Computing A Glimpse of Randomness

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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.
16 pages; Experimental Mathematics (accepted)

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Chaotic Dynamics, Adaptation and Self-Organizing Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/80132

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0112022
 http://arxiv.org/abs/nlin/0112022

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arXiv