We consider the task of testing properties of Boolean functions that
are invariant under linear transformations of the Boolean cube. Previous
work in property testing, including the linearity test and the test
for Reed-Muller codes, has mostly focused on such tasks for linear
properties. The one exception is a test ... more >>>

It has been shown that for every perfect matching $M$ of the $d$-dimensional
$n$-vertex hypercube, $d\geq 2, n=2^d$, there exists a second perfect matching
$M'$ such that the union of $M$ and $M'$ forms a Hamiltonian circuit of the
$d$-dimensional hypercube. We prove a generalization of a special case of ... more >>>

Motivated by the quantum algorithm in \cite{MN05} for testing
commutativity of black-box groups, we study the following problem:
Given a black-box finite ring $R=\angle{r_1,\cdots,r_k}$ where
$\{r_1,r_2,\cdots,r_k\}$ is an additive generating set for $R$ and a
multilinear polynomial $f(x_1,\cdots,x_m)$ over $R$ also accessed as
a ... more >>>