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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/15637
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:50:30Zoai: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:34982025-09-29 09:50:30.893CONICET 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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1844613556309327872 |
score |
13.070432 |