Automatic Sequences: Theory, Applications, Generalizations [Hardcover]

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

Book Description

Publication Date: July 21, 2003 | ISBN-10: 0521823323 | ISBN-13: 978-0521823326

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.

Editorial Reviews

Review

"[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

Book Description

This book, combining concepts of mathematics and computer science, 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, the book starts from first principles and develops the basic theory. Then it shows how these ideas can be applied to solve problems in number theory and physics.

Product Details

• Hardcover: 588 pages
• Publisher: Cambridge University Press (July 21, 2003)
• Language: English
• ISBN-10: 0521823323
• ISBN-13: 978-0521823326
• Product Dimensions: 10.5 x 7 x 1.5 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,678,399 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 13 people found the following review helpful:

5.0 out of 5 stars It will be the prime resource of the area for years to come, March 24, 2004

By 

L. Bourke "cbourke3" (Lincoln, NE United States) - See all my reviews
(REAL NAME)   

This review is from: Automatic Sequences: Theory, Applications, Generalizations (Hardcover)

In 1983 Lothaire's "Combinatorics on Words" became the definitive resource on the area of stringology. 20 years later, Jean-Paul Allouche and Jeffrey Shallit's "Automatic Sequences" is set to be its heir. Pulling in countless concepts from many seemingly dissimilar disciplines, Allouche and Shallit are successful in bringing them together in an extremely informative and concise way. With detailed chapter notes and an immense bibliography the possible areas of exploration on each topic prove endless. A great resource for everyone from the serious researcher to the casually interested, this text is applicable to almost every area of mathematics and computer science. As the authors put it, "Sequences, both finite and infinite are ubiquitous in mathematics and theoretical computer science." If quality were synonymous popularity then this book will be equally ubiquitous.

5.0 out of 5 stars Great Book Great Price, February 20, 2012

By 

cpagirl - See all my reviews

Amazon Verified Purchase

This review is from: Automatic Sequences: Theory, Applications, Generalizations (Hardcover)

I was happy to find a reasonably priced copy of this book. It is on nice paper and has a sturdy hard cover. I have had this in and out of a few different style bags and it fits in all of the bags very well. It has stayed relatively undamaged despite me using it hard. Also the content is very well organized and thoroughly explained.

4.0 out of 5 stars Excellent reference book, August 29, 2011

By 

bembsj - See all my reviews

Amazon Verified Purchase

This review is from: Automatic Sequences: Theory, Applications, Generalizations (Hardcover)

I am enjoying this book immensely. It fills a real need in the literature of automatic sequences. The references and end notes at each chapter conclusion are very useful. Basically this book brings together a lot of disparate ideas and forms them into a coherent and well laid out presentation. My only reservation with the book is that there are minor errors with some of the proofs that can be annoying (but easily fixable). The style is accessible, the ideas are fast moving and the comprehensiveness of ideas and references is inspirational. Definitely worth purchasing.