Detection of Planted Solutions for Flat Satisfiability Problems
Statistics Theory
2019-03-07 v2 Computational Complexity
Machine Learning
Statistics Theory
Abstract
We study the detection problem of finding planted solutions in random instances of flat satisfiability problems, a generalization of boolean satisfiability formulas. We describe the properties of random instances of flat satisfiability, as well of the optimal rates of detection of the associated hypothesis testing problem. We also study the performance of an algorithmically efficient testing procedure. We introduce a modification of our model, the light planting of solutions, and show that it is as hard as the problem of learning parity with noise. This hints strongly at the difficulty of detecting planted flat satisfiability for a wide class of tests.
Cite
@article{arxiv.1502.06144,
title = {Detection of Planted Solutions for Flat Satisfiability Problems},
author = {Quentin Berthet and Jordan S. Ellenberg},
journal= {arXiv preprint arXiv:1502.06144},
year = {2019}
}