Bi-Immunity Separates Strong NP-Completeness Notions

Authors:
Aduri Pavan;Alan L. Selman
Affiliations:
-;-
Venue:
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Year:
2002

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Abstract

We prove that if for some 驴 0, NP contains a set that is DTIME(2n驴)-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.