Yuval Filmus, Noam Lifshitz, Dor Minzer and Elchanan Mossel

STOC 2020

If an $n$-bit Boolean function $f$ satisfies $f(x \land y) = f(x) \land f(y)$ then it is either constant or an AND. Nehama showed that if this equation holds most of the time, then $f$ is close to a constant or an AND. However, his bounds deteriorate with $n$.

We give a bound which is independent of $n$. This can be seen as a one-sided version of linearity testing, that should perhaps be called *oligarchy testing*.

@inproceedings{FLMM2020,

author = {Yuval Filmus and Noam Lifshitz and Dor Minzer and Elchanan Mossel},

title = {{AND} testing and robust judgement aggregation},

booktitle = {52nd ACM Symposium on Theory of Computing (STOC'20)},

year = {2020}

}

copy to clipboard
author = {Yuval Filmus and Noam Lifshitz and Dor Minzer and Elchanan Mossel},

title = {{AND} testing and robust judgement aggregation},

booktitle = {52nd ACM Symposium on Theory of Computing (STOC'20)},

year = {2020}

}