I'd really like your help with the following question:
For $G$ a context free grammar, and $R$, $S$ regular expressions,
To which class does $\{ \langle G,R,S \rangle : L(G) \cap L(R) = L(S) \}$ belong?
Is it in $R$, $RE/R$, co-$RE/R$?
I know that Intersection of CFG and Regular expressions is CFG, and to compare two regular expressions is in $R$, but I'm not sure what is the answer.
Thank you