ECCC-Report TR20-027https://eccc.weizmann.ac.il/report/2020/027Comments and Revisions published for TR20-027en-usWed, 26 Feb 2020 21:45:16 +0200
Paper TR20-027
| The Power of Many Samples in Query Complexity |
Mika Göös,
Andrew Bassilakis,
Andrew Drucker,
Li-Yang Tan,
Lunjia Hu,
Weiyun Ma
https://eccc.weizmann.ac.il/report/2020/027The randomized query complexity $R(f)$ of a boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is famously characterized (via Yao's minimax) by the least number of queries needed to distinguish a distribution $D_0$ over $0$-inputs from a distribution $D_1$ over $1$-inputs, maximized over all pairs $(D_0,D_1)$. We ask: Does this task become easier if we allow query access to infinitely many samples from either $D_0$ or $D_1$? We show the answer is no: There exists a hard pair $(D_0,D_1)$ such that distinguishing $D_0^\infty$ from $D_1^\infty$ requires $\Theta(R(f))$ many queries. As an application, we show that for any composed function $f\circ g$ we have $R(f\circ g) \geq \Omega(\mathrm{fbs}(f)R(g))$ where $\mathrm{fbs}$ denotes fractional block sensitivity.Wed, 26 Feb 2020 21:45:16 +0200https://eccc.weizmann.ac.il/report/2020/027