Determining a regular language by glider-based structures called phases fi_1 in Rule 110

TL;DR

This paper introduces a method to encode initial conditions of Rule 110 cellular automaton using regular expressions derived from de Bruijn diagrams and tiles, focusing on glider phases for understanding its computational complexity.

Contribution

It presents a novel approach to represent and analyze Rule 110's initial states through regular expressions based on glider phases, aiding in the study of its computational universality.

Findings

Regular expressions effectively encode initial conditions.

De Bruijn diagrams and tiles identify glider phases.

The method enhances understanding of Rule 110's dynamics.

Abstract

Rule 110 is a complex elementary cellular automaton able of supporting universal computation and complicated collision-based reactions between gliders. We propose a representation for coding initial conditions by means of a finite subset of regular expressions. The sequences are extracted both from de Bruijn diagrams and tiles specifying a set of phases fi_1 for each glider in Rule 110. The subset of regular expressions is explained in detail.