Theory of Computing Systems

, Volume 42, Issue 2, pp 131–142

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

  • John M. Hitchcock
  • A. Pavan
  • N. V. Vinodchandran

DOI: 10.1007/s00224-007-9000-2

Cite this article as:
Hitchcock, J.M., Pavan, A. & Vinodchandran, N.V. Theory Comput Syst (2008) 42: 131. doi:10.1007/s00224-007-9000-2


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.


Turing completenessMany-one completenessBi-immunityScaled dimension

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • John M. Hitchcock
    • 1
  • A. Pavan
    • 2
  • N. V. Vinodchandran
    • 3
  1. 1.Department of Computer ScienceUniversity of WyomingLaramieUSA
  2. 2.Department of Computer ScienceIowa State UniversityAmesUSA
  3. 3.Department of Computer Science and EngineeringUniversity of Nebraska-LincolnLincolnUSA