Motivated by the classical problem of privacy amplification, Dodis and Wichs (STOC '09) introduced the notion of a non-malleable extractor, significantly strengthening the notion of a strong extractor. A non-malleable extractor is a function $nmExt : \{0,1\}^n \times \{0,1\}^d \rightarrow \{0,1\}^m$ that takes two inputs: a weak source $W$ and ... more >>>

In the setting known as DLOGTIME-uniformity,
the fundamental complexity classes
$AC^0\subset ACC^0\subseteq TC^0\subseteq NC^1$ have several
robust characterizations.
In this paper we refine uniformity further and examine the impact
of these refinements on $NC^1$ and its subclasses.
When applied to the logarithmic circuit depth characterization of $NC^1$,
some refinements leave ... more >>>

A folklore result in arithmetic complexity shows that the number of multiplications required to compute some $n$-variate polynomial of degree $d$ is $\sqrt{{n+d \choose n}}$. We complement this by an almost matching upper bound, showing that any $n$-variate polynomial of degree $d$ over any field can be computed with only ... more >>>