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原文摘要

In 2010, Seshadhri and Vondrák asked: is submodularity testable? For functions $f : \{ 0, 1 \}^n \to \mathbb{R}$, they gave a tester that makes $2^{O(\sqrt{n} \log n)}$ queries. We show that every tester, even an adaptive one with two-sided error, must make $2^{Ω(\sqrt{n})}$ queries, thereby concluding: submodularity is barely testable.