Measuring in PSPACE
Results of the kind "Almost every oracle in exponential space separates P from NP" or "Almost every set in exponential time is P-bi-immune" can be precisely formulated via a new approach in Structural Complexity recently introduced by Lutz. He defines a resource bounded measure i...
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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:2117/369631 |
| Acceso en línea: | https://hdl.handle.net/2117/369631 |
| Access Level: | acceso abierto |
| Palabra clave: | Computational complexity Complexitat computacional Àrees temàtiques de la UPC::Informàtica |
| Sumario: | Results of the kind "Almost every oracle in exponential space separates P from NP" or "Almost every set in exponential time is P-bi-immune" can be precisely formulated via a new approach in Structural Complexity recently introduced by Lutz. He defines a resource bounded measure in exponential time and space classes that generalizes Lebesgue measure, a powerful mathematical tool. This resource bounded measure is mainly used to distinguish between "big" and "small" classes, and to investigate the properties that hold for "typical" languages in a class. We investigate here the possibility of extending this resource bounded measure to other classes, mainly PSPACE. We prove here that the natural candidate of resource bound for measuring in PSPACE is not valid unless some unlikely consequences are true. We also obtain a way of measuring in PSPACE that does not have as many properties as resource bounded measure in bigger classes. |
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