# Is equivalence of a CFG and an RG undecidable?

I know that the equivalence of two context-free grammars is undecidable, but what about the equivalence of a regular grammar and a context-free grammar?

It is undecidable whether for a given CFG $G$, $L(G)=\Delta^*$, the set of all strings (over the terminal alphabet of $G$). That answers your question, by chosing the most simple regular grammar.
• @babou Indeed. You made me smile. Nevertheless the concept "empty language" might be very confusing to some. In a recent exam some students noted that $\{a,b,c,d\}$ had $17$ subsets: $2^4$ usual ones, plus the empty set. – Hendrik Jan Mar 4 '15 at 17:18