The book I am reading have proof for the statement
Every context-free language there exist a pushdown automata $M$ s.t. $L=L_{e}(M)$
For the case $\epsilon\not\in L$. The proof uses greibach normal form (hence the reason for the condition $\epsilon\not\in L$)
How can I prove this statement (preferably not having to re-prove everything again) for the general case ?
I understand that we can add the single rule $S\to\epsilon$ to the grammar after it's in greibach normal form, but how can I make the pushdown automata also accept $\epsilon$ ?