Please do not copy the answer elsewhere. I need help with this specific question.

Please provide a detailed answer. Thank you.

Let $L=\{\begin{array}{c}{g}^m{0}^n{g}^k{l}^r\end{array}$ where $n,h0,f1,f=m,$ and $\{$:$2n=k\}$

a$.$ Construct a final$-$state PDA with that recognizes the strings of L$.(15$ points$)$

b$.$ Convert the generated final$-$state PDA into an empty$-$stack PDA using the

approach studied in lectures. $(15$ points$)$

c$.$ Does the word goggle belong to L$?$ Justify your answer with a sequence of

moves of the empty$-$stack PDA and explain its indication. $(10$ points$)$