《an introduction to symbolic dynamics and coding P495》求取 ⇩
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CHAPTER 1.SHIFT SPACES1
1.1.Full Shifts1
1.2.Shift Spaces5
1.3.Languages9
1.4.Higher Block Shifts and Higher Power Shifts12
1.5.Sliding Block Codes15
1.6.Convolutional Encoders23
CHAPTER 2.SHIFTS OF FINITE TYPE28
2.1.Finite Type Constraints28
2.2.Graphs and Their Shifts33
2.3.Graph Representations of Shifts of Finite Type41
2.4.State Splitting49
2.5.Data Storage and Shifts of Finite Type58
CHAPTER 3.SOFIC SHIFTS64
3.1.Presentations of Sofic Shifts64
3.2.Characterizations of Sofic Shifts70
3.3.Minimal Right-Resolving Presentations75
3.4.Constructions and Algorithms86
CHAPTER 4.ENTROPY99
4.1.Definition and Basic Properties99
4.2.Perron-Frobenius Theory106
4.3.Computing Entropy112
4.4.Irreducible Components117
4.5.Cyclic Structure125
CHAPTER 5.FINITE-STATE CODES136
5.1.Road Colorings and Right-Closing Labelings137
5.2.Finite-State Codes144
5.3.Approximate Eigenvectors149
5.4.Code Construction156
5.5.Sliding Block Decoders164
CHAPTER 6. SHIFTS AS DYNAMICAL SYSTEMS171
6.1. Metric Spaces172
6.2. Dynamical Systems183
6.3. Invariants187
6.4. Zeta Functions192
6.5. Markov Partitions201
CHAPTER 7. CONJUGACY216
7.1. The Decomposition Theorem217
7.2. Strong Shift Equivalence225
7.3. Shift Equivalence233
7.4. Invariants for Shift Equivalence241
7.5. Shift Equivalence and the Dimension Group251
CHAPTER 8. FINITE-TO-ONE CODES AND FINITE EQUIVALENCE264
8.1. Finite-to-One Codes264
8.2. Right-Resolving Codes275
8.3. Finite Equivalence282
8.4. Right-Resolving Finite Equivalence294
CHAPTER 9. DEGREES OF CODES AND ALMOST CONJUGACY301
9.1. The Degree of a Finite-to-One Code301
9.2. Almost Invertible Codes313
9.3. Almost Conjugacy322
9.4. Typical Points According to Probability328
CHAPTER 10. EMBEDDINGS AND FACTOR CODES337
10.1. The Embedding Theorem337
10.2. The Masking Lemma354
10.3. Lower Entropy Factor Codes358
CHAPTER 11. REALIZATION367
11.1. Realization of Entropies367
11.2. Realization of Zeta Functions382
11.3. Pure Subgroups of Dimension Groups396
CHAPTER 12. EQUAL ENTROPY FACTORS402
12.1. Right-Closing Factors403
12.2. Eventual Factors of Equal Entropy411
12.3. Ideal Classes416
12.4. Sufficiency of the Ideal Class Condition424
CHAPTER 13. GUIDE TO ADVANCED TOPICS431
13.1. More on Shifts of Finite Type and Sofic Shifts431
13.2. Automorphisms of Shifts of Finite Type435
13.3. Symbolic Dynamics and Stationary Processes441
13.4. Symbolic Dynamics and Ergodic Theory445
13.5. Sofic-like Shifts450
13.6. Continuous Flows453
13.7. Minimal Shifts457
13.8. One-Sided Shifts461
13.9. Shifts with a Countable Alphabet463
13.10. Higher Dimensional Shifts466
BIBLIOGRAPHY471
NOTATION INDEX486
INDEX489
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高度相关资料
- AN INTRODUCTION TO DYNAMICS AND CONTROL
- 1979 LONGMAN LONDON AND NEW YORK
- INTRODUCTION TO SPACE DYNAMICS
- JOHN WILEY & SONS
- Error control coding An introduction
- 1991 Prenice Hall International(UK)Ltd
- Introduction to coding theory
- 1982 Springer-Verlag
- An introduction to symbolic logic Second revised Edition
- 1953 Dover Publications
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