Show, that every context free grammar can be transformed into equivalent context free grammar ( with possible loss of $\lambda $ ) where $a \in V_t$ and $A,B,C \in V_n $ with rewriting rules of following type:
$ A \rightarrow a $
$ A \rightarrow aB $
$ A \rightarrow aBC $
My thoughts are that I need to show that every context free rule i can be written into set of context free rules that when applied generate same string as rule i.
Is that correct? If not, could you give me any hints on how to do it properly?
How I`m trying to do it:
Greibach normal form has rules of type:
$A \rightarrow aA_1A_2...A_n$
So I need to break long rules into shorter rules Chomsky normal form style.