Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

@inproceedings{Baleshzar2017OptimalUT,
  title={Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps},
  author={Roksana Baleshzar and Deeparnab Chakrabarty and Ramesh Krishnan S. Pallavoor and Sofya Raskhodnikova and Seshadhri Comandur},
  booktitle={ICALP},
  year={2017}
}
We study the problem of testing unateness of functions $f:\{0,1\}^d \to \mathbb{R}.$ We give a $O(\frac{d}{\epsilon} \cdot \log\frac{d}{\epsilon})$-query nonadaptive tester and a $O(\frac{d}{\epsilon})$-query adaptive tester and show that both testers are optimal for a fixed distance parameter $\epsilon$. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the dimension both for the adaptive and the nonadaptive case. Moreover… CONTINUE READING

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