Transform PDA with acceptance of final state + empty stack to just final state
Given a PDA $M$, you can define the following associated languages:


The language of all words $w$ such that there is a computation path for the PDA on $w$ in which it ends at a final state with an empty stack. We denote this language by $L_1(M)$.
The language of all words $w$ such that there is a computation path for the PDA on $w$ in which it ends at a final state. We denote this language by $L_2(M)$.


The two languages are not always the same, that is, it could well be that $L_1(M) \neq L_2(M)$. You have to show that for each PDA $M$ there is another PDA $M'$ such that $L_1(M) = L_2(M')$.