2. (7 points) Common Pumping Lemma Misunderstandings (a) (2 points) You are a CS4510 TA, and you are grading the following question: "Is the language L = {w w is a binary string with at least as many l's as O's} regular? Prove your answer." Bob, a student in the class, has submitted the following answer: I will prove that L is not regular, using the pumping lemma. i. Let p e Z+. ii. Let w = 01', so that we L and (w p. iii. Let w = xyz, with x = e, y = 0, and 2 = 1P, so that wyl

0. iv. Then typ+lz is not in L. Identify the single incorrect line in Bob's proof and explain what he did wrong. (NOTE: do not list small mistakes, typos, etc.; explain the major logical error which invalidates Bob's proof.)