Computing a glimpse of randomness
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| Venue: | Experimental Mathematics |
| Citations: | 14 - 6 self |
BibTeX
@ARTICLE{Calude_computinga,
author = {Cristian S. Calude and Michael J. Dinneen and Chi-kou Shu},
title = {Computing a glimpse of randomness},
journal = {Experimental Mathematics},
year = {},
pages = {2002}
}
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Abstract
A Chaitin Omega number is the halting probability of a universal Chaitin (selfdelimiting 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 63 bits of a Chaitin Omega: 000000100000010000100000100001110111001100100111100010010011100. Full description of programs and proofs will be given elsewhere. 1
