2. Design a PDA for the language L = \{0$^m$1$^n$| m = n or n = 2m where m, n > 0\}.
3. Convert the following PDA which accepts by empty stack to CFG.
(\{q$_0$, q$_1$, q$_2\}$, \{a, b\}, \{Z, X\}, \delta, q$_0$, Z, \{}) where \delta is defined as follows.
\delta( q$_0$, a, Z) = \{(q$_0$, XZ)\}
\delta( q$_0$, a, X) = \{(q$_0$, XX)\}
\delta( q$_0$, b, X) = \{(q$_1$, \epsilon)\}
\delta( q$_0$, \epsilon, Z) = \{(q$_1$, Z)\}
\delta( q$_1$, b, X) = \{(q$_1$, \epsilon)\}
\delta( q$_1$, a, Z) = \{(q$_0$, XZ)\}
\delta( q$_1$, a, X) = \{(q$_0$, XX)\}
\delta( q$_1$, \epsilon, Z) = \{(q$_2$, \epsilon)\}
Also eliminate useless symbols, if there are any, from the resulting CFG.
