Feasible analysis, randomness, and base invariance

Autores
Figueira, Santiago; Nies, André
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that polynomial time randomness of a real number does not depend on the choice of a base for representing it. Our main tool is an ‘almost Lipschitz’ condition that we show for the cumulative distribution function associated to martingales with the savings property. Based on a result of Schnorr, we prove that for any base r, n⋅log2n-randomness in base r implies normality in base r, and that n4-randomness in base r implies absolute normality. Our methods yield a construction of an absolutely normal real number which is computable in polynomial time.
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Nies, André. The University Of Auckland; Nueva Zelanda
Materia
Base Invariance
Polynomial Time Randomness
Analysis
Normality
Martingales
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15637
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15637
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Feasible analysis, randomness, and base invarianceFigueira, SantiagoNies, AndréBase InvariancePolynomial Time RandomnessAnalysisNormalityMartingaleshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We show that polynomial time randomness of a real number does not depend on the choice of a base for representing it. Our main tool is an ‘almost Lipschitz’ condition that we show for the cumulative distribution function associated to martingales with the savings property. Based on a result of Schnorr, we prove that for any base r, n⋅log2n-randomness in base r implies normality in base r, and that n4-randomness in base r implies absolute normality. Our methods yield a construction of an absolutely normal real number which is computable in polynomial time.Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nies, André. The University Of Auckland; Nueva ZelandaSpringer2015-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15637Figueira, Santiago; Nies, André; Feasible analysis, randomness, and base invariance; Springer; Theory Of Computing Systems; 56; 3; 4-2015; 439-4641432-43501433-0490enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00224-013-9507-7info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00224-013-9507-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:41:33Zoai:ri.conicet.gov.ar:11336/15637instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-12 09:41:33.444CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Feasible analysis, randomness, and base invariance
title Feasible analysis, randomness, and base invariance
spellingShingle Feasible analysis, randomness, and base invariance
Figueira, Santiago
Base Invariance
Polynomial Time Randomness
Analysis
Normality
Martingales
title_short Feasible analysis, randomness, and base invariance
title_full Feasible analysis, randomness, and base invariance
title_fullStr Feasible analysis, randomness, and base invariance
title_full_unstemmed Feasible analysis, randomness, and base invariance
title_sort Feasible analysis, randomness, and base invariance
dc.creator.none.fl_str_mv Figueira, Santiago
Nies, André
author Figueira, Santiago
author_facet Figueira, Santiago
Nies, André
author_role author
author2 Nies, André
author2_role author
dc.subject.none.fl_str_mv Base Invariance
Polynomial Time Randomness
Analysis
Normality
Martingales
topic Base Invariance
Polynomial Time Randomness
Analysis
Normality
Martingales
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that polynomial time randomness of a real number does not depend on the choice of a base for representing it. Our main tool is an ‘almost Lipschitz’ condition that we show for the cumulative distribution function associated to martingales with the savings property. Based on a result of Schnorr, we prove that for any base r, n⋅log2n-randomness in base r implies normality in base r, and that n4-randomness in base r implies absolute normality. Our methods yield a construction of an absolutely normal real number which is computable in polynomial time.
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Nies, André. The University Of Auckland; Nueva Zelanda
description We show that polynomial time randomness of a real number does not depend on the choice of a base for representing it. Our main tool is an ‘almost Lipschitz’ condition that we show for the cumulative distribution function associated to martingales with the savings property. Based on a result of Schnorr, we prove that for any base r, n⋅log2n-randomness in base r implies normality in base r, and that n4-randomness in base r implies absolute normality. Our methods yield a construction of an absolutely normal real number which is computable in polynomial time.
publishDate 2015
dc.date.none.fl_str_mv 2015-04
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/11336/15637
Figueira, Santiago; Nies, André; Feasible analysis, randomness, and base invariance; Springer; Theory Of Computing Systems; 56; 3; 4-2015; 439-464
1432-4350
1433-0490
url http://hdl.handle.net/11336/15637
identifier_str_mv Figueira, Santiago; Nies, André; Feasible analysis, randomness, and base invariance; Springer; Theory Of Computing Systems; 56; 3; 4-2015; 439-464
1432-4350
1433-0490
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00224-013-9507-7
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00224-013-9507-7
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.976206

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