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

Authors:
John M. Hitchcock;A. Pavan;N. V. Vinodchandran
Affiliations:
University of Wyoming, Department of Computer Science, 82071, Laramie, WY, USA;Iowa State University, Department of Computer Science, 50011, Ames, IA, USA;University of Nebraska-Lincoln, Department of Computer Science and Engineering, 68588, Lincoln, NE, USA
Venue:
Theory of Computing Systems
Year:
2008

Citing 0
Cited 5

SIGACT news complexity theory column 48

ACM SIGACT News
Comparing reductions to NP-complete sets

Information and Computation
Pushdown dimension

Theoretical Computer Science
Two open problems on effective dimension

CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Comparing reductions to NP-complete sets

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

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.