所有经典Adjuster方法对全函数都是等价的
All Classical Adversary Methods are Equivalent for Total Functions
摘要：
我们发现，所有已知的经典对手的随机查询复杂度的下界是等价的总功能，并等于分数块敏感度$\text{fbs}(f)$。这包括Laplante和Magniez的Kolmogorov复杂性界限以及Aaronson早期的关系对手界限。这种等价性也意味着对于全函数，关系对手等价于一个更简单的下界，我们称之为秩1关系对手。对于部分功能，我们展示了无界分离之间的$\text{fbs}(f)$和其他对手的界限，以及对手之间的界限本身。我们还表明，对于部分功能，分数块灵敏度不能给出下限大于$\sqrt{n \cdot \text{bs}(f)}$，其中$n$是变量的数量和$\text{bs}(f)$是块灵敏度。然后，我们展示了一个部分函数$f$，它与这个上界$\text{fbs}(f) = Ω(\sqrt{n \cdot \text{bs}(f)})$相匹配。
英文摘要：
We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions, and are equal to the fractional block sensitivity $\text{fbs}(f)$. That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. This equivalence also implies that for total functions, the relational adversary is equivalent to a simpler lower bound, which we call rank-1 relational adversary. For partial functions, we show unbounded separations between $\text{fbs}(f)$ and other adversary bounds, as well as between the adversary bounds themselves. We also show that, for partial functions, fractional block sensitivity cannot give lower bounds larger than $\sqrt{n \cdot \text{bs}(f)}$, where $n$ is the number of variables and $\text{bs}(f)$ is the block sensitivity. Then we exhibit a partial function $f$ that matches this upper bound, $\text{fbs}(f) = Ω(\sqrt{n \cdot \text{bs}(f)})$.
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