Title

Relativized Worlds without Worst-Case to Average-Case Reductions for NP

Abstract

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 errorless-average-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 strong restrictions on the number of queries the reductions can make. © 2012, ACM. All rights reserved.

Publication Title

ACM Transactions on Computation Theory

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