Computing A Glimpse of Randomness
混沌动力学
2007-05-23 v3 适应与自组织系统
摘要
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.
引用
@article{arxiv.nlin/0112022,
title = {Computing A Glimpse of Randomness},
author = {Cristian S. Calude and Michael J. Dinneen and Chi-Kou Shu},
journal= {arXiv preprint arXiv:nlin/0112022},
year = {2007}
}
备注
16 pages; Experimental Mathematics (accepted)