point without residual auxiliary data, and extends to higher dimensions and larger alphabets.

Contribution

It presents a novel sequential cellular automaton approach utilizing an intermediate alphabet for the density classification task, applicable to arbitrary finite alphabets and higher-dimensional configurations.

Findings

Converges to a fixed point with no auxiliary information

Applicable to arbitrary finite alphabets

Extensible to higher-dimensional configurations

Abstract

We present a sequential cellular automaton of radius 2 1 as a solution to the density classification task that makes use of an intermediate alphabet, and converges to a clean fixed point with no remaining auxiliary or intermediate information. We extend this solution to arbitrary finite alphabets and to configurations in higher dimensions.