PDA accepting of a specific symmetric language
There are general constructions that give a PDA given a CFG.
In this case, start with the PDA for $\{a^n b^n \colon n &gt; 0\}$, instead of storing one $A$ on the stack for each input $a$, store two, and the same for $b$. When reaching the middle, start discounting and accept by empty stack.