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Exploring RANDOMNESS

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Cover of 'Exploring RANDOMNESS'

Table of Contents

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    Book Overview
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    Chapter 1 Historical introduction — A century of controversy over the foundations of mathematics
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    Chapter 2 What is LISP? Why do I like it?
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    Chapter 3 How to program my universal Turing machine in LISP
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    Chapter 4 A self-delimiting Turing machine considered as a set of (program, output) pairs
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    Chapter 5 How to construct self-delimiting Turing machines: the Kraft inequality
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    Chapter 6 The connection between program-size complexity and algorithmic probability: H(x) =-log 2 P(x) + O (1). Occam’s razor: there are few minimum-size programs
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    Chapter 7 The basic result on relative complexity: H(y∣x)=H(x,y)-H(x)+O(1)
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    Chapter 8 Theoretical interlude—What is randomness? My definitions
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    Chapter 9 Proof that Martin-Löf randomness is equivalent to Chaitin randomness
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    Chapter 10 Proof that Solovay randomness is equivalent to Martin-Löf randomness
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    Chapter 11 Proof that Solovay randomness is equivalent to strong Chaitin randomness
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    Chapter 12 Extending AIT to the size of programs for computing infinite sets and to computations with oracles
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    Chapter 13 Postscript—Letter to a daring young reader
Attention for Chapter 10: Proof that Solovay randomness is equivalent to Martin-Löf randomness
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Chapter title
Proof that Solovay randomness is equivalent to Martin-Löf randomness
Chapter number 10
Book title
Exploring RANDOMNESS
Published by
Springer, London, January 2001
DOI 10.1007/978-1-4471-0307-3_10
Book ISBNs
978-1-4471-1085-9, 978-1-4471-0307-3
Authors

Gregory J. Chaitin, Chaitin, Gregory J.

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