Cellular Automata and Discrete Complex Systems

Henryk Fukś ,Francis Kwaku Combert

doi:10.1007/978-3-319-92675-9

Abstract

Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications, finite-dimensional approximations have been proposed. The most commonly used one is known as the local structure theory, developed by H. Gutowitz et al. in 1987. In spite of the popularity of this approximation in CA research, examples of rigorous evaluations of its accuracy are lacking. In an attempt to fill this gap, we construct a local structure approximation for rule 14, and study its dynamics in a rigorous fashion, without relying on numerical experiments. We then compare the outcome with known exact results.

Highlights

Hadn’t this question already been answered? We all know about computation-universal Turing Machines
A lot of information has been unearthed in the last two decades about algebraic aspects of these machines, but relatively little is known about their automata-theoretic properties and the numerous computational problems associated with them
It is quite difficult to pin down the computational complexity of the orbits of maps defined by invertible transducers

Summary

Introduction

Hadn’t this question already been answered? We all know about computation-universal Turing Machines. 22nd IFIP WG 1.5 International Workshop, AUTOMATA 2016 Zurich, Switzerland, June 15–17, 2016 Editors Matthew Cook University of Zurich Zurich Switzerland

Results

Conclusion