We study the problem of non-interactive correlation distillation
(NICD). Suppose Alice and Bob each has a string, denoted by
$A=a_0a_1\cdots a_{n-1}$ and $B=b_0b_1\cdots b_{n-1}$,
respectively. Furthermore, for every $k=0,1,...,n-1$, $(a_k,b_k)$ is
independently drawn from a distribution $\noise$, known as the ``noise
mode''. Alice and Bob wish to ``distill'' the correlation
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Entanglement is an essential resource for quantum communication and quantum computation, similar to shared random bits in the classical world. Entanglement distillation extracts nearly-perfect entanglement from imperfect entangled state. The classical communication complexity of these protocols is the minimal amount of classical information that needs to be exchanged for the ... more >>>

We introduce a ``Statistical Query Sampling'' model, in which
the goal of an algorithm is to produce an element in a hidden set
$S\subseteq\bit^n$ with reasonable probability. The algorithm
gains information about $S$ through oracle calls (statistical
queries), where the algorithm submits a query function $g(\cdot)$
and receives ... more >>>

We prove two lower bounds on the Statistical Query (SQ) learning
model. The first lower bound is on weak-learning. We prove that for a
concept class of SQ-dimension $d$, a running time of
$\Omega(d/\log d)$ is needed. The SQ-dimension of a concept class is
defined to be the maximum number ... more >>>

In this paper, we study the problem of using statistical
query (SQ) to learn highly correlated boolean functions, namely, a
class of functions where any
pair agree on significantly more than a fraction 1/2 of the inputs.
We give a limit on how well ... more >>>

Informally, an <i>obfuscator</i> <b>O</b> is an (efficient, probabilistic)
"compiler" that takes as input a program (or circuit) <b>P</b> and
produces a new program <b>O(P)</b> that has the same functionality as <b>P</b>
yet is "unintelligible" in some sense. Obfuscators, if they exist,
would have a wide variety of cryptographic ... more >>>

In this paper, we address the problem of evaluating the
Integer Circuit (IC), or the $\{\cup, \times, +\}$-circuit over
the set of natural numbers. The problem is a natural extension
to the integer expression by Stockmeyer and Mayer, and is also studied
by Mckenzie, Vollmer and Wagner in ... more >>>