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Automatic Sequences: Theory, Applications, Generalizations / Edition 1

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Uniting dozens of disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences ... generated by the simple model of computation called the finite automaton. The authors develop the theory of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. Further, they discuss applications to number theory (particularly formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Results are presented from the first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and more than 1,600 citations to the literature. 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. 571 pages with index, bibliography, and hints, references, and solutions for select exercises. Laminated cover, remainder mark on the bottom. 7 1/8" x 10 1/4 Read more Show Less

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Overview

Combining concepts of mathematics and computer science, this book is about the sequences of symbols that can be generated by simple models of computation called "finite automata". Suitable for graduate students or advanced undergraduates, it starts from elementary principles and develops the basic theory. The study then progresses to show how these ideas can be applied to solve problems in number theory and physics.

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Editorial Reviews

From the Publisher
"[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

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Product Details

  • ISBN-13: 9780521823326
  • Publisher: Cambridge University Press
  • Publication date: 7/28/2003
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 571
  • Product dimensions: 6.97 (w) x 9.96 (h) x 1.50 (d)

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; A. Hints … for selected exercises.

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