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

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), AmbosSpies 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.

• Type: Journal
• Year: 2008
• Where: MST
• Authors: John M. Hitchcock, Aduri Pavan, N. V. Vinodchandran
• Keywords: Many-one Completeness Notions, MST 2008, NP-completeness Notions, Theoretical Computer Science