2. Solve:

1. Give a regular expression for the language of strings over {a,b} that have no occurences of substring aa.
2. Give a regular expression and a NFA for the language {w {a,b,c}^* | if aa occurs, then no bb occurs after it}
3. Give a regular expression and a NFA for the language {w {0,1}^* | #₁(w)₄2}
4. Use the construction given in class to find a DFA that is equivalent to the following NFA. ({A,B,C,D}, {a,b}, , A, {B}), where (A,a)={D} (A,b)={B} (A,)={D} (B,a)={} (B,b)={C} (C,a)={A} (C,)={A} (D,a)={C} (D,b)={A,C}
5. Prove that the following language is not regular, by using the Pumping Lemma. L₀ ={w {a,b}^*| #_a(w) > 2* #_b(w)}.