QUESTION 1 Let A be the following pushdown automaton (PDA) with alphabet ? = {0,1}
and stack alphabet ?<sub>st</sub> = {$,0,1}:
1. Give a formal definition of A as a 6-tuple A = (?, ?<sub>st</sub>, Q, ?, q<sub>0</sub>, F).
2. Give three words accepted by A, and three words that are not accepted. Make sure you
consider the empty word ?. Give an accepting run for each accepted word.
3. Describe in English, or give a formal definition of, the language accepted by A.
4. Give a context-free grammar accepting the same language.
5. Now draw a PDA accepting the language of the following grammar G:
S ? ? | 1 | 0 | 0S0 | 1S1
Recall that the language L(G) is the set of palindromes on ?, that is, the set of all strings
in {0,1}* that can be read the same way forwards and backwards.