# Complexity and hardness of undirected path

Let $$PATH = \{(G,s,t) \mid \exists \text{path from}~s\text{ to }t\text{ in }G\}$$, where $$G$$ is a directed graph. We know that $$PATH$$ is $$NL$$ complete. I am wondering what the complexity class of $$PATH$$ on undirected graphs is and whether any hardness results for $$PATH$$ on undirected graphs are known?

USTCON is trivially complete for L with respect to logspace reductions. I don't know if it is L-complete with respect to weaker reductions such as $$\mathsf{AC}^0$$ reductions; see this question.