We study the polynomial reconstruction problem for low-degree
multivariate polynomials over finite fields. In the GF[2] version of this problem, we are given a set of points on the hypercube and target values $f(x)$ for each of these points, with the promise that there is a polynomial over GF[2] of ... more >>>

We solve an open problem of Kushilevitz and Nisan
(1997) in communication complexity. Let $R_{eps}(f)$
and $D^{mu}_{eps}(f)$ denote the randomized and
$mu$-distributional communication complexities of
f, respectively ($eps$ a small constant). Yao's
well-known Minimax Principle states that
R_{eps}(f) = max_{mu} { D^{mu}_{eps}(f) }.
Kushilevitz and Nisan (1997) ask whether ... more >>>

We show that several reducibility notions coincide when applied to the
Graph Isomorphism (GI) problem. In particular we show that if a set is
many-one logspace reducible to GI, then it is in fact many-one AC^0
reducible to GI. For the case of Turing reducibilities we show that ... more >>>