In this paper, we propose a quantification of distributions on a set
of strings, in terms of how close to pseudorandom the distribution
is. The quantification is an adaptation of the theory of dimension of
sets of infinite sequences first introduced by Lutz
\cite{Lutz:DISS}.
We show that this definition ... more >>>

We show that if $f(x_1,\ldots,x_n)$ is a polynomial with $s$ monomials and $g(x_1,\ldots,x_n)$ divides $f$ then $g$
has at most $\max(s^{O(\log s \log\log s)},d^{O(\log d)})$ monomials, where $d$ is a bound on the individual degrees
of $f$. This answers a question of von zur Gathen and Kaltofen (JCSS ... more >>>

We study set-disjointness in a generalized model of randomized two-party communication where the probability of acceptance must be at least alpha(n) on yes-inputs and at most beta(n) on no-inputs, for some functions alpha(n)>beta(n). Our main result is a complete characterization of the private-coin communication complexity of set-disjointness for all functions ... more >>>