  Due to Savitch's theorem we know $NL\subseteq DSPACE(\log^2(n))$. To show
this upper bound, Savitch constructed an algorithm with $O(\log^2(n))$ space on
the working tape. We will show that Savitch's algorithm also described a lower
bound under the Strong Exponential Time Hypothesis. Every algorithm for the
Connectivity Problem needs $O(\log^2(n))$ space in this case.
