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Partial Bi-immunity, Scaled Dimension, and NP-Completeness

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Abstract

The Turing and many-one completeness notions for NP have been previously separated under measure, genericity, and bi-immunity hypotheses on NP. The proofs of all these results rely on the existence of a language in NP with almost everywhere hardness.

In this paper we separate the same NP-completeness notions under a partial bi-immunity hypothesis that is weaker and only yields a language in NP that is hard to solve on most strings. This improves the results of Lutz and Mayordomo (Theoretical Computer Science, 1996), Ambos-Spies and Bentzien (Journal of Computer and System Sciences, 2000), and Pavan and Selman (Information and Computation, 2004). The proof of this theorem is a significant departure from previous work. We also use this theorem to separate the NP-completeness notions under a scaled dimension hypothesis on NP.

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Authors and Affiliations

  1. Department of Computer Science, University of Wyoming, Laramie, WY, 82071, USA

    John M. Hitchcock

  2. Department of Computer Science, Iowa State University, Ames, IA, 50011, USA

    A. Pavan

  3. Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA

    N. V. Vinodchandran

Authors
  1. John M. Hitchcock
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  2. A. Pavan
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  3. N. V. Vinodchandran
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Corresponding author

Correspondence to John M. Hitchcock.

Additional information

Part of this research was done while J.M. Hitchcock was visiting the University of Nebraska-Lincoln. Research of J.M. Hitchcock supported in part by NSF grant CCF-0515313.

Research of A. Pavan supported in part by NSF grants CCR-0344187 and CCF-0430807.

Research of N.V. Vinodchandran supported in part by NSF grant CCF-0430991 and University of Nebraska Layman Award.

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Hitchcock, J.M., Pavan, A. & Vinodchandran, N.V. Partial Bi-immunity, Scaled Dimension, and NP-Completeness. Theory Comput Syst 42, 131–142 (2008). https://doi.org/10.1007/s00224-007-9000-2

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