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

Authors:
Thomas Watson
Affiliations:
University of California, Berkeley
Venue:
ACM Transactions on Computation Theory (TOCT)
Year:
2012

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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 BPP∥NP. 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.