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Exploring randomness

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Author(s): Bridges, Douglas S.; Calude, Cristian S.; Chaitin, Gregory J
Publisher: Springer London
Year: 2001

Language: English
Pages: 163
City: London

Content: Discrete Mathematics and Theoretical Computer Science
Exploring RANDOMNESS
Copyright
Preface
Contents
Part I Introduction
Historical introduction-A century of controversy over the foundations of mathematics
What is LISP? Why do I like it?
How to program my universal Turing machine in LISP
Part II Program Size
A self-delimiting Turing machine considered as a set of (program, output) pairs
How to construct self-delimiting Turing machines: the Kraft inequality. The connection between program-size complexity and algorithmic probability: H(x) = -log2 P(x) + O(1). Occam's razor: there are few minimum-size programsThe basic result on relative complexity: H(y|x) = H(x, y) --
H(x) + O(1)
Part III Randomness
Theoretical interlude-What is randomness? My definitions
Proof that Martin-Löf randomness is equivalent to Chaitin randomness1
Proof that Solovay randomness is equivalent to Martin-Löf randomness
Proof that Solovay randomness is equivalent to strong Chaitin randomness1
Part IV Future Work.