Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All Classical Adversary Methods are Equivalent for Total Functions   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, $\text{fbs}(f) =
\Omega(\sqrt{n \cdot \text{bs}(f)})$.

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The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org