| Description |
1 online resource (xvi, 571 pages) : illustrations |
| Contents |
Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Goals of This Book -- Prerequisites -- Algorithm Descriptions -- Acknowledgments -- 1 Stringology -- 1.1 Alpha Words -- 1.2 Topology and Measure -- 1.3 Languages and Regular Expressions -- 1.4 Morphisms -- 1.5 The Theorems of Lyndon and Schützenberger -- 1.6 Repetitions in Words -- 1.7 Overlap-Free Binary Words -- 1.8 Additional Topics on Repetitions -- 1.9 Exercises -- 1.10 Open Problems -- 1.11 Notes on Chapter 1 -- 2 Number Theory and Algebra -- 2.1 Divisibility and Valuations |
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2.2 Rational and Irrational Numbers -- 2.3 Algebraic and Transcendental Numbers -- 2.4 Continued Fractions -- 2.5 Basics of Diophantine Approximation -- 2.6 The Three-Distance Theorem -- 2.7 Algebraic Structures -- 2.8 Vector Spaces -- 2.9 Fields -- 2.10 Polynomials, Rational Functions, and Formal Power Series -- 2.11 Rho-adic Numbers -- 2.12 Asymptotic Notation -- 2.13 Some Useful Estimates -- 2.14 Exercises -- 2.15 Open Problems -- 2.16 Notes on Chapter 2 -- 3 Numeration Systems -- 3.1 Numeration Systems -- 3.2 Sums of Digits -- 3.3 Block Counting and Digital Sequences |
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3.4 Representation of Real Numbers -- 3.5 Sums of Sums of Digits -- 3.6 Base-k Representation with Alternate Digit Sets -- 3.7 Representations in Negative Bases -- 3.8 Fibonacci Representation -- 3.9 Ostrowski's Alpha-Numeration System -- 3.10 Representations in Complex Bases -- 3.11 Exercises -- 3.12 Open Problems -- 3.13 Notes on Chapter 3 -- 4 Finite Automata and Other Models of Computation -- 4.1 Finite Automata -- 4.2 Proving Languages Nonregular -- 4.3 Finite Automata with Output -- 4.4 Context-Free Grammars and Languages -- 4.5 Context-Sensitive Grammars and Languages |
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4.6 Turing Machines -- 4.7 Exercises -- 4.8 Open Problems -- 4.9 Notes on Chapter 4 -- 5 Automatic Sequences -- 5.1 Automatic Sequences -- 5.2 Robustness of the Automatic Sequence Concept -- 5.3 Two-Sided Automatic Sequences -- 5.4 Basic Properties of Automatic Sequences -- 5.5 Nonautomatic Sequences -- 5.6 Kappa-Automatic Sets -- 5.7 1-Automatic Sequences -- 5.8 Exercises -- 5.9 Open Problems -- 5.10 Notes on Chapter 5 -- 6 Uniform Morphisms and Automatic Sequences -- 6.1 Fixed Points of Uniform Morphisms -- 6.2 The Thue-Morse Infinite Word -- 6.3 Cobham's Theorem |
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6.4 The Tower of Hanoi and Iterated Morphisms -- 6.5 Paperfolding and Continued Fractions -- 6.6 The Kappa-Kernel -- 6.7 Cobham's Theorem for (Kappa, lota)-Numeration Systems -- 6.8 Basic Closure Properties -- 6.9 Uniform Transduction of Automatic Sequences -- 6.10 Sums of Digits, Polynomials, and Automatic Sequences -- 6.11 Exercises -- 6.12 Open Problems -- 6.13 Notes on Chapter 6 -- 7 Morphic Sequences -- 7.1 The Infinite Fibonacci Word -- 7.2 Finite Fixed Points -- 7.3 Morphic Sequences and Infinite Fixed Points -- 7.4 Two-Sided Infinite Fixed Points -- 7.5 More on Infinite Fixed Points |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 481-554) and index |
| Notes |
English |
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Print version record |
| Subject |
Sequential machine theory.
|
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Sequences (Mathematics)
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MATHEMATICS -- Infinity.
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Sequences (Mathematics)
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Sequential machine theory
|
| Form |
Electronic book
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| Author |
Shallit, Jeffrey Outlaw
|
| ISBN |
0511062087 |
|
9780511062087 |
|
9780511546563 |
|
0511546564 |
|
9780521823326 |
|
0521823323 |
|
1280436530 |
|
9781280436536 |
|
1316085899 |
|
9781316085899 |
|
9786610436538 |
|
6610436533 |
|
0511205465 |
|
9780511205460 |
|
0511169515 |
|
9780511169519 |
|
0511308361 |
|
9780511308369 |
|
0511070543 |
|
9780511070549 |
|
