All reports by Author Siyao Guo:

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TR19-173
| 28th November 2019
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Divesh Aggarwal, Siyao Guo, Maciej Obremski, Joao Ribeiro, Noah Stephens-Davidowitz#### Extractor Lower Bounds, Revisited

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TR17-136
| 10th September 2017
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Salman Beigi, Andrej Bogdanov, Omid Etesami, Siyao Guo#### Complete Classification of Generalized Santha-Vazirani Sources

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TR16-136
| 31st August 2016
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Clement Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer#### Testing k-Monotonicity

Revisions: 1

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TR16-131
| 21st August 2016
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Andrej Bogdanov, Siyao Guo, Ilan Komargodski#### Threshold Secret Sharing Requires a Linear Size Alphabet

Divesh Aggarwal, Siyao Guo, Maciej Obremski, Joao Ribeiro, Noah Stephens-Davidowitz

We revisit the fundamental problem of determining seed length lower bounds for strong extractors and natural variants thereof. These variants stem from a ``change in quantifiers'' over the seeds of the extractor: While a strong extractor requires that the average output bias (over all seeds) is small for all input ... more >>>

Salman Beigi, Andrej Bogdanov, Omid Etesami, Siyao Guo

Let $\mathcal{F}$ be a finite alphabet and $\mathcal{D}$ be a finite set of distributions over $\mathcal{F}$. A Generalized Santha-Vazirani (GSV) source of type $(\mathcal{F}, \mathcal{D})$, introduced by Beigi, Etesami and Gohari (ICALP 2015, SICOMP 2017), is a random sequence $(F_1, \dots, F_n)$ in $\mathcal{F}^n$, where $F_i$ is a sample from ... more >>>

Clement Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer

A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of the classical monotone functions, which are the $1$-monotone functions.

Motivated by the ... more >>>

Andrej Bogdanov, Siyao Guo, Ilan Komargodski

We prove that for every $n$ and $1 < t < n$ any $t$-out-of-$n$ threshold secret sharing scheme for one-bit secrets requires share size $\log(t + 1)$. Our bound is tight when $t = n - 1$ and $n$ is a prime power. In 1990 Kilian and Nisan proved ... more >>>