A Linear Acceleration Theorem for 2D Cellular Automata on all Complete Neighborhoods

TL;DR

This paper introduces a general linear acceleration technique applicable to all two-dimensional cellular automata operating on complete neighborhoods, broadening the scope of acceleration results beyond specific cases.

Contribution

It provides the first universal linear acceleration method for 2D cellular automata on all complete neighborhoods, filling a significant gap in the theoretical understanding.

Findings

Established a general linear acceleration technique for 2D cellular automata.

Applied the method to all languages recognized by automata on complete neighborhoods.

Extended the scope of acceleration theorems to broader classes of cellular automata.

Abstract

Linear acceleration theorems are known for most computational models. Although such results have been proved for two-dimensional cellular automata working on specific neighborhoods, no general construction was known. We present here a technique of linear acceleration for all two-dimensional languages recognized by cellular automata working on complete neighborhoods.