We present a deterministic, log-space algorithm that solves
st-connectivity in undirected graphs. The previous bound on the
space complexity of undirected st-connectivity was
log^{4/3}() obtained by Armoni, Ta-Shma, Wigderson and
Zhou. As undirected st-connectivity is
complete for the class of problems solvable by symmetric,
non-deterministic, log-space computations (the class SL), ... more >>>

Building on Barak's work (Random'02),
Fortnow and Santhanam (FOCS'04) proved a time hierarchy
for probabilistic machines with one bit of advice.
Their argument is based on an implicit translation technique,
which allow to translate separation results for short (say logarithmic)
advice (as shown by Barak) into separations for ... more >>>

A string $\alpha\in\Sigma^n$ is called {\it p-periodic},
if for every $i,j \in \{1,\dots,n\}$, such that $i\equiv j \bmod p$,
$\alpha_i = \alpha_{j}$, where $\alpha_i$ is the $i$-th place of $\alpha$.
A string $\alpha\in\Sigma^n$ is said to be $period(\leq g)$,
if there exists $p\in \{1,\dots,g\}$ such that $\alpha$ ... more >>>