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Tables of Contents for An Introduction to Symbolic Dynamics and Coding
Chapter/Section Title
Page #
Page Count
Preface
xi
Shift Spaces
1
27
Full Shifts
1
4
Shift Spaces
5
4
Languages
9
3
Higher Block Shifts and Higher Power Shifts
12
3
Sliding Block Codes
15
8
Convolutional Encoders
23
5
Shifts of Finite Type
28
36
Finite Type Constraints
28
5
Graphs and Their Shifts
33
8
Graph Representations of Shifts of Finite Type
41
8
State Splitting
49
9
Data Storage and Shifts of Finite Type
58
6
Sofic Shifts
64
35
Presentations of Sofic Shifts
64
6
Characterizations of Sofic Shifts
70
5
Minimal Right-Resolving Presentations
75
11
Constructions and Algorithms
86
13
Entropy
99
37
Definition and Basic Properties
99
7
Perron-Frobenius Theory
106
6
Computing Entropy
112
5
Irreducible Components
117
8
Cyclic Structure
125
11
Finite-State Codes
136
35
Road Colorings and Right-Closing Labelings
137
7
Finite-State Codes
144
5
Approximate Eigenvectors
149
7
Code Construction
156
8
Sliding Block Decoders
164
7
Shifts As Dynamical Systems
171
45
Metric Spaces
172
11
Dynamical Systems
183
4
Invariants
187
5
Zeta Functions
192
9
Markov Partitions
201
15
Conjugacy
216
48
The Decomposition Theorem
217
8
Strong Shift Equivalence
225
8
Shift Equivalence
233
8
Invariants for Shift Equivalence
241
10
Shift Equivalence and the Dimension Group
251
13
Finite-To-One Codes and Finite Equivalence
264
37
Finite-to-One Codes
264
11
Right-Resolving Codes
275
7
Finite Equivalence
282
12
Right-Resolving Finite Equivalence
294
7
Degrees of Codes and Almost Conjugacy
301
36
The Degree of a Finite-to-One Code
301
12
Almost Invertible Codes
313
9
Almost Conjugacy
322
6
Typical Points According to Probability
328
9
Embeddings and Factor Codes
337
30
The Embedding Theorem
337
17
The Masking Lemma
354
4
Lower Entropy Factor Codes
358
9
Realization
367
35
Realization of Entropies
367
15
Realization of Zeta Functions
382
14
Pure Subgroups of Dimension Groups
396
6
Equal Entropy Factors
402
29
Right-Closing Factors
403
8
Eventual Factors of Equal Entropy
411
5
Ideal Classes
416
8
Sufficiency of the Ideal Class Condition
424
7
Guide to Advanced Topics
431
40
More on Shifts of Finite Type and Sofic Shifts
431
4
Automorphisms of Shifts of Finite Type
435
6
Symbolic Dynamics and Stationary Processes
441
4
Symbolic Dynamics and Ergodic Theory
445
5
Sofic-like Shifts
450
3
Continuous Flows
453
4
Minimal Shifts
457
4
One-Sided Shifts
461
2
Shifts with a Countable Alphabet
463
3
Higher Dimensional Shifts
466
5
Bibliography
471
15
Notation Index
486
3
Index
489