Integer multiplication as one of the basic arithmetic functions has been
in the focus of several complexity theoretical investigations.
Ordered binary decision diagrams (OBDDs) are one of the most common
dynamic data structures for boolean functions.
Among the many areas of application are verification, model checking,
computer-aided design, relational algebra, ... more >>>

This article accompanies a tutorial talk given at the 40th ACM STOC conference. In it, we give a brief introduction to Fourier analysis of boolean functions and then discuss some applications: Arrow?s Theorem and other ideas from the theory of Social Choice; the Bonami-Beckner Inequality as an extension of Chernoff/Hoeffding ... more >>>

We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes achieve the list-decoding capacity with high probability. In particular, for any $0 < \rho < 1/2$ and $\epsilon > 0$, there exist concatenated codes of ... more >>>