Since every context free grammar is equivalent to a Push down automaton, to show that a grammar $G$ generates a language $L$, is it sufficient to draw a PDA equivalent to $G$ and then show the PDA recognizes that language $L$?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
It will work (if, as dtldarek said, you also prove that the automaton is actually equivalent to the grammar). But it doesn't in general feel like a productive strategy. Of course this can depend a lot on how the language $L$ is given -- but how many tools do you have which you can you can use on automatons, and not as well apply directly to the original grammar?