Random reals à la Chaitin with or without prefix-freeness
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 parti...
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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_Becher |
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paperaa:paper_03043975_v385_n1-3_p193_Becher2023-06-12T16:47:27Z Random reals à la Chaitin with or without prefix-freeness Theor Comput Sci 2007;385(1-3):193-201 Becher, V. Grigorieff, S. Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Function evaluation Probability Problem solving Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Theorem proving 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. 2007 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_Becher |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
language |
Inglés |
orig_language_str_mv |
eng |
topic |
Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Function evaluation Probability Problem solving Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Theorem proving |
spellingShingle |
Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Function evaluation Probability Problem solving Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Theorem proving Becher, V. Grigorieff, S. Random reals à la Chaitin with or without prefix-freeness |
topic_facet |
Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Function evaluation Probability Problem solving Algorithmic randomness Kolmogorov complexity Omega numbers Random reals Theorem proving |
description |
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. |
format |
Artículo Artículo publishedVersion |
author |
Becher, V. Grigorieff, S. |
author_facet |
Becher, V. Grigorieff, S. |
author_sort |
Becher, V. |
title |
Random reals à la Chaitin with or without prefix-freeness |
title_short |
Random reals à la Chaitin with or without prefix-freeness |
title_full |
Random reals à la Chaitin with or without prefix-freeness |
title_fullStr |
Random reals à la Chaitin with or without prefix-freeness |
title_full_unstemmed |
Random reals à la Chaitin with or without prefix-freeness |
title_sort |
random reals à la chaitin with or without prefix-freeness |
publishDate |
2007 |
url |
http://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_Becher |
work_keys_str_mv |
AT becherv randomrealsalachaitinwithorwithoutprefixfreeness AT grigorieffs randomrealsalachaitinwithorwithoutprefixfreeness |
_version_ |
1769810287303589888 |