Cellular Automata as Generators of Interleaving Sequences

TL;DR

This paper explores how one-dimensional cellular automata can be used to generate interleaving sequences, bridging a gap between cellular automata sequence generation and interleaving sequence theory.

Contribution

It introduces two families of cellular automata specifically designed to generate interleaving sequences, expanding the understanding of cellular automata applications.

Findings

Demonstrates cellular automata can generate interleaving sequences

Provides two new families of automata for this purpose

Bridges a gap between sequence generation and interleaving theory

Abstract

An interleaving sequence is obtained by combining or intertwining elements from two or more sequences. On the other hand, cellular automata are known to be generators for keystream sequences. In this paper we present two families of one-dimensional cellular automata as generators of interleaving sequences. This study aims to close a notable gap within the current body of literature by exploring the capacity of cellular automata to generate interleaving sequences. While previous works have separately examined cellular automata as sequence generators and interleaving sequences, there exists limited literature interconnecting these two topics. Our study seeks to bridge this gap, providing perspectives on the generation of interleaving sequences through the utilisation of cellular automata, thereby fostering a deeper understanding of both disciplines.