Parity-L, also known as $\oplus$L, is the set of languages recognized by a non-deterministic Turing machine which can only distinguish between an even number or odd number of "acceptance" paths. A recent related question was asked by Niel de Beaudrap.
My question is the following:
Do we know if NL $\subseteq$ $\oplus$L? Or are these two classes believed to be incomparable?