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 BPPpath. The latter class contains P ∥NP and captures the power of randomized computations conditioned on efficiently testable events. We also handle reductions from NP to the polynomial-time hierarchy and beyond, under restrictions on the number of queries the reductions can make. © 2010 Springer-Verlag.
Publication Title
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Recommended Citation
Watson, T. (2010). Relativized worlds without worst-case to average-case reductions for NP. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6302 LNCS, 752-765. https://doi.org/10.1007/978-3-642-15369-3_56
