Normal numbers and finite automata

Autores
Becher, Veronica Andrea; Heiber, Pablo Ariel
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input–output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov’s theorem on the preservation of normality on subsequences selected by finite automata.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Heiber, Pablo Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Normal Numbers
Finite State Automata
Agafonov Theorem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15850
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15850
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network_name_str CONICET Digital (CONICET)
spelling Normal numbers and finite automataBecher, Veronica AndreaHeiber, Pablo ArielNormal NumbersFinite State AutomataAgafonov Theoremhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input–output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov’s theorem on the preservation of normality on subsequences selected by finite automata.Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Heiber, Pablo Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2013-03info: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/11336/15850Becher, Veronica Andrea; Heiber, Pablo Ariel; Normal numbers and finite automata; Elsevier Science; Theoretical Computer Science; 477; 3-2013; 109-1160304-3975enginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2013.01.019info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304397513000698?via%3Dihubinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:35:37Zoai:ri.conicet.gov.ar:11336/15850instacron: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:34982025-11-05 10:35:37.428CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Normal numbers and finite automata
title Normal numbers and finite automata
spellingShingle Normal numbers and finite automata
Becher, Veronica Andrea
Normal Numbers
Finite State Automata
Agafonov Theorem
title_short Normal numbers and finite automata
title_full Normal numbers and finite automata
title_fullStr Normal numbers and finite automata
title_full_unstemmed Normal numbers and finite automata
title_sort Normal numbers and finite automata
dc.creator.none.fl_str_mv Becher, Veronica Andrea
Heiber, Pablo Ariel
author Becher, Veronica Andrea
author_facet Becher, Veronica Andrea
Heiber, Pablo Ariel
author_role author
author2 Heiber, Pablo Ariel
author2_role author
dc.subject.none.fl_str_mv Normal Numbers
Finite State Automata
Agafonov Theorem
topic Normal Numbers
Finite State Automata
Agafonov Theorem
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 give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input–output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov’s theorem on the preservation of normality on subsequences selected by finite automata.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Heiber, Pablo Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input–output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov’s theorem on the preservation of normality on subsequences selected by finite automata.
publishDate 2013
dc.date.none.fl_str_mv 2013-03
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/11336/15850
Becher, Veronica Andrea; Heiber, Pablo Ariel; Normal numbers and finite automata; Elsevier Science; Theoretical Computer Science; 477; 3-2013; 109-116
0304-3975
url http://hdl.handle.net/11336/15850
identifier_str_mv Becher, Veronica Andrea; Heiber, Pablo Ariel; Normal numbers and finite automata; Elsevier Science; Theoretical Computer Science; 477; 3-2013; 109-116
0304-3975
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2013.01.019
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304397513000698?via%3Dihub
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 13.087074

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