An introduction to symbolic dynamics and coding:
Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C *$-algebras....
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Cambridge mathematical library
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C *$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition |
| Beschreibung: | Literaturverzeichnis Seite 515-540 |
| Beschreibung: | xix, 550 Seiten |
| ISBN: | 9781108820288 |
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| adam_text | CONTENTS PREFACE TO THE FIRST EDITION........................................xiii PREFACE TO THE SECOND EDITION.................................. xix CHAPTER 1. SHIFT SPACES........................................................ 1 §1.1 §1.2 §1.3 §1.4 §1.5 §1.6 . . . . . . Full Shifts...................................................................................... 1 Shift Spaces.................................................................................. 5 Languages .................................................................................. 9 Higher Block Shifts and Higher Power Shifts........................ 12 Sliding Block Codes................................................................ 15 Convolutional Encoders............................................................ 23 CHAPTER 2. SHIFTS OF FINITE TYPE ................................. 28 §2.1 §2.2 §2.3 §2.4 §2.5 . . . . . Finite Type Constraints ........................................................ 28 Graphs and Their Shifts ........................................................ 33 Graph Representations of Shifts of Finite Type................ 41 State Splitting............................................................................ 49 Data Storage and Shifts of FiniteType................................. 59 CHAPTER 3. SOFIC SHIFTS...................................................... 64 §3.1 §3.2 §3.3 §3.4 . . . . Presentations of Sofie Shifts.................................................... 64 Characterizations of Sofie Shifts............................................ 70 Minimal
Right-Resolving Presentations................................ 76 Constructions and Algorithms................................................ 86 CHAPTER 4. ENTROPY............................................................ 100 §4.1 §4.2 §4.3 §4.4 §4.5 . . . . . Definition and Basic Properties.......................................... 100 Perron-Frobenius Theory...................................................... 107 Computing Entropy....................................................... . 113 Irreducible Components.......................................................... 118 Cyclic Structure...................................................................... 126 CHAPTER 5. FINITE-STATE CODES §5.1 §5.2 §5.3 §5.4 §5.5 . . . . . .................................. 137 Road Colorings and Right-Closing Labelings.......................138 Finite-State Codes.................................................................. 145 Approximate Eigenvectors...................................................... 150 Code Construction.................................................................. 157 Sliding Block Decoders.......................................................... 165 ix
Contents x CHAPTER 6. SHIFTS AS DYNAMICAL SYSTEMS §6.1 §6.2 §6.3 §6.4 §6.5 . . . . . Metric Spaces.......................................................................... 173 Dynamical Systems.................................................................. 184 Invariants.................................................................................. 188 Zeta Functions.......................................................................... 193 Markov Partitions.................................................................. 202 CHAPTER 7. CONJUGACY §7.1 §7.2 §7.3 §7.4 §7.5 . . . . . . . .172 .................................................... 217 The Decomposition Theorem.............................................. 218 Strong Shift Equivalence...................................................... 226 Shift Equivalence .................................................................. 234 Invariants for Shift Equivalence.......................................... 242 Shift Equivalence and theDimension Group........................252 CHAPTER 8. FINITE-TO-ONE CODES AND FINITE EQUIVALENCE .............. 265 §8.1 §8.2 §8.3 §8.4 . . . . Finite-to-One Codes.............................................................. 265 Right-Resolving Codes.......................................................... 276 Finite Equivalence.................................................................. 283 Right-Resolving Finite Equivalence...................................... 295 CHAPTER 9. DEGREES OF CODES AND ALMOST CONJUGACY .................. 302 §9.1 §9.2 §9.3 §9.4 . . . . The
