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
Recommended Citation
Watson, T. (2012). Relativized Worlds without Worst-Case to Average-Case Reductions for NP. ACM Transactions on Computation Theory, 4 (3), 1-30. https://doi.org/10.1145/2355580.2355583
