Automatic Sequences
Automatic Sequences
$117.00
USDUniting 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.
- Unites, using a consistent notation, dozens of open problems for further research
- Many results appear in English for the first time
- Contains hundreds of exercises and dozens of open problems for further research
Reviews & endorsements
"[A] fine book...I highly recommend Automatic Sequences, whether as text, reference, or all the more as an excellent read, both to rank beginners and to those already acquainted with parts of the subject."
Alf van der Poorten, Centre for Number Theory Research, Mathematics of Computation
"Every serious sequence lover will want to own a copy!"
Neil Sloane, AT&T Research
"...this book will soon become the Bible on the subject..."
Jia-Yan Yao, Wuhan University
"The book is a successful combination of a monograph (almost encyclopedic) and an introduction to the subject. Professional mathematicians and theoretical computer scientists will find the most important results, applications and examples of the theory, with motivation, cleverly collected and clearly represented. Selected applications in number theory, combinatorics on words and physics show the strength of the theory. Lists of open questions show the way for further development. All this is supplemented with a bibliographical notes and comments, and an impressive list of references...This is a good and carefully written book by two experts in the field."
Guentcho Skordev, University of Bremen
"It is extremely valuable as a reference text for researchers... I strongly recommend this book to anybody interested in interaction between theoretical computer science and mathematics."
Jean Berstel, SIGACT News
Product details
December 2004Adobe eBook Reader
9780511055751
0 pages
0kg
170 b/w illus. 548 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 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.
