CFG and PDA for the grammar that has perfectly nested parentheses and brackets I gotta make a CFG and PDA for the grammar that has perfectly nested parentheses and brackets.

$\qquad\begin{align}
 S &amp;\to [S] \\
 S &amp;\to (S) \\
 S &amp;\to SS \\
 S &amp;\to \varepsilon
\end{align}$

Not sure if this is correct, or how to make the PDA from it?
The language you study is a classic, the one-sided Dyck language (on two pairs of brackets). You can directly make a PDA by considering the following property of nested strings: every symbol closing bracket you read should match the last unmatched opening bracket. Keep the unmatched $[$ and $($ on the stack and you are ready to go.