Give a regular expression and a NFA for the language {w {a,b,c}* | if aa occurs, then no bb occurs after it}

Give a regular expression and a NFA for the language {w {0,1}* | #1(w)2 mod4}

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}

Prove that the following language is not regular, by using the Pumping Lemma.

L0 ={w {a,b}*| #a(w) > 2 #b(w)}.