Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimal Algorithm for Certifying Monotone Functions   Given query access to a monotone function $f\colon\{0,1\}^n\to\{0,1\}$ with
certificate complexity $C(f)$ and an input $x^{\star}$, we design an algorithm
that outputs a size-$C(f)$ subset of $x^{\star}$ certifying the value of
$f(x^{\star})$. Our algorithm makes $O(C(f) \cdot \log n)$ queries to $f$,
which matches the information-theoretic lower bound for this problem and
resolves the concrete open question posed in the STOC '22 paper of Blanc, Koch,
Lange, and Tan [BKLT22].
  We extend this result to an algorithm that finds a size-$2C(f)$ certificate
for a real-valued monotone function with $O(C(f) \cdot \log n)$ queries. We
also complement our algorithms with a hardness result, in which we show that
finding the shortest possible certificate in $x^{\star}$ may require
$\Omega\left(\binom{n}{C(f)}\right)$ queries in the worst case.

11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas