Tech article
Randomized query complexity can beat certificate complexity
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Hacker News | Sep 15, 2026 | porridgeraisin
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Abstract: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. The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal. Computational Complexity (cs.
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