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2002 Computing a Glimpse of Randomness
Cristian S. Calude, Michael J. Dinneen, Chi-Kou Shu
Experiment. Math. 11(3): 361-370 (2002).

Abstract

A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing,converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly noncomputable. The aim of this paper is to describe a procedure, that combines Java programming and mathematical proofs, to compute the exact values of the first 64 bits of a Chaitin Omega:

0000001000000100000110001000011010001111110010111011101000010000.

Full description of programs and proofs will be given elsewhere.

Citation

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Cristian S. Calude. Michael J. Dinneen. Chi-Kou Shu. "Computing a Glimpse of Randomness." Experiment. Math. 11 (3) 361 - 370, 2002.

Information

Published: 2002
First available in Project Euclid: 9 July 2003

zbMATH: 1117.68385
MathSciNet: MR1959748

Subjects:
Primary: 68Q30
Secondary: 68Q17

Rights: Copyright © 2002 A K Peters, Ltd.

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Vol.11 • No. 3 • 2002
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