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Computing A Glimpse of Randomness

Cristian S. Calude·Michael J. Dinneen·Chi-Kou Shu
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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 non-computable. The aim of this paper is to describe a procedure, which combines Java programming and mathematical proofs, for computing the exact values of the first 64 bits of a Chaitin Omega: 0000001000000100000110001000011010001111110010111011101000010000. Full description of programs and proofs will be given elsewhere.

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Cristian S. Calude, Michael J. Dinneen, Chi-Kou Shu. 2002-02-11. Computing A Glimpse of Randomness. https://arxiv.org/abs/nlin/0112022

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