Finite-State Independence

Autores
Becher, Veronica Andrea; Carton, Olivier; Heiber, Pablo Ariel
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we introduce a notion of independence based on finite-state automata: two infinite words are independent if no one helps to compress the other using one-to-one finite-state transducers with auxiliary input. We prove that, as expected, the set of independent pairs of infinite words has Lebesgue measure 1. We show that the join of two independent normal words is normal. However, the independence of two normal words is not guaranteed if we just require that their join is normal. To prove this we construct a normal word x1x2x3… where x2n = xn for every n. This construction has its own interest.
Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Carton, Olivier. Université Paris Diderot - Paris 7; Francia
Fil: Heiber, Pablo Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Materia
Finite-State Automata
Independence
Infinite Sequences
Normal Sequences
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:11336/60112
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/60112
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite-State IndependenceBecher, Veronica AndreaCarton, OlivierHeiber, Pablo ArielFinite-State AutomataIndependenceInfinite SequencesNormal Sequenceshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1In this work we introduce a notion of independence based on finite-state automata: two infinite words are independent if no one helps to compress the other using one-to-one finite-state transducers with auxiliary input. We prove that, as expected, the set of independent pairs of infinite words has Lebesgue measure 1. We show that the join of two independent normal words is normal. However, the independence of two normal words is not guaranteed if we just require that their join is normal. To prove this we construct a normal word x1x2x3… where x2n = xn for every n. This construction has its own interest.Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Carton, Olivier. Université Paris Diderot - Paris 7; FranciaFil: Heiber, Pablo Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaSpringer2018-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60112Becher, Veronica Andrea; Carton, Olivier; Heiber, Pablo Ariel; Finite-State Independence; Springer; Theory Of Computing Systems; 62; 7; 10-2018; 1555-15721432-4350CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00224-017-9821-6info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00224-017-9821-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:45:51Zoai:ri.conicet.gov.ar:11336/60112instacron: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 09:45:51.783CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite-State Independence
title Finite-State Independence
spellingShingle Finite-State Independence
Becher, Veronica Andrea
Finite-State Automata
Independence
Infinite Sequences
Normal Sequences
title_short Finite-State Independence
title_full Finite-State Independence
title_fullStr Finite-State Independence
title_full_unstemmed Finite-State Independence
title_sort Finite-State Independence
dc.creator.none.fl_str_mv Becher, Veronica Andrea
Carton, Olivier
Heiber, Pablo Ariel
author Becher, Veronica Andrea
author_facet Becher, Veronica Andrea
Carton, Olivier
Heiber, Pablo Ariel
author_role author
author2 Carton, Olivier
Heiber, Pablo Ariel
author2_role author
author
dc.subject.none.fl_str_mv Finite-State Automata
Independence
Infinite Sequences
Normal Sequences
topic Finite-State Automata
Independence
Infinite Sequences
Normal Sequences
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we introduce a notion of independence based on finite-state automata: two infinite words are independent if no one helps to compress the other using one-to-one finite-state transducers with auxiliary input. We prove that, as expected, the set of independent pairs of infinite words has Lebesgue measure 1. We show that the join of two independent normal words is normal. However, the independence of two normal words is not guaranteed if we just require that their join is normal. To prove this we construct a normal word x1x2x3… where x2n = xn for every n. This construction has its own interest.
Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Carton, Olivier. Université Paris Diderot - Paris 7; Francia
Fil: Heiber, Pablo Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
description In this work we introduce a notion of independence based on finite-state automata: two infinite words are independent if no one helps to compress the other using one-to-one finite-state transducers with auxiliary input. We prove that, as expected, the set of independent pairs of infinite words has Lebesgue measure 1. We show that the join of two independent normal words is normal. However, the independence of two normal words is not guaranteed if we just require that their join is normal. To prove this we construct a normal word x1x2x3… where x2n = xn for every n. This construction has its own interest.
publishDate 2018
dc.date.none.fl_str_mv 2018-10
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/11336/60112
Becher, Veronica Andrea; Carton, Olivier; Heiber, Pablo Ariel; Finite-State Independence; Springer; Theory Of Computing Systems; 62; 7; 10-2018; 1555-1572
1432-4350
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60112
identifier_str_mv Becher, Veronica Andrea; Carton, Olivier; Heiber, Pablo Ariel; Finite-State Independence; Springer; Theory Of Computing Systems; 62; 7; 10-2018; 1555-1572
1432-4350
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00224-017-9821-6
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00224-017-9821-6
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
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
_version_ 1842268758327951360
score 13.13397

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