Randomized query complexity can beat certificate complexity

View PDF HTML (experimental) 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. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors. 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. Comments: 6 pages Subjects: Computational Complexity (cs.CC); Quantum Physics (quant-ph) Cite as: arXiv:2609.15063 [cs.CC] (or arXiv:2609.15063v1 [cs.CC] for this version) https://doi.org/10.48550/arXiv.2609.15063 arXiv-issued DOI via DataCite Submission history From: Robin Kothari [view email] [v1] Mon, 14 Sep 2026 05:29:42 UTC (9 KB)