The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant-fraction of error, while blowing up the communication by only a constant factor. Since ... more >>>

In the "correlated sampling" problem, two players, say Alice and Bob, are given two distributions, say $P$ and $Q$ respectively, over the same universe and access to shared randomness. The two players are required to output two elements, without any interaction, sampled according to their respective distributions, while trying to ... more >>>

Let $D$ be a $b$-wise independent distribution over
$\{0,1\}^m$. Let $E$ be the ``noise'' distribution over
$\{0,1\}^m$ where the bits are independent and each bit is 1
with probability $\eta/2$. We study which tests $f \colon
\{0,1\}^m \to [-1,1]$ are $\e$-fooled by $D+E$, i.e.,
$|\E[f(D+E)] - \E[f(U)]| \le \e$ where ... more >>>

A local tester for a code probabilistically looks at a given word at a small set of coordinates and based on this local view accepts codewords with probability one while rejecting words far from the code with constant probabilility. A local tester for a code is said to be ``robust'' ... more >>>

An $r$-simple $k$-path is a {path} in the graph of length $k$ that
passes through each vertex at most $r$ times. The \simpath{r}{k}
problem, given a graph $G$ as input, asks whether there exists an
$r$-simple $k$-path in $G$. We first show that this problem is
NP-Complete. We then show ... more >>>

In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of "affine-invariant'' codes. Affine-invariant codes are codes whose coordinates are associated with a vector space and are invariant under affine transformations of the coordinate space. Affine-invariant linear codes ... more >>>

We consider the task of compression of information when the source of the information and the destination do not agree on the prior, i.e., the distribution from which the information is being generated. This setting was considered previously by Kalai et al. (ICS 2011) who suggested that this was a ... more >>>

We consider the problem of testing if a given function $f : \F_q^n \rightarrow \F_q$ is close to a $n$-variate degree $d$ polynomial over the finite field $\F_q$ of $q$ elements. The natural, low-query, test for this property would be to pick the smallest dimension $t = t_{q,d}\approx d/q$ such ... more >>>

In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the following results. 1. We give a canonical representation for degree three or four polynomials that have a significant bias ... more >>>