We suggest a generalization of Karchmer-Wigderson communication games to the multiparty setting. Our generalization turns out to be tightly connected to circuits consisting of threshold gates. This allows us to obtain new explicit constructions of such circuits for several functions. In particular, we provide an explicit (polynomial-time computable) log-depth monotone ... more >>>

A hitting set is a "one-sided" variant of a pseudorandom generator (PRG), naturally suited to derandomizing algorithms that have one-sided error. We study the problem of using a given hitting set to derandomize algorithms that have two-sided error, focusing on space-bounded algorithms. For our first result, we show that if ... more >>>

We prove new lower bounds for computing some functions $f:\{0,1\}^{n}\to\{0,1\}$ in $E^{NP}$ by polynomials modulo $2$, constant-depth circuits with parity gates ($AC^{0}[\oplus]$), and related classes. Results include:

(1) $\Omega(n/\log^{2}n)$ lower bounds probabilistic degree. This is optimal up to a factor $O(\log^{2}n)$. The previous best lower bound was $\Omega(\sqrt{n})$ proved in ... more >>>