consider this question of finding words with no self embedded nonterminal in their derivation. The author(cohen) says that If CFG is in CNF then all the words with length greater than 2^p are guaranteed to have self embedded nonterminal. So, all i need to do to solve these questions is to consider words that have length less than 2^p (where p is no. of "live" productions aka productions containing atleast one Nonterminal, in the grammar). But consider question 5 in image, i can easily tell any word of length >= 4 will have self embedded nonterminal in its derivation, without converting it into CNF. and this pattern is repeating in many questions. Do i really need to convert CFG in CNF? what could go wrong if i don't? Does this restriction on length still holds if CFG is not in CNF?
