Automata theory lies at the foundation of computer science, and is vital to a theoretical understanding of how computers work and what constitutes formal methods. This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways. The first part of the book is organised around notions of rationality and recognisability. The second part deals with relations between words realised by finite automata, which not only exemplifies the automata theory but also illustrates the variety of its methods and its fields of application. Many exercises are included, ranging from those that test the reader, to those that are technical results, to those that extend ideas presented in the text. Solutions or answers to many of these are included in the book.

• Goes beyond the elementary results presented in other books on the subject • Provides full proofs for all required elementary results in linear algebra • Contains over 500 exercises and solutions

### Contents

Foreword; 0. Fundamental structures; 1. The simplest possible machine; 2. The power of algebra; 3. The pertinence of enumeration; 4. The richness of transducers; 5. The simplicity of functional transducers; Bibliography; Index.

### Review

'… a rich exposition … expertly translated by Reuben Thomas … its motivating ideas and substantive cross-currents fill almost every page … Nothing seems to be missing … should be on the shelf of every serious student and professional. It will enjoy a very long stay on my own.' Computing Reviews