We study the problem of constructing randomness extractors for samplable sources, introduced by Trevisan and Vadhan (FOCS 2000), a natural computational model of imperfect randomness, where the source $\mathbb{X}$ (on $n$ bits) is generated by a polynomial-size circuit. They showed how to extract from sources with min-entropy $(1-\alpha)n$ (for small ... more >>>

The work of Rothblum, Vadhan, and Wigderson ({\em STOC}, 2013) is pivotal to the study of interactive proofs of proximity (IPPs).
We present the main contents of their work, while clarify a few (conceptual) aspects.
Specifically, starting with the definition of IPP systems, our main focus is on ... more >>>

In this work, we study the space complexity of sketching the intersection profile of a distribution $D$ on $2^{[n]}$. Specifically, we seek a succinct data structure that, for any query set $S \subseteq [n]$, approximates the quantity $\Pr_{T \sim D}[T \cap S \neq \emptyset]$ to within a small constant additive ... more >>>