# The query complexity of certification

@article{Blanc2022TheQC, title={The query complexity of certification}, author={Guy Blanc and Caleb M. Koch and Jane Lange and Li-Yang Tan}, journal={Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing}, year={2022} }

We study the problem of certification: given queries to a function f : {0,1}n → {0,1} with certificate complexity ≤ k and an input x⋆, output a size-k certificate for f’s value on x⋆. For monotone functions, a classic local search algorithm of Angluin accomplishes this task with n queries, which we show is optimal for local search algorithms. Our main result is a new algorithm for certifying monotone functions with O(k8 logn) queries, which comes close to matching the information-theoretic…

## 4 Citations

### Certification with an NP Oracle

- Computer Science, MathematicsITCS
- 2023

This work considers certiﬁcation with stricter instance-wise guarantees, and obtains an optimal inapproximability ratio, adding to a small handful of problems in the higher levels of the polynomial hierarchy for which optimal inassistability is known.

### Logic-Based Explainability in Machine Learning

- Computer ScienceArXiv
- 2022

This paper overviews the ongoing research efforts on computing rigorous model-based explanations of ML models, including the actual definitions of explanations, the characterization of the complexity of computing explanations, and also how to make explanations interpretable for human decision makers, among others.

### A query-optimal algorithm for finding counterfactuals

- Computer ScienceICML
- 2022

A lower bound is proved of S ( f ) Ω (∆ f ( x ⋆ )) +Ω(log d ) on the query complexity of any algorithm, thereby showing that the guarantees of the algorithm are essentially optimal.

### An Optimal Algorithm for Certifying Monotone Functions

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2022

The algorithm makes O ( C ( f ) · 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.

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