Sophistication vs Logical Depth
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://repositorio.inesctec.pt/handle/123456789/7055 http://dx.doi.org/10.1007/s00224-016-9672-6 |
Resumo: | Sophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string that is shortest within some precision; the second can be defined as the minimal computation time of a program that is shortest within some precision. We show that the Busy Beaver function of the sophistication of a string exceeds its logical depth with logarithmically bigger precision, and that logical depth exceeds the Busy Beaver function of sophistication with logarithmically bigger precision. We also show that sophistication is unstable in its precision: constant variations can change its value by a linear term in the length of the string. |
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Sophistication vs Logical DepthSophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string that is shortest within some precision; the second can be defined as the minimal computation time of a program that is shortest within some precision. We show that the Busy Beaver function of the sophistication of a string exceeds its logical depth with logarithmically bigger precision, and that logical depth exceeds the Busy Beaver function of sophistication with logarithmically bigger precision. We also show that sophistication is unstable in its precision: constant variations can change its value by a linear term in the length of the string.2018-01-19T10:40:03Z2017-01-01T00:00:00Z2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://repositorio.inesctec.pt/handle/123456789/7055http://dx.doi.org/10.1007/s00224-016-9672-6engLuís Filipe AntunesBauwens,BSouto,AAndreia Sofia Teixeirainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-05-15T10:20:23Zoai:repositorio.inesctec.pt:123456789/7055Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:53:02.192167Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Sophistication vs Logical Depth |
title |
Sophistication vs Logical Depth |
spellingShingle |
Sophistication vs Logical Depth Luís Filipe Antunes |
title_short |
Sophistication vs Logical Depth |
title_full |
Sophistication vs Logical Depth |
title_fullStr |
Sophistication vs Logical Depth |
title_full_unstemmed |
Sophistication vs Logical Depth |
title_sort |
Sophistication vs Logical Depth |
author |
Luís Filipe Antunes |
author_facet |
Luís Filipe Antunes Bauwens,B Souto,A Andreia Sofia Teixeira |
author_role |
author |
author2 |
Bauwens,B Souto,A Andreia Sofia Teixeira |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Luís Filipe Antunes Bauwens,B Souto,A Andreia Sofia Teixeira |
description |
Sophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string that is shortest within some precision; the second can be defined as the minimal computation time of a program that is shortest within some precision. We show that the Busy Beaver function of the sophistication of a string exceeds its logical depth with logarithmically bigger precision, and that logical depth exceeds the Busy Beaver function of sophistication with logarithmically bigger precision. We also show that sophistication is unstable in its precision: constant variations can change its value by a linear term in the length of the string. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-01-01T00:00:00Z 2017 2018-01-19T10:40:03Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://repositorio.inesctec.pt/handle/123456789/7055 http://dx.doi.org/10.1007/s00224-016-9672-6 |
url |
http://repositorio.inesctec.pt/handle/123456789/7055 http://dx.doi.org/10.1007/s00224-016-9672-6 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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