Universality probability of a prefix-free machine-Reference-Cited by-同舟云学术

Universality probability of a prefix-free machine

Published:2012-07-28 Issue:1971 Volume:370 Page:3488-3511
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Barmpalias George¹,Dowe David L.²

Affiliation:

1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, PO Box 8718, Beijing 100190, People's Republic of China

2. School of Computer Science and Software Engineering, Clayton School of I.T., Monash University, Clayton, Victoria 3800, Australia

Abstract

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2011.0319

Reference27 articles.

1. On computable numbers with an application to the Entscheidungsproblem;Turing A. M.;Proc. Lond. Math. Soc.,1936

2. Three approaches to the definition of the concept ‘quantity of information’;Kolmogorov A. N.;Problemy Peredači Informacii,1965

3. A formal theory of inductive inference. Part I

4. Logical basis for information theory and probability theory

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