Normal numbers and finite automata

Autores
Becher, V.; Heiber, P.A.
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.© 2012 Elsevier B.V. All rights reserved.
Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Heiber, P.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Theor Comput Sci 2013;477:109-116
Materia
Finite state transducers
Finite-state
Input-output
Lossless
Normal numbers
Output transition
Real number
Number theory
Theorem proving
Finite automata
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_v477_n_p109_Becher
Acceder
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oai_identifier_str paperaa:paper_03043975_v477_n_p109_Becher
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Normal numbers and finite automataBecher, V.Heiber, P.A.Finite state transducersFinite-stateInput-outputLosslessNormal numbersOutput transitionReal numberNumber theoryTheorem provingFinite automataWe 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.© 2012 Elsevier B.V. All rights reserved.Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Heiber, P.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2013info: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_v477_n_p109_BecherTheor Comput Sci 2013;477:109-116reponame: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/ar2025-09-04T09:48:44Zpaperaa:paper_03043975_v477_n_p109_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 09:48:45.817Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Normal numbers and finite automata
title Normal numbers and finite automata
spellingShingle Normal numbers and finite automata
Becher, V.
Finite state transducers
Finite-state
Input-output
Lossless
Normal numbers
Output transition
Real number
Number theory
Theorem proving
Finite automata
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, V.
Heiber, P.A.
author Becher, V.
author_facet Becher, V.
Heiber, P.A.
author_role author
author2 Heiber, P.A.
author2_role author
dc.subject.none.fl_str_mv Finite state transducers
Finite-state
Input-output
Lossless
Normal numbers
Output transition
Real number
Number theory
Theorem proving
Finite automata
topic Finite state transducers
Finite-state
Input-output
Lossless
Normal numbers
Output transition
Real number
Number theory
Theorem proving
Finite automata
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.© 2012 Elsevier B.V. All rights reserved.
Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Heiber, P.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; 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.© 2012 Elsevier B.V. All rights reserved.
publishDate 2013
dc.date.none.fl_str_mv 2013
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_v477_n_p109_Becher
url http://hdl.handle.net/20.500.12110/paper_03043975_v477_n_p109_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 2013;477:109-116
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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