$(50$ Points$)$ Given the following language,

$L_1=\{{10}^n{10}^m|m>n>0\}$ and ${\displaystyle \underset{?}{\overset{?}{}}}=\{0,1].$

$($a$)(5$ Points$)$ List $2$ strings are in $L_1.$

$[$ANSWER$]$

$($b$)(15$ Points$)$ Build a context$-$free grammar $($CFG$)$ that generates strings in $L_1.$

$[$ANSWER$]$

$($c$)(10$ Points$)$ Write down the pseudo code algorithm in English for pushdown

automaton $($PDA$)$ that recognizes $L_1.$

$[$ANSWER$]$

$($d$)(20$ Points$)$ Build a graphical PDA that recognizes $L_1.$ Please note that no

transition tables needed.

$[$ANSWER$]$