Random reals à la Chaitin with or without prefix-freeness

En:

Theor Comput Sci 2007;385(1-3):193-201

Fecha:

2007

Formato:

application/pdf

Tipo de documento:

info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion

Descriptores:

Algorithmic randomness -  Kolmogorov complexity -  Omega numbers -  Random reals -  Function evaluation -  Probability -  Problem solving -  Algorithmic randomness -  Kolmogorov complexity

Descripción:

We give a general theorem that provides examples of n-random reals à la Chaitin, for every n ≥ 1; these are halting probabilities of partial computable functions that are universal by adjunction for the class of all partial computable functions, The same result holds for the class functions of partial computable functions with prefix-free domain. Thus, the usual technical requirement of prefix-freeness on domains is an option which we show to be non-critical when dealing with universality by adjunction. We also prove that the condition of universality by adjunction (which, though particular, is a very natural case of optimality) is essential in our theorem. © 2007 Elsevier Ltd. All rights reserved.
Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Identificador(es):

http://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_Becher

Derechos:

info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar