All reports by Author Christopher Williamson:

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TR19-082
| 2nd June 2019
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Andrej Bogdanov, Nikhil Mande, Justin Thaler, Christopher Williamson#### Approximate degree, secret sharing, and concentration phenomena

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TR15-182
| 13th November 2015
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Andrej Bogdanov, Yuval Ishai, Emanuele Viola, Christopher Williamson#### Bounded Indistinguishability and the Complexity of Recovering Secrets

Revisions: 1

Andrej Bogdanov, Nikhil Mande, Justin Thaler, Christopher Williamson

The $\epsilon$-approximate degree $\widetilde{\text{deg}}_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there exists a pair of probability distributions, also known as a dual polynomial, that are perfectly ... more >>>

Andrej Bogdanov, Yuval Ishai, Emanuele Viola, Christopher Williamson

We say that a function $f\colon \Sigma^n \to \{0, 1\}$ is $\epsilon$-fooled by $k$-wise indistinguishability if $f$ cannot distinguish with advantage $\epsilon$ between any two distributions $\mu$ and $\nu$ over $\Sigma^n$ whose projections to any $k$ symbols are identical. We study the class of functions $f$ that are fooled by ... more >>>