[Solved]: Eliminating Null Productions from Context Free Grammar

Problem Detail: 

Here is a problem I am trying to solve:

S -> 0A0 | 1B1 | BB A -> C B -> S | A C -> S | e 

I know that C is nullable (since it produces an epsilon) and A is nullable (since it produces C, which is nullable). My question is if B is nullable too since it produces A which produces C which are both nullable?

Asked By : ipoood

Answered By : D.W.

Yes, absolutely. We have the derivation $B \to A \to C \to \epsilon$, so $B$ is nullable.

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Question Source : http://cs.stackexchange.com/questions/33675