Abstract
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 truth-table 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.
This author's research was supported in part by National Science Foundation Grant CCR-9157382, with matching funds from Rockwell International and Microware Systems Corporation.
This author's research, performed while visiting Iowa State University, was supported in part by the ESPRIT EC project 3075 (ALCOM), in part by National Science Foundation Grant CCR-9157382, and in part by Spanish Government Grant FPI PN90.
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Lutz, J.H., Mayordomo, E. (1994). Cook versus Karp-Levin: Separating completeness notions if NP is not small. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_159
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