Problem $41($Homework $4$ Problem $5).$ Let us say that an NPDA is a binary stack NPDA if the size of its set of stack symbols $$ is $2$ ; assume $=\{0,1\}$ for concreteness. Prove that binary stack NPDAs and NPDAs are equivalent in terms of computation power. Clearly, every binary stack NPDA is also an NPDA. Thus, it is sufficient to prove that for every NPDA $P$ there exists a binary stack NPDA $P^{\text{'}}$ such that $L(P^{\text{'}})=L(P).$