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Near-Optimal Separations of Certificate Complexity from Randomized and Quantum Query Complexity
We study how large the certificate complexity ${C}(f)$ of a total Boolean function can be relative to its randomized and quantum query complexities. We construct a total Boolean function $f$ whose randomized query complexity with one-sided error satisfies ${R}_1(f) = Θ(\sqrt{{C}(f)})$. This separati
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