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» On Worst-Case to Average-Case Reductions for NP Problems
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FOCS
2003
IEEE
14 years 4 months ago
On Worst-Case to Average-Case Reductions for NP Problems
We show that if an NP-complete problem has a non-adaptive self-corrector with respect to a samplable distribution then coNP is contained in NP/poly and the polynomial hierarchy co...
Andrej Bogdanov, Luca Trevisan
STACS
2010
Springer
14 years 5 months ago
Collapsing and Separating Completeness Notions under Average-Case and Worst-Case Hypotheses
This paper presents the following results on sets that are complete for NP. (i) If there is a problem in NP that requires 2nΩ(1) time at almost all lengths, then every many-one N...
Xiaoyang Gu, John M. Hitchcock, Aduri Pavan
APPROX
2007
Springer
104views Algorithms» more  APPROX 2007»
14 years 5 months ago
Worst-Case to Average-Case Reductions Revisited
Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomial-time samplable distribution (e.g., the uniform distribution) and...
Dan Gutfreund, Amnon Ta-Shma
FOCS
2004
IEEE
14 years 2 months ago
Worst-Case to Average-Case Reductions Based on Gaussian Measures
We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost line...
Daniele Micciancio, Oded Regev
APPROX
2010
Springer
132views Algorithms» more  APPROX 2010»
14 years 13 days ago
Relativized Worlds without Worst-Case to Average-Case Reductions for NP
We prove that relative to an oracle, there is no worst-case to average-case reduction for NP. We also handle classes that are somewhat larger than NP, as well as worst-case to err...
Thomas Watson