We report progress on the \NL\ vs \UL\ problem.
\begin{itemize}
\item[-] We show unconditionally that the complexity class $\ReachFewL\subseteq\UL$. This improves on the earlier known upper bound $\ReachFewL \subseteq \FewL$.
\item[-] We investigate the complexity of min-uniqueness - a central
notion in studying the \NL\ vs \UL\ problem.
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We prove that TAUT has a $p$-optimal proof system if and only if $L_\le$, a logic introduced in [Gurevich, 88], is a P-bounded logic for P. Furthermore, using the method developed in [Chen and Flum, 10], we show that TAUT has no \emph{effective} $p$-optimal proof system under some reasonable complexity-theoretic ... more >>>

We prove the following results concerning the list decoding of error-correcting codes:

We show that for any code with a relative distance of $\delta$
(over a large enough alphabet), the
following result holds for random errors: With high probability,
for a $\rho\le \delta -\eps$ fraction of random errors (for any ... more >>>