Bi-Immunity Separates Strong NP-Completeness Notions

We prove that if for some > 0, NP contains a set that is DTIME(2n )-bi-immune, then NP contains a set that is 2-Turing complete for NP (hence 3-truth-table complete) but not 1-truth-table complete for NP. Thus this hypothesis implies a strong separation of completeness notions for NP. Lutz and Mayordomo [LM96] and Ambos-Spies and Bentzien [ASB00] previously obtained the same consequence using strong hypotheses involving resource-bounded measure and/or category theory. Our hypothesis is weaker and involves no assumptions about stochastic properties of NP.

• Type: Journal
• Year: 2002
• Where: ECCC
• Authors: Aduri Pavan, Alan L. Selman
• Keywords: Completeness Notions, ECCC 2002, Strong Hypotheses, Strong Separation