$\{\begin{array}{c}{1}^m{0}^k{1}^n\end{array}$

$(50$ points Total$)$ We have a language $L=\{1^l{0}^m{1}^n|l=m+n$;$l,m,n0\}.$ Note that L contains strings such as $,1001$ or $10000111.$

$(20$ points$)$ Give a context$-$free grammar for $L.$

$(15$ points$)$ Convert your context$-$free grammar given in $3-1)$ to a NPDA by drawing the transition graph.

$(15$ points$)$ Show the configuration sequences on string $110001$ which leads to acceptance.