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### Paper:

TR14-126 | 9th October 2014 20:08

#### Separating Cook Completeness from Karp-Levin Completeness under a Worst-Case Hardness Hypothesis

TR14-126
Authors: Debasis Mandal, A. Pavan, Rajeswari Venugopalan
Publication: 10th October 2014 12:45
We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a {\em worst-case} hardness hypothesis. Our hypothesis asserts the existence of a non-deterministic, double-exponential time machine that runs in time $O(2^{2^{n^c}})$ (for some $c > 1$) accepting $\Sigma^*$ whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time $O(2^{2^{\beta 2^{n^c}}})$ (for some $\beta > 0$).