Degree of a Finite-to-One Code.................................. 302 Almost Invertible Codes ...................................................... 314 Almost Conjugacy.................................................................. 323 Typical Points According to Probability .......................... 330 CHAPTER 10. EMBEDDINGS AND FACTOR CODES . . 338 §10.1 §10.2 §10.3 . The Embedding Theorem.................................................. 338 . The Masking Lemma.......................................................... 355 . Lower Entropy Factor Codes.............................................. 359 CHAPTER 11. REALIZATION................................................. 369 §11.1 §11.2 §11.3 . Realization of Entropies...................................................... 370 . Realization of Zeta Functions.............................................. 385 . Pure Subgroups of Dimension Groups.............................. 397 CHAPTER 12. EQUAL ENTROPYFACTORS..................... 402 §12.1 §12.2 §12.3 §12.4 . . . . Right-Closing Factors.......................................................... 403 Eventual Factors of Equal Entropy.................................. 411 Ideal Classes.......................................................................... 416 Sufficiency of the Ideal Class Condition.......................... 424
Contents xi CHAPTER 13. GUIDE TO ADVANCED TOPICS.............. 430 §13.1 §13.2 §13.3 §13.4 §13.5 §13.6 §13.7 §13.8 §13.9 §13.10 . . . . . . . . . More on Shifts of Finite Type and Sofie Shifts.............. 430 Automorphisms of Shifts of Finite Type.......................... 434 Symbolic Dynamics and Stationary Processes.................. 440 Symbolic Dynamics and Ergodic Theory.......................... 444 Sofic-like Shifts...................................................................... 449 Continuous Flows.................................................................. 452 Minimal Shifts...................................................................... 456 One-Sided Shifts.................................................................. 460 Shifts with a Countable Alphabet...................................... 462 . Higher Dimensional Shifts.................................................. 465 ADDENDUM.................................................................................... 471 §A.l. §A.2. §A.3. §A.4. §A.5. §A.6. §A.7. §A.8. §A.9. Classification Problems................................................................. 471 Factor Codes and Embeddings ..................................................476 Symbolic Models for Smooth Systems......................................478 Realization..................................................................................... 479 Automorphism Groups of Shifts.................................................. 481 Higher Dimensional Shifts ..........................................................485
Equilibrium States..........................................................................495 Symbolic Dynamics over Countable Groups.............................. 502 Symbolic Representations of Algebraic Actions...................... 508 BIBLIOGRAPHY.............................................................................515 ADDENDUM BIBLIOGRAPHY................................................. 531 NOTATION INDEX........................................................................ 541 INDEX................................................................................................ 544
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| adam_txt |
CONTENTS PREFACE TO THE FIRST EDITION.xiii PREFACE TO THE SECOND EDITION. xix CHAPTER 1. SHIFT SPACES. 1 §1.1 §1.2 §1.3 §1.4 §1.5 §1.6 . . . . . . Full Shifts. 1 Shift Spaces. 5 Languages . 9 Higher Block Shifts and Higher Power Shifts. 12 Sliding Block Codes. 15 Convolutional Encoders. 23 CHAPTER 2. SHIFTS OF FINITE TYPE . 28 §2.1 §2.2 §2.3 §2.4 §2.5 . . . . . Finite Type Constraints . 28 Graphs and Their Shifts . 33 Graph Representations of Shifts of Finite Type. 41 State Splitting. 49 Data Storage and Shifts of FiniteType. 59 CHAPTER 3. SOFIC SHIFTS. 64 §3.1 §3.2 §3.3 §3.4 . . . . Presentations of Sofie Shifts. 64 Characterizations of Sofie Shifts. 70 Minimal
