## Cook versus Karp-Levin: Separating Completeness Notions If NP Is Not Small (1992)

Venue: | Theoretical Computer Science |

Citations: | 59 - 14 self |

### BibTeX

@INPROCEEDINGS{Lutz92cookversus,

author = {Jack H. Lutz and Elvira Mayordomo},

title = {Cook versus Karp-Levin: Separating Completeness Notions If NP Is Not Small},

booktitle = {Theoretical Computer Science},

year = {1992},

pages = {415--426},

publisher = {Springer-Verlag}

}

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### 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 show n that there is a language that is P T -complete ("Cook complete "), but not P m -complete ("Karp-Levin complete"), for NP. This conclusion, widely believed to be true, is not known to follow from P 6= 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 6= NE, and the existence of NP search problems that are not reducible to the corresponding decision problems. This research was supported in part by National Science Foundation Grant CCR9157382, with matching funds from Rockwell International. 1 Introduction The NP-completeness of decision problems has...