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 >>>

We present the first explicit construction of two-sided lossless expanders in the unbalanced setting (bipartite graphs that have many more nodes on the left than on the right). Prior to our work, all known explicit constructions in the unbalanced setting achieved only one-sided lossless expansion.

Specifically, we show ... more >>>