I am looking for a CFG of given language but I can not be sure about the correctness of my CFG.
Given language is $0^n|v|, |v|=n$
I find this CFG which I belive it solves it.
$S -> 0SX$
$X-> 0|1$
I tried some strings and my CFG works well but it seems too simple for this language so maybe I missed some part.
I have two questions. 1) Does my CFG is correct for a given language?
2) How can I prove the correctness of my CFG?