Universality probability of a prefix-free machine.
We study the notion of universality probability of a universal prefix-free machine, as introduced by C. S. Wallace. We show that it is random relative to the third iterate of the halting problem and determine its Turing degree and its place in the arithmetical hierarchy of complexity. Furthermore, we give a computational characterization of the real numbers that are universality probabilities of universal prefix-free machines.
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, People's Republic of China. barmpalias@gmail.com
George
G
Barmpalias
David L
DL
Dowe