Learning is a central task in computer science, and there are various
formalisms for capturing the notion. One important model studied in
computational learning theory is the PAC model of Valiant (CACM 1984).
On the other hand, in cryptography the notion of ``learning nothing''
is often modelled by the simulation ... more >>>

We prove lower bounds on the redundancy necessary to
represent a set $S$ of objects using a number of bits
close to the information-theoretic minimum $\log_2 |S|$,
while answering various queries by probing few bits. Our
main results are:

\begin{itemize}
\item To represent $n$ ternary values $t \in
\zot^n$ in ... more >>>

We extend the ``method of multiplicities'' to get the following results, of interest in combinatorics and randomness extraction.
\begin{enumerate}
\item We show that every Kakeya set in $\F_q^n$, the $n$-dimensional vector space over the finite field on $q$ elements, must be of size at least $q^n/2^n$. This bound is tight ... more >>>