1. Exercise 2.6d. Even though the question specifically asks you to give a context-free grammar, I'll accept if you give a PDA for the language instead.
2. Do Exercise 2.11.
3. Do Problem 2.44.
4. Figure 2.19 on page 116 shows a PDA M3
that recognizes the language
{ wwR : w ∈ {0,1}* }
and Figure 1.20 on page 43 shows a DFA D
that recognizes the language
{ w ∈ {0,1}* : |w|1 is odd }.
Use the algorithm we did in class to construct a PDA that
recognizes L(M3) ∩ L(D).
5. Use the Pumping Lemma to show that the language
{ 0n12n0n : n ≥ 0 }.
is not context-free.
6. Do Problem 2.31.
Extra credit. Do Problem 2.28.