Automatic Sequences
Theory, Applications, Generalizations

This book is the first integrated treatment of sequences generated by finite automata and their generalizations.

Jean-Paul Allouche (Author), Jeffrey Shallit (Author)

9780521823326, Cambridge University Press

Hardback, published 21 July 2003

588 pages, 170 b/w illus. 548 exercises
26.6 x 17.9 x 3.8 cm, 1.157 kg

'Allouche and Shallit's books presents an introduction to the fascinating subject of automatic sequences. This is the first book that systematically develops the theory of these sequences.' Zentralblatt MATH

Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

Preface
1. Stringology
2. Number theory and algebra
3. Numeration systems
4. Finite automata and other models of computation
5. Automatic sequences
6. Uniform morphisms and automatic sequences
7. Morphic sequences
8. Frequency of letters
9. Characteristic words
10. Subwords
11. Cobham's theorem
12. Formal power series
13. Automatic real numbers
14. Multidimensional automatic sequences
15. Automaticity
16. k-regular sequences
17. Physics
Appendix. Hints, references and solutions for selected exercises
Bibliography
Index.

Subject Areas: Mathematical theory of computation [UYA], Number theory [PBH]