Bulking II: Classifications of Cellular Automata

TL;DR

This paper introduces three notions of simulation for cellular automata, analyzes the resulting quasi-order structures, and provides tools for classifying cellular automata based on their space-time diagram rescaling behaviors.

Contribution

It presents new simulation notions and studies the quasi-order structures they induce, advancing the classification framework for cellular automata.

Findings

Defined three new simulation notions for cellular automata

Analyzed the quasi-order structures and their properties

Provided formal tools for cellular automata classification

Abstract

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools allowing to classify cellular automata.