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5. (20 points) For each of the languages L{a,b} below, use the pumping lemma to show that it
cannot be accepted by an FA: a) L={aibij=2i, and i,j are positive integers } b) L={a(i+1)2i1 and i are
positive integers } 6. (10 points) For the FA pictured right, use the minimization algorithm to find a
minimum-state FA recognizing the same language. (It's possible that the given FA may already be
minimal.) Fill in the table below to mark the pass numbers, then draw the final minimum-state FA.

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