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Computing a Glimpse of Randomness …
Computing a Glimpse of Randomness
Cristian S. Calude, Michael J. Dinneen, and Chi-Kou Shu
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:
0000001000000100000110001000011010001111110010111011101000010000.
Full description of programs and proofs will be given elsewhere
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