Automata and automatic sequences

TL;DR

This paper explores infinite sequences over finite alphabets generated by finite automata, discussing their properties and classifications across seven structured, self-contained sections.

Contribution

It provides a comprehensive, structured analysis of automata-generated sequences, offering new insights into their classifications and properties.

Findings

Automata can generate a wide variety of infinite sequences.

Classification schemes for automata-generated sequences are developed.

The paper consolidates existing knowledge with new perspectives on sequence properties.

Abstract

In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless to say, we feel that the order we propose is the most natural one. References appear at the end of each one of the parts which implies some redundancy. Extra references are listed at the very end of our paper.