Logarithmic space counting classes
We consider the logarithmic space counting classes #L, opt-L, and span-L, which are defined analogously to their polynomial time counterparts. We obtain complete functions for these three classes in terms of graphs and finite automata. We show that #L and opt-L are both contained in NCsuper2, but th...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1990 |
| 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:2117/192752 |
| Acceso en línea: | https://hdl.handle.net/2117/192752 |
| Access Level: | acceso abierto |
| Palabra clave: | Logarithms Polynomials Logaritmes Polinomis Àrees temàtiques de la UPC::Informàtica |
| Sumario: | We consider the logarithmic space counting classes #L, opt-L, and span-L, which are defined analogously to their polynomial time counterparts. We obtain complete functions for these three classes in terms of graphs and finite automata. We show that #L and opt-L are both contained in NCsuper2, but that, surprisingly, span-L seems to be a much harder counting class than #L and opt-L. We demonstrate that span-L-functions can be computed in polynomial time if and only if P = NP = PH = P(#P), i.e. iff the class P(#P) and all the classes of the polynomial time hierarchy are contained in P. This result follows from the fact that span-L and #P are very similar: span-L C #P, and any function in #P can be represented as a subtraction of two functions in span-L. Nevertheless, #P C span-L would imply NL = P = NP. We furthermore investigate various restrictions of the classes opt-L and span-L, and show, e.g., that if opt-L coincides with one of its restricted versions, then L = NL follows. |
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