AND testing and robust judgement aggregation

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.


 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}
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