Raz (2009) proved that multilinear formulas computing the determinant of a generic $n \times n$ matrix require size $n^{\Omega(\log n)}$. A fundamental question in understanding this lower bound is identifying which structural properties of the determinant drive this hardness. In pursuit of this question, we prove the existence of $n ... more >>>

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 >>>