Universality probability of a prefix-free machine

被引：7
|
作者：
Barmpalias, George [1 ]
Dowe, David L. [2 ]
机构：
[1] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China
[2] Monash Univ, Clayton Sch IT, Sch Comp Sci & Software Engn, Clayton, Vic 3800, Australia
来源：
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2012年 / 370卷 / 1971期
基金：
中国国家自然科学基金;
关键词：
Kolmogorov complexity; prefix-free complexity; universality probability; algorithmic randomness; RANDOMNESS; CHAITIN; REALS;
D O I：
10.1098/rsta.2011.0319
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
引用
收藏
页码：3488 / 3511
页数：24
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