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Bi-Immunity Separates Strong NP-Completeness Notions

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

We prove that if for some ε > 0, NP contains a set that is DTIME(2nε)-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.

Work done while the author was at University at Buffalo.

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Author information

Authors and Affiliations

  1. NEC Research Institute, 4 Independence way, 08540, Princeton, NJ

    A. Pavan

  2. Department of Computer Science and Engineering, University at Buffalo, 14260, Buffalo, NY

    Alan L. Selman

Authors
  1. A. Pavan
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  2. Alan L. Selman
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Pavan, A., Selman, A.L. (2002). Bi-Immunity Separates Strong NP-Completeness Notions. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_33

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  • DOI: https://doi.org/10.1007/3-540-45841-7_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

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