PDA accepting of a specific symmetric language Assume we have PDA that accepts a specific symmetric language on $\{a,b\}^*$.
if we have $a$ This side of the string, on the other side of the string we have $aa$.
and if we have $b$ This side of the string, on the other side of the string we have $bb$.
Examples of words in this language (middle point emphasized):
$ab\, bbaa$
$aaa\, aaaaaa$
$bab\, bbaabb$
What is a PDA accepting this language?
I can find a grammar for this language but I can't find a PDA.
The grammar: $S \to aSaa \mid bSbb \mid aaa\mid bbb$
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.