# The problem of equivalence of a CFG and a RG? [duplicate]

Given a context-free grammar and a regular grammar, check whether they are equivalent. It's a fact that it's undecidable, but how could I prove it?

I want to clarify that my question is not about determining whether a CFG describes a regular language. In my problem I am given a CFG and a regular language and I need to tell whether they are equal or not. These are different problems as far as I understand, mine is easier than that one.

## marked as duplicate by Apass.Jack, Evil, xskxzr, Yuval Filmus, Discrete lizard♦May 14 at 10:40

There is no algorithm which can determine for any context-free grammar $$G_1$$ and regular grammar $$G_2$$ whether $$L(G_1) = L(G_2)$$.
However, it may well be possible to determine for particular $$G_1$$ and $$G_2$$, using heuristic proof techniques (aka human intuition).