Abstract:
We prove that if for some epsilon > 0 NP contains a set that is DTIME(2^{n^{epsilon}})-bi-immune, then NP contains a set that 2-Turing complete for NP but not 1-truth-table complete for NP. Lutz and Mayordomo (LM96) and Ambos-Spies and Bentzien (AB00) previously obtained the same consequence using strong hypotheses involving resource-bounded measure and.or category theory.