I am working on my midterm sample problems and got stuck on this one. Is this language undecidable?
$\qquad L = \{\langle G_1, G_2 \rangle: G_1, G_2 \text{ are CFG and have strings that can be parsed in both grammars }\}$
Is this one the same as $L' = \{\langle G_1, G_2 \rangle: L(G_1) \cap L(G_2) \ne \emptyset\}$? My professor said the above problem can be reduced to Post Correspondence Problem but I found it closer to the decidable of $L'$.