Procedures for calculating reversible one-dimensional cellular automata

Juan Carlos Seck Tuoh Mora,Sergio V Chapa Vergara,Genaro Juárez Martínez,Harold V Mcintosh

doi:10.1016/j.physd.2005.01.018

Abstract

We describe two algorithms for calculating reversible one-dimensional cellular automata of neighborhood size 2. We explain how this kind of automaton represents all the other cases. Using two basic properties of reversible automata such as uniform multiplicity of ancestors and Welch indices, these algorithms only require matrix products and transitive closures of binary relations to classify all the possible reversible automata of neighborhood size 2. We expose the features, advantages and differences with other well-known methods. Finally, we present results for reversible automata from three to six states and neighborhood size 2.

Highlights

One way of studying the behavior of a given system is understanding the local interactions of its parts
This paper presents the properties of these systems and proposes two original procedures for calculating and classifying all the possible reversible one-dimensional cellular automata of 3, 4, 5 and 6 states
Both process were implemented for calculating reversible one-dimensional cellular automata of 3, 4, 5 and 6 states; for the second and the fourth case there are two types of automata, one with a Welch index 1 and another with a Welch index 2

Summary

Introduction

One way of studying the behavior of a given system is understanding the local interactions of its parts. With very simple matrix operations (products and transitive closures) these algorithms detect the invertible behavior of reversible one-dimensional cellular automata. A sequence of states evolves in a single way, but it can be generated by one, many, or no ancestors.

Results

Conclusion