4. Using Pumping Lemma (slides 24 and 25 of the notes 'Regular Languages& Finite Automata-IV) one can show the language L- (a"b" ne N is not regular. This is done by way of contradiction. We assume L is regular. Since L is infinite, Pumping Lemma applies. We then consider the string s = am bm where m is the number of states of the DFA that recognizes L. Since the length of s is bigger than m, by Pumping Lemma, there exists strings x,y and z such that s-xyz, y#, lxyl 2m and xyk2EL for all k E N. If Ixyl = 2m then the first repeated state on the acceptance path must be a final state. Why? (3 points) 5. Fill out the following blanks to make it a context-free grammar for the given language over the alphabet {a, b): { a3nbn+3 1 n >:0} (2 points)