Ran Raz, Omer Reingold, Salil Vadhan

We give explicit constructions of extractors which work for a source of

any min-entropy on strings of length n. These extractors can extract any

constant fraction of the min-entropy using O(log^2 n) additional random

bits, and can extract all the min-entropy using O(log^3 n) additional

random bits. Both of these ...
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Tzvika Hartman, Ran Raz

Weak designs were defined by Raz, Reingold and Vadhan (1999) and are

used in constructions of extractors. Roughly speaking, a weak design

is a collection of subsets satisfying some near-disjointness

properties. Constructions of weak designs with certain parameters are

given in [RRV99]. These constructions are explicit in the sense that

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Shachar Lovett, Sankeerth Rao, Alex Vardy

A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been introduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain conditions, a randomly chosen structure has the required properties of a $t-(n,k,?)$ combinatorial design with tiny, yet ... more >>>

Nutan Limaye, Karteek Sreenivasiah, Srikanth Srinivasan, Utkarsh Tripathi, S Venkitesh

The $\delta$-Coin Problem is the computational problem of distinguishing between coins that are heads with probability $(1+\delta)/2$ or $(1-\delta)/2,$ where $\delta$ is a parameter that is going to $0$. We study the complexity of this problem in the model of constant-depth Boolean circuits and prove the following results.

1. Upper ... more >>>