Randomized query complexity can beat certificate complexity

@misc{bendavid2026randomized,
  title = {{Randomized query complexity can beat certificate complexity}},
  author = {Shalev Ben-David and Robin Kothari},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15063},
  eprint = {2609.15063},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15063},
}

TY  - UNPB
TI  - Randomized query complexity can beat certificate complexity
AU  - Shalev Ben-David
AU  - Robin Kothari
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15063
UR  - https://arxiv.org/abs/2609.15063
AB  - 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.
ER  -