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Automatic Sequences

2003-07-21 Computers
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Release : 2003-07-21
Genre : Computers
Kind : eBook
Book Rating : 326/5 ( reviews)

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Book Synopsis Automatic Sequences by : Jean-Paul Allouche

Download or read book Automatic Sequences written by Jean-Paul Allouche. This book was released on 2003-07-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Logical Approach to Automatic Sequences

2022-09-30 Computers
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Release : 2022-09-30
Genre : Computers
Kind : eBook
Book Rating : 979/5 ( reviews)

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Book Synopsis The Logical Approach to Automatic Sequences by : Jeffrey Shallit

Download or read book The Logical Approach to Automatic Sequences written by Jeffrey Shallit. This book was released on 2022-09-30. Available in PDF, EPUB and Kindle. Book excerpt: Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.

Automatic Sequences

2008-08-22 Mathematics
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Release : 2008-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 960/5 ( reviews)

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Book Synopsis Automatic Sequences by : von Friedrich Haeseler

Download or read book Automatic Sequences written by von Friedrich Haeseler. This book was released on 2008-08-22. Available in PDF, EPUB and Kindle. Book excerpt: Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular: · a general introduction to automatic sequences · the basic (combinatorial) properties of automatic sequences · the algebraic approach to automatic sequences · geometric objects related to automatic sequences.

Sequences, Groups, and Number Theory

2018-04-09 Mathematics
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Release : 2018-04-09
Genre : Mathematics
Kind : eBook
Book Rating : 52X/5 ( reviews)

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Book Synopsis Sequences, Groups, and Number Theory by : Valérie Berthé

Download or read book Sequences, Groups, and Number Theory written by Valérie Berthé. This book was released on 2018-04-09. Available in PDF, EPUB and Kindle. Book excerpt: This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Recurrence Sequences

2015-09-03 Mathematics
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Release : 2015-09-03
Genre : Mathematics
Kind : eBook
Book Rating : 154/5 ( reviews)

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Book Synopsis Recurrence Sequences by : Graham Everest

Download or read book Recurrence Sequences written by Graham Everest. This book was released on 2015-09-03. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

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