Problem
Research questions and friction points this paper is trying to address.
Randomized Query Complexity
Certificate Complexity
Boolean Function
Randomized query complexity can beat certificate complexity
🤖 AI Summary
本文通过构造一个函数，证明了随机查询复杂度可以显著小于证书复杂度，并且该函数的量子查询复杂度也得到了优化。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
randomized query complexity
certificate complexity
quantum query complexity
🔎 Similar Papers
2024-01-25arXiv.orgCitations: 0
