Automatic Sequences

Theory, Applications, Generalizations

Jean-Paul Allouche, Jeffrey Shallit

572 pages, parution le 21/10/2003

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Résumé

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.

Stringology
Number theory and algebra
Numeration systems
Finite automata and other models of computation
Automatic sequences
Uniform morphisms and automatic sequences
Morphic sequences
Frequency of letters
Characteristic words
Subwords
Cobham's theorem
Formal power series
Automatic real numbers
Multidimensional automatic sequences
Automaticity
k-regular sequences
Physics
A. Hints ... for selected exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Jean-Paul Allouche, Jeffrey Shallit
Parution	21/10/2003
Nb. de pages	572
Format	18 x 26
Couverture	Relié
Poids	1155g
Intérieur	Noir et Blanc
EAN13	9780521823326
ISBN13	978-0-521-82332-6