We define a combinatorial checkerboard to be a function $f:\{1,\ldots,m\}^d\to\{1,-1\}$ of the form $f(u_1,\ldots,u_d)=\prod_{i=1}^df_i(u_i)$ for some functions $f_i:\{1,\ldots,m\}\to\{1,-1\}$. This is a variant of combinatorial rectangles, which can be defined in the same way but using $\{0,1\}$ instead of $\{1,-1\}$. We consider the problem of constructing explicit pseudorandom generators for combinatorial ... more >>>

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called sps(k,d,n) circuits) over base field F.
It is a major open problem to design a deterministic polynomial time blackbox algorithm
that tests if C is identically zero.
Klivans & Spielman (STOC 2001) observed ... more >>>

We show that it is possible to encode any communication protocol
between two parties so that the protocol succeeds even if a $(1/4 -
\epsilon)$ fraction of all symbols transmitted by the parties are
corrupted adversarially, at a cost of increasing the communication in
the protocol by a constant factor ... more >>>