  In this paper, we discuss an algorithm for the problem of undirected
st-connectivity that is deterministic and log-space, namely that of Reingold
within his 2008 paper "Undirected Connectivity in Log-Space". We further
present a separate proof by Rozenman and Vadhan of $\text{USTCONN} \in L$ and
discuss its similarity with Reingold's proof. Undirected st-connectively is
known to be complete for the complexity class SL--problems solvable by
symmetric, non-deterministic, log-space algorithms. Likewise, by Aleliunas et.
al., it is known that undirected st-connectivity is within the RL complexity
class, problems solvable by randomized (probabilistic) Turing machines with
one-sided error in logarithmic space and polynomial time. Finally, our paper
also shows that undirected st-connectivity is within the L complexity class,
problems solvable by deterministic Turing machines in logarithmic space.
Leading from this result, we shall explain why SL = L and discuss why is it
believed that RL = L.
