Title :
Relativized Separations of Worst-Case and Average-Case Complexities for NP
Author :
Impagliazzo, Russell
Author_Institution :
IAS, U.C. San Diego, San Diego, CA, USA
Abstract :
Non-relativization of complexity issues can be interpreted as showing that these issues cannot be resolved by "black-box" techniques. We show that the assumption DistNP ⊆ AvgP does not imply that NP ⊆ BPP by relativizing techniques. More precisely, we give an oracle relative to which the assumption holds but the conclusion fails. Moreover, relative to our oracle, there are problems in NP ∩ Co-NP that require exponential circuit complexity. We also give an alternate version where DistNP ⊆ AvgP is true, but a problem in the second level of the polynomial hierarchy is hard on the uniform distribution.
Keywords :
circuit complexity; NP-hard problem; average case complexity; black box techniques; exponential circuit complexity; polynomial hierarchy; uniform distribution; worst case relativized separation; Cryptography; Error probability; Heuristic algorithms; NP-complete problem; Polynomials; Probabilistic logic; P vs. NP; average-case complexity; heuristica; oracles; relativization;
Conference_Titel :
Computational Complexity (CCC), 2011 IEEE 26th Annual Conference on
Conference_Location :
San Jose, CA
Print_ISBN :
978-1-4577-0179-5
Electronic_ISBN :
1093-0159
DOI :
10.1109/CCC.2011.34
