Equivalence of Context-Free-Grammar and Context-Free-Grammar in CNF Given any Context-Free-Grammar, $G$, and another in Chomsky Normal Form, $G_c$, how can we check if both $G$ and $G_c$ generate the same language?


One of the trivial ways I know of is to convert $G$ into a CNF form. which motivates my second question,


Can two different Context-Free-Grammars in CNF, $G_c$ and $G_c^\prime$, generate the same language? (I would appreciate a proof of it)
Chomsky normal forms are not unique. If they were, we'd have an algorithm for deciding whether two CF grammars are equal. But equivalence of CF grammars is undecidable.