4. Convert the following regular expressions to -NFA's. (a) (000)(+011+001)(111) (b) (0+1)(001+010+100)(0+1) 1 5. Apply the Pumping Lemma to prove that the following languages are not regular. (a) {akbn:n=2k} (b) {vw:v{a,b},w{c,d},v=w} 6. Complete the proof of Theorem 4.8 of textbook, by showing by an induction on w that ^((qL,qM),w)=(^L(qL,w),^M(qM,w)) 7. Let h be the homomorphism h:{a,b}{0,1} given by h(a)=01,h(b)=011, and define L={w{0,1}:n1(w)=0(mod3)}. Construct a DFA for h1(L)