We introduce a new lower bound method for bounded-error quantum communication complexity,
the \emph{singular value method (svm)}, based on sums of squared singular values of the
communication matrix, and we compare it with existing methods.

The first finding is a constant factor improvement of lower bounds based on the
spectral ... more >>>

In 1994, Y. Mansour conjectured that for every DNF formula on $n$ variables with $t$ terms there exists a polynomial $p$ with $t^{O(\log (1/\epsilon))}$ non-zero coefficients such that $\E_{x \in \{0,1\}}[(p(x)-f(x))^2] \leq \epsilon$. We make the first progress on this conjecture and show that it is true for several natural ... more >>>

Much work has been done on learning various classes of ``simple'' monotone functions under the uniform distribution. In this paper we give the first unconditional lower bounds for learning problems of this sort by showing that polynomial-time algorithms cannot learn constant-depth monotone Boolean formulas under the uniform distribution in the ... more >>>