Almost every set in exponential time is P-Bi-Immune
A set A is P-bi-immune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of P-bi-immune languages in linear-exponential time (E). We prove that the class of P-bi-immune sets has measure 1 in E. This implies that "almost" every language in E is P...
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1991 |
| 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:2117/330405 |
| Acceso en línea: | https://hdl.handle.net/2117/330405 |
| Access Level: | acceso abierto |
| Palabra clave: | Computational complexity Complexitat computacional Àrees temàtiques de la UPC::Informàtica |
| Sumario: | A set A is P-bi-immune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of P-bi-immune languages in linear-exponential time (E). We prove that the class of P-bi-immune sets has measure 1 in E. This implies that "almost" every language in E is P-bi-immune. A bit further, we show that every p-random (pseudorandom) language is E-bi-immune. Regarding the existence of P-bi-immune sets in N P, we show that if N P does not have measure 0 in E, then N P contains a P-bi-immune set. Another consequence is that the class of =[super p sub m] -complete languages for E has measure 0 in E. In contrast, it is shown that in E, and even in REC, the class of P-bi-immune languages lacks the property of Baire (the Baire category analogue of Lebesgue measurability). |
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