We define tests of boolean functions which
distinguish between linear (or quadratic) polynomials, and functions
which are very far, in an appropriate sense, from these
polynomials. The tests have optimal or nearly optimal trade-offs
between soundness and the number of queries.

In particular, we show that functions with small ... more >>>

A coloring of a graph is {\it convex} if it
induces a partition of the vertices into connected subgraphs.
Besides being an interesting property from a theoretical point of
view, tests for convexity have applications in various areas
involving large graphs. Our results concern the important subcase
of testing for ... more >>>

We show that the Closest Vector
Problem with Preprocessing over infty Norm
is NP-hard to approximate to within a factor of $(\log
n)^{1/2-\epsilon}$. The result is the same as Regev and Rosen' result, but our proof methods are different from theirs. Their
reductions are based on norm embeddings. However, ... more >>>