# Proving that a grammar generates a language

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 $L$?

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I also read it this way the first time: "it is sufficient..." instead of "is it sufficient" ;-) –  dtldarek Mar 13 '12 at 20:05
Sorry for bad punctuation. Edited. –  atlantis Mar 13 '12 at 20:06
It is sufficient to draw some PDA, prove that it is equivalent to $G$, and then show that this PDA recognizes $L$. –  dtldarek Mar 13 '12 at 20:07
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?