Cook Versus Karp-Levin: Separating Completeness Notions if NP Is not Small (Extended 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 ≤ T P -complete (“Cook complete”), but not ≤ m P -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.

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