Computing a Glimpse of Randomness
Calude, Cristian S. ; Dinneen, Michael J. ; Shu, Chi-Kou
Experiment. Math., Tome 11 (2002) no. 3, p. 361-370 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2002-05-14
Classification:  Chaitin Omega number,  halting problem,  algorithmic randomness,  68Q30,  68Q17 
@article{1057777428,
     author = {Calude, Cristian S. and Dinneen, Michael J. and Shu, Chi-Kou},
     title = {Computing a Glimpse of Randomness},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 361-370},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057777428}
}

Calude, Cristian S.; Dinneen, Michael J.; Shu, Chi-Kou. Computing a Glimpse of Randomness. Experiment. Math., Tome 11 (2002) no. 3, pp.  361-370. http://gdmltest.u-ga.fr/item/1057777428/