# $⊕P$-completeness of$⊕2SAT$

Is $⊕2SAT$ - the parity of the number of solutions of $2$-$CNF$ formulae $\oplus P$ complete?

This is listed as an open problem in Valiant's 2005 paper https://link.springer.com/content/pdf/10.1007%2F11533719.pdf. Has this been resolved?

Is there any consequence if $⊕2SAT\in P$?

It is shown to be $\oplus P$-complete by Faben:
• @Turbo: the solutions of a monotone 2SAT instance of the form $F = \bigwedge_{(i,j) \in E} \neg x_i \vee \neg x_j$ are exactly the independent sets of the graph $(V,E)$ where $V = \{x_1 \ldots x_n\}$. – holf Nov 22 '17 at 20:07