A language A is in NL if \exists a deterministic Turing Machine V that runs in logspace where x \in A \Leftrightarrow \exists w \in \left\{0,1\right\}^{\text{poly}\left(|x|\right)} (if and only if!! same as NP) such that V \left(x,w\right) = 1, where x—the real input x is on input tape one which is read-only, and the witness w is on input tape two which is read-once (because otherwise the same definition is equivalent to NP). Given this definition, STCONN is in NL is in \text{NL}, witness is simply s to t path.