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 errorlessaverage-case reductions. In fact, we prove that relative to an oracle, there is no worst-case to errorless-average-case reduction from NP to BPPNP . We also handle reductions from NP to the polynomial-time hierarchy and beyond, under restrictions on the number of queries the reductions can make.

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: Thomas Watson
• Keywords: Algorithms, APPROX 2010, Average-case Reduction, Errorlessaverage-case Reductions, Worst-case