Recognizing strongly connected digraphs in NL
Because nondeterministic space classes are closed under complementation by the Immerman&ndash;Szelepcsényi theorem. So, you can't literally just invert the answer from $\text{PATH}(a,b)$ but the fact that there is an $\mathrm{NL}$ algorithm for $\text{PATH}(a,b)$ implies that there is also an $\mathrm{NL}$ algorithm for $\text{NOT-PATH}(a,b)$, and you use that.