Optimal Testing for Planted Satisfiability Problems
Statistics Theory
2015-02-10 v3 Computational Complexity
Probability
Statistics Theory
Abstract
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the study of the number of satisfying assignments, for which we prove new results. We also address algorithmic issues, and give a computationally efficient test with optimal statistical performance. This result is compared to an average-case hypothesis on the hardness of refuting satisfiability of random formulas.
Cite
@article{arxiv.1401.2205,
title = {Optimal Testing for Planted Satisfiability Problems},
author = {Quentin Berthet},
journal= {arXiv preprint arXiv:1401.2205},
year = {2015}
}