Design $($discuss$)$ a pushdown automaton $P$ that accepts the following languages on the binary

alphabet $=\{0,1\}.$ Provide the formal description of $P.$

$($c$)L(R)$ where $R$ is the RegEx ${11}^{**}{00}^{**}$

$($d$)L=\{\begin{array}{c}{1}^a{0}^b{1}_{?}={?}^c\text{:}a+c=b\end{array}$ where $\{$:$a,b,c0\}$