Measure, stochasticity and the density of hard languages

Ogiwara and Watanabe have recently shown that the hypothesis P ¿ NP implies that no (polynomially) sparse language is =Pbtt-hard for NP. Their technique does not appear to allow significant relaxation of either the query bound or the sparseness criterion. It is shown here that a stronger hypothesis...

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Detalhes bibliográficos
Autores: Lutz, Jack H., Mayordomo, Elvira
Tipo de documento: relatório científico
Data de publicação:1992
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/369817
Acesso em linha:https://hdl.handle.net/2117/369817
Access Level:Acceso aberto
Palavra-chave:Computational complexity
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica
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spelling Measure, stochasticity and the density of hard languagesLutz, Jack H.Mayordomo, ElviraComputational complexityComplexitat computacionalÀrees temàtiques de la UPC::InformàticaOgiwara and Watanabe have recently shown that the hypothesis P ¿ NP implies that no (polynomially) sparse language is =Pbtt-hard for NP. Their technique does not appear to allow significant relaxation of either the query bound or the sparseness criterion. It is shown here that a stronger hypothesis -- namely, that NP does not have measure 0 in exponential time -- implies the stronger conclusion that, for every real a < 1, every =Pna-tt-hard language for NP is (exponentially) dense. The proof of this fact also yields two absolute results (not involving unproven hypotheses) concerning the structure of exponential fime: First, almost every language decidable in exponential time has a stochasticity property, ensurig that it is statistically unpredictable by feasible deterministic algorithms, even with linear nonuniform advice. Second, for a < 1, only a measure 0 subset of the languages decidable in exponential time are =Pna-tt-reducible to languages that are not exponentially dense.19921992-03-1620222022-07-07reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/369817reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3698172026-05-27T15:37:01Z
dc.title.none.fl_str_mv Measure, stochasticity and the density of hard languages
title Measure, stochasticity and the density of hard languages
spellingShingle Measure, stochasticity and the density of hard languages
Lutz, Jack H.
Computational complexity
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica
title_short Measure, stochasticity and the density of hard languages
title_full Measure, stochasticity and the density of hard languages
title_fullStr Measure, stochasticity and the density of hard languages
title_full_unstemmed Measure, stochasticity and the density of hard languages
title_sort Measure, stochasticity and the density of hard languages
dc.creator.none.fl_str_mv Lutz, Jack H.
Mayordomo, Elvira
author Lutz, Jack H.
author_facet Lutz, Jack H.
Mayordomo, Elvira
author_role author
author2 Mayordomo, Elvira
author2_role author
dc.subject.none.fl_str_mv Computational complexity
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica
topic Computational complexity
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica
description Ogiwara and Watanabe have recently shown that the hypothesis P ¿ NP implies that no (polynomially) sparse language is =Pbtt-hard for NP. Their technique does not appear to allow significant relaxation of either the query bound or the sparseness criterion. It is shown here that a stronger hypothesis -- namely, that NP does not have measure 0 in exponential time -- implies the stronger conclusion that, for every real a < 1, every =Pna-tt-hard language for NP is (exponentially) dense. The proof of this fact also yields two absolute results (not involving unproven hypotheses) concerning the structure of exponential fime: First, almost every language decidable in exponential time has a stochasticity property, ensurig that it is statistically unpredictable by feasible deterministic algorithms, even with linear nonuniform advice. Second, for a < 1, only a measure 0 subset of the languages decidable in exponential time are =Pna-tt-reducible to languages that are not exponentially dense.
publishDate 1992
dc.date.none.fl_str_mv 1992
1992-03-16
2022
2022-07-07
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/369817
url https://hdl.handle.net/2117/369817
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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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