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情報とランダム性：アルゴリズム的観点（第２版）
Information and Randomness : An Algorithmic Perspective. Forew. by Gregory J. Chaitin and Arto Salomaa (EATCS Monographs on Theoretical Computer Science) （New ed. 2002. XVI, 240 p. 24 cm）
Calude, Cristian S.
Hardcover:ハードカバー版 |
Mathematical Background 1 (20)
Prerequisites 1 (3)
Computability Theory 4 (2)
Topology 6 (2)
Probability Theory 8 (11)
Exercises and Problems 19 (2)
Noiseless Coding 21 (12)
Prefix-free Sets 21 (3)
Instantaneous Coding 24 (6)
Exercises and Problems 30 (2)
History of Results 32 (1)
Program-size 33 (20)
An Example 33 (1)
Computer and Complexities 34 (9)
Algorithmic Properties of Complexities 43 (2)
Quantitative Estimates 45 (2)
Hating Probabilities 47 (2)
Exercises and Problems 49 (3)
History of Results 52 (1)
Computably Enumerable Instantaneous Codes 53 (42)
The Kraft-Chaitin Theorem 53 (7)
Relativized Complexities and Probabilities 60 (10)
Speed-up Theorem 70 (4)
Algorithmic Coding Theorem 74 (11)
Binary vs Non-binary Coding (1) 85 (4)
Exercises and Problems 89 (2)
History of Results 91 (4)
Random Strings 95 (52)
An Empirical Analysis 95 (7)
Chaitin's Definition of Random Strings 102(5)
Relating Complexities K and H 107(2)
A Statistical Analysis 109(10)
A Computational Analysis 119(4)
Borel Normality 123(8)
Extensions of Random Strings 131(5)
Binary vs Non-binary Coding (2) 136(4)
Exercises and Problems 140(5)
History of Results 145(2)
Random Sequences 147(90)
From Random Strings to Random Sequences 147(11)
The Definition of Random Sequences 158(11)
Characterizations of Random Sequences 169(15)
Properties of Random Sequences 184(20)
The Reducibility Theorem 204(25)
The Randomness Hypothesis 229(2)
Exercises and Problems 231(2)
History of Results 233(4)
Computably Enumerable Random Reals 237(78)
Chaitin's Omega Number 237(3)
Is Randomnes Base Invariant? 240(13)
Most Reals Obey No Probability Laws 253(7)
Computable and Uncomputable Reals 260(11)
Computably Enumerable Reals, Domination and 271(23)
Degrees
A Characterization of Computably Enumerable 294(8)
Random Reals
Degree-theoretic Properties of Computably 302(8)
Enumerable Random Reals
Exercises and Problems 310(3)
History of Results 313(2)
Randomness and Incompleteness 315(46)
The Incompleteness Phenomenon 315(5)
Information-theoretic Incompleteness (1) 320(4)
Information-theoretic Incompleteness (2) 324(4)
Information-theoretic Incompleteness (3) 328(4)
Coding Mathematical Knowledge 332(3)
Finitely Refutable Mathematical Problems 335(8)
Computing 64 Bits of a Computably 343(12)
Enumerable Random Real
Turing's Barrier Revisited 355(3)
History of Results 358(3)
Applications 361(54)
The Infinity of Primes 361(1)
The Undecidability of the Halting Problem 362(1)
Counting as a Source of Randomness 363(3)
Randomness and Chaos 366(1)
Randomness and Cellular Automata 367(16)
Random Sequences of Reals and Riemann's 383(6)
Zeta-function
Probabilistic Algorithms 389(4)
Structural Complexity 393(5)
What Is Life? 398(7)
Randomness in Physics 405(4)
Metaphysical Themes 409(6)
Open Problems 415(4)
Bibliography 419(36)
Notation Index 455(2)
Subject Index 457(4)
Name Index 461
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