Right-Resolving Presentations. 76 Constructions and Algorithms. 86 CHAPTER 4. ENTROPY. 100 §4.1 §4.2 §4.3 §4.4 §4.5 . . . . . Definition and Basic Properties. 100 Perron-Frobenius Theory. 107 Computing Entropy. . 113 Irreducible Components. 118 Cyclic Structure. 126 CHAPTER 5. FINITE-STATE CODES §5.1 §5.2 §5.3 §5.4 §5.5 . . . . . . 137 Road Colorings and Right-Closing Labelings.138 Finite-State Codes. 145 Approximate Eigenvectors. 150 Code Construction. 157 Sliding Block Decoders. 165 ix
Contents x CHAPTER 6. SHIFTS AS DYNAMICAL SYSTEMS §6.1 §6.2 §6.3 §6.4 §6.5 . . . . . Metric Spaces. 173 Dynamical Systems. 184 Invariants. 188 Zeta Functions. 193 Markov Partitions. 202 CHAPTER 7. CONJUGACY §7.1 §7.2 §7.3 §7.4 §7.5 . . . . . . . .172 . 217 The Decomposition Theorem. 218 Strong Shift Equivalence. 226 Shift Equivalence . 234 Invariants for Shift Equivalence. 242 Shift Equivalence and theDimension Group.252 CHAPTER 8. FINITE-TO-ONE CODES AND FINITE EQUIVALENCE . 265 §8.1 §8.2 §8.3 §8.4 . . . . Finite-to-One Codes. 265 Right-Resolving Codes. 276 Finite Equivalence. 283 Right-Resolving Finite Equivalence. 295 CHAPTER 9. DEGREES OF CODES AND ALMOST CONJUGACY . 302 §9.1 §9.2 §9.3 §9.4 . . . . The
Degree of a Finite-to-One Code. 302 Almost Invertible Codes . 314 Almost Conjugacy. 323 Typical Points According to Probability . 330 CHAPTER 10. EMBEDDINGS AND FACTOR CODES . . 338 §10.1 §10.2 §10.3 . The Embedding Theorem. 338 . The Masking Lemma. 355 . Lower Entropy Factor Codes. 359 CHAPTER 11. REALIZATION. 369 §11.1 §11.2 §11.3 . Realization of Entropies. 370 . Realization of Zeta Functions. 385 . Pure Subgroups of Dimension Groups. 397 CHAPTER 12. EQUAL ENTROPYFACTORS. 402 §12.1 §12.2 §12.3 §12.4 . . . . Right-Closing Factors. 403 Eventual Factors of Equal Entropy. 411 Ideal Classes. 416 Sufficiency of the Ideal Class Condition. 424
Contents xi CHAPTER 13. GUIDE TO ADVANCED TOPICS. 430 §13.1 §13.2 §13.3 §13.4 §13.5 §13.6 §13.7 §13.8 §13.9 §13.10 . . . . . . . . . More on Shifts of Finite Type and Sofie Shifts. 430 Automorphisms of Shifts of Finite Type. 434 Symbolic Dynamics and Stationary Processes. 440 Symbolic Dynamics and Ergodic Theory. 444 Sofic-like Shifts. 449 Continuous Flows. 452 Minimal Shifts. 456 One-Sided Shifts. 460 Shifts with a Countable Alphabet. 462 . Higher Dimensional Shifts. 465 ADDENDUM. 471 §A.l. §A.2. §A.3. §A.4. §A.5. §A.6. §A.7. §A.8. §A.9. Classification Problems. 471 Factor Codes and Embeddings .476 Symbolic Models for Smooth Systems.478 Realization. 479 Automorphism Groups of Shifts. 481 Higher Dimensional Shifts .485
Equilibrium States.495 Symbolic Dynamics over Countable Groups. 502 Symbolic Representations of Algebraic Actions. 508 BIBLIOGRAPHY.515 ADDENDUM BIBLIOGRAPHY. 531 NOTATION INDEX. 541 INDEX. 544 |
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| spelling | Lind, Douglas A. 1946- Verfasser (DE-588)130081078 aut An introduction to symbolic dynamics and coding Douglas Lind, University of Washington, Brian Marcus, University of British Columbia Second edition Cambridge Cambridge University Press 2021 xix, 550 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical library Literaturverzeichnis Seite 515-540 Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C *$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Symbolic dynamics Coding theory Dynamisches System (DE-588)4013396-5 s Codierungstheorie (DE-588)4139405-7 s DE-604 Marcus, Brian 1949- Verfasser (DE-588)1145614140 aut Erscheint auch als Online-Ausgabe 978-1-108-90196-3 Erscheint auch als Online-Ausgabe 978-1-108-82028-8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032524371&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lind, Douglas A. 1946- Marcus, Brian 1949- An introduction to symbolic dynamics and coding Codierungstheorie (DE-588)4139405-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4013396-5 |
| title | An introduction to symbolic dynamics and coding |
| title_auth | An introduction to symbolic dynamics and coding |
| title_exact_search | An introduction to symbolic dynamics and coding |
| title_exact_search_txtP | An introduction to symbolic dynamics and coding |
| title_full | An introduction to symbolic dynamics and coding Douglas Lind, University of Washington, Brian Marcus, University of British Columbia |
| title_fullStr | An introduction to symbolic dynamics and coding Douglas Lind, University of Washington, Brian Marcus, University of British Columbia |
| title_full_unstemmed | An introduction to symbolic dynamics and coding Douglas Lind, University of Washington, Brian Marcus, University of British Columbia |
| title_short | An introduction to symbolic dynamics and coding |
| title_sort | an introduction to symbolic dynamics and coding |
| topic | Codierungstheorie (DE-588)4139405-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Codierungstheorie Dynamisches System |
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