I need help with the question listed below. Please read very carefully $($especially the screenshot$).$ Do not copy the answer from elsewhere. If confused, take the Arabic letters as symbols $($that are taken from right to left$).$ Please provide a detailed answer if you can. Thank you.

$2.$ For $\backslash$Sigma $=\{,,,\}$ the language R $=\{$vw $|$ v $\{,\}*$ while w $\{,\}*$ where,$||+||=||\}$ given that $||>=0,||>=0,||>=0,||>=0\}$

Note that for being Arabic Words they are processed from right to left.

a$.$ Construct an empty$-$stack PDA that recognizes this language. $(15$ points$)$

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

approach studied in lectures. $(10$ points$)$

d$.$ Does the string $$ belong to R$?$ Justify your answer with a sequence of

moves of the final$-$state PDA. $(10$ points$)$