Collapsing and Separating Completeness Notions Under Average-Case and Worst-Case Hypotheses

被引：2

作者：

Gu, Xiaoyang ^{[1
]}

Hitchcock, John M. ^{[2
]}

Pavan, A. ^{[3
]}

机构：

[1] Linked Corp, Mountain View, CA USA

[2] Univ Wyoming, Dept Comp Sci, Laramie, WY 82071 USA

[3] Iowa State Univ, Dept Comp Sci, Ames, IA USA

来源：

THEORY OF COMPUTING SYSTEMS | 2012年 / 51卷 / 02期

基金：

美国国家科学基金会;

关键词：

Computational complexity; NP-completeness; Turing completeness; Length-increasing reductions; Approximable sets; PSEUDORANDOM GENERATORS; BI-IMMUNITY; NP; DENSITY;

D O I：

10.1007/s00224-011-9365-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper presents the following results on sets that are complete for NP. (i) If there is a problem in NP that requires 2(n Omega(1)) time at almost all lengths, then every many-one NP-complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. (ii) If there is a problem in co-NP that cannot be solved by polynomial-size nondeterministic circuits, then every many-one NP-complete set is complete under length-increasing reductions that are computed by polynomial-size circuits. (iii) If there exist a one-way permutation that is secure against subexponential-size circuits and there is a hard tally language in NP boolean AND co-NP, then there is a Turing complete language for NP that is not many-one complete.

引用

页码：248 / 265

页数：18

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