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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/15850
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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 Técnicas2025-09-03T10:06:32Zoai: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:34982025-09-03 10:06:32.475CONICET 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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1842269962730733568 |
score |
13.13397 |