Push down automata for $\{a^n b^n c^n | n \ge 0\}$
Your PDA would also accept strings of the form $a^nb^ic^j$ where $i+j=2n$ and $i,j&gt;0$. For example the string "aaabbbbbc" is accepted. There is no way to tell that there are exactly $n$ $a$'s still remaining on the stack once you've finished reading the $b$'s.