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 and Perl programming and mathematical
proofs, for computing the exact values of the first 80 bits of a Chaitin Omega:
0.0000000000000000000010000001000000100000010000010000011100100111000101
0001010000. Full description of programs and proofs will be given elsewhere.
