Quadratic Maps Are Hard to Sample

Author:

Viola Emanuele1

Affiliation:

1. Northeastern University, Boston, MA

Abstract

This note proves the existence of a quadratic GF(2) map p : {0, 1} n → {0, 1} such that no constant-depth circuit of size poly( n ) can sample the distribution ( u , p ( u )) for uniform u .

Funder

National Science Foundation

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Theory and Mathematics,Theoretical Computer Science

Reference10 articles.

Cited by 3 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. Locality Bounds for Sampling Hamming Slices;Proceedings of the 56th Annual ACM Symposium on Theory of Computing;2024-06-10

2. A Lower Bound for Sampling Disjoint Sets;ACM Transactions on Computation Theory;2020-07-23

3. Sampling Lower Bounds: Boolean Average-Case and Permutations;SIAM Journal on Computing;2020-01

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