Random reals à la Chaitin with or without prefix-freeness

Autores
Becher, V.; Grigorieff, S.
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
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.
Fuente
Theor Comput Sci 2007;385(1-3):193-201
Materia
Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Function evaluation
Probability
Problem solving
Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Theorem proving
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_03043975_v385_n1-3_p193_Becher
Acceder
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oai_identifier_str paperaa:paper_03043975_v385_n1-3_p193_Becher
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Random reals à la Chaitin with or without prefix-freenessBecher, V.Grigorieff, S.Algorithmic randomnessKolmogorov complexityOmega numbersRandom realsFunction evaluationProbabilityProblem solvingAlgorithmic randomnessKolmogorov complexityOmega numbersRandom realsTheorem provingWe 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.2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_BecherTheor Comput Sci 2007;385(1-3):193-201reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-04T09:48:40Zpaperaa:paper_03043975_v385_n1-3_p193_BecherInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-04 09:48:42.773Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Random reals à la Chaitin with or without prefix-freeness
title Random reals à la Chaitin with or without prefix-freeness
spellingShingle Random reals à la Chaitin with or without prefix-freeness
Becher, V.
Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Function evaluation
Probability
Problem solving
Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Theorem proving
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
dc.creator.none.fl_str_mv Becher, V.
Grigorieff, S.
author Becher, V.
author_facet Becher, V.
Grigorieff, S.
author_role author
author2 Grigorieff, S.
author2_role author
dc.subject.none.fl_str_mv Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Function evaluation
Probability
Problem solving
Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Theorem proving
topic Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Function evaluation
Probability
Problem solving
Algorithmic randomness
Kolmogorov complexity
Omega numbers
Random reals
Theorem proving
dc.description.none.fl_txt_mv 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.
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.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_Becher
url http://hdl.handle.net/20.500.12110/paper_03043975_v385_n1-3_p193_Becher
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Theor Comput Sci 2007;385(1-3):193-201
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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