Abstract
We prove that if for some ε > 0, NP contains a set that is DTIME(2(Formuls Present))-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.
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CITATION STYLE
Pavan, A., & Selman, A. L. (2002). Bi-immunity separates strong NP-completeness notions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2285, pp. 408–418). Springer Verlag. https://doi.org/10.1007/3-540-45841-7_33
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