Computing a Glimpse of Randomness
Cristian S. Calude, Michael J. Dinneen, Chi-Kou Shu · Experimental Mathematics · 2002
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: Full description of programs and proofs will be given elsewhere.