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...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1992 |
| 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:2117/369817 |
| Acceso en línea: | https://hdl.handle.net/2117/369817 |
| Access Level: | acceso abierto |
| Palabra clave: | Computational complexity Complexitat computacional Àrees temàtiques de la UPC::Informàtica |
| Sumario: | 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. |
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