Compressibility of infinite binary sequences

It is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov comp...

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Detalles Bibliográficos
Autores: Balcázar Navarro, José Luis|||0000-0003-4248-4528, Gavaldà Mestre, Ricard|||0000-0003-4736-7179, Hermo Huguet, Montserrat
Tipo de recurso: informe técnico
Fecha de publicación:1996
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/82554
Acceso en línea:https://hdl.handle.net/2117/82554
Access Level:acceso abierto
Palabra clave:Kolmogorov complexity
Infinite binary sequences
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Compressibility of infinite binary sequencesBalcázar Navarro, José Luis|||0000-0003-4248-4528Gavaldà Mestre, Ricard|||0000-0003-4736-7179Hermo Huguet, MontserratKolmogorov complexityInfinite binary sequencesÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaIt is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov complexity that are not polynomial-time computable. This motivates the study of several resource-bounded variants in search for a characterization, similar in spirit, of the polynomial-time computable sequences. We propose some definitions, based on Kobayashi's notion of compressibility, and compare them to both the standard resource-bounded Kolmogorov complexity of infinite strings, and the uniform complexity. Some nontrivial coincidences and disagreements are proved. The resource-unbounded case is also considered.19961996-02-0620162016-02-04reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/postscripthttps://hdl.handle.net/2117/82554reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/825542026-05-27T15:37:01Z
dc.title.none.fl_str_mv Compressibility of infinite binary sequences
title Compressibility of infinite binary sequences
spellingShingle Compressibility of infinite binary sequences
Balcázar Navarro, José Luis|||0000-0003-4248-4528
Kolmogorov complexity
Infinite binary sequences
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Compressibility of infinite binary sequences
title_full Compressibility of infinite binary sequences
title_fullStr Compressibility of infinite binary sequences
title_full_unstemmed Compressibility of infinite binary sequences
title_sort Compressibility of infinite binary sequences
dc.creator.none.fl_str_mv Balcázar Navarro, José Luis|||0000-0003-4248-4528
Gavaldà Mestre, Ricard|||0000-0003-4736-7179
Hermo Huguet, Montserrat
author Balcázar Navarro, José Luis|||0000-0003-4248-4528
author_facet Balcázar Navarro, José Luis|||0000-0003-4248-4528
Gavaldà Mestre, Ricard|||0000-0003-4736-7179
Hermo Huguet, Montserrat
author_role author
author2 Gavaldà Mestre, Ricard|||0000-0003-4736-7179
Hermo Huguet, Montserrat
author2_role author
author
dc.subject.none.fl_str_mv Kolmogorov complexity
Infinite binary sequences
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Kolmogorov complexity
Infinite binary sequences
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description It is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov complexity that are not polynomial-time computable. This motivates the study of several resource-bounded variants in search for a characterization, similar in spirit, of the polynomial-time computable sequences. We propose some definitions, based on Kobayashi's notion of compressibility, and compare them to both the standard resource-bounded Kolmogorov complexity of infinite strings, and the uniform complexity. Some nontrivial coincidences and disagreements are proved. The resource-unbounded case is also considered.
publishDate 1996
dc.date.none.fl_str_mv 1996
1996-02-06
2016
2016-02-04
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/82554
url https://hdl.handle.net/2117/82554
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/postscript
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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