Cook versus Karp-Levin : separating completeness notions if NP is not small
Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is shown that there is a language that is =PT-complete ("Cook complete"), but not =Pm-complete ("Karp-Levin complete"), for NP. This conclusion...
| Authors: | , |
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| Format: | report |
| Publication Date: | 1992 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/370683 |
| Online Access: | https://hdl.handle.net/2117/370683 |
| Access Level: | Open access |
| Keyword: | Computational complexity Complexitat computacional Àrees temàtiques de la UPC::Informàtica |
| Summary: | Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is shown that there is a language that is =PT-complete ("Cook complete"), but not =Pm-complete ("Karp-Levin complete"), for NP. This conclusion, widely believed to be true, is not known to follow from P ¿ NP or other traditional complexity-theoretic hypotheses. Evidence is presented that "NP does not have p-measure 0" is a reasonable hypothesis with many credible consequences. Additional such consequences proven here include the separation of many truthtable reducibilities in NP (e.g., k queries versus k + 1 queries), the class separation E ¿ NE, and the existence of NP search problems that are not reducible to the corresponding decision problems. |
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