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
Cited by
3 articles.
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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