Affiliation:
1. University of California, Berkeley
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.
Funder
Division of Graduate Education
Division of Computing and Communication Foundations
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On Worst-Case Learning in Relativized Heuristica;2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS);2022-02
2. Average-case hardness of NP from exponential worst-case hardness assumptions;Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing;2021-06-15
3. Distributed Point Functions and Their Applications;Advances in Cryptology – EUROCRYPT 2014;2014
4. A New View on Worst-Case to Average-Case Reductions for NP Problems;Lecture Notes in Computer Science;2014