Pumping Lemma for Regular Languages PROOF IN 4 MINUTES - Easy Theory

Here we give a very quick proof of the pumping lemma for regular languages. The question just asks about strings that are also accepted in a given DFA. We partition the string up into pieces (as long as the string was accepted and at least the number of states), and repeat the middle piece, yielding another accepted string. Then, we make observations about where the middle piece can be.

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▶ADDITIONAL QUESTIONS◀
1. Is any one of the three conditions unnecessary?
2. Does the initial string have to be accepted?
3. Does the initial string have to be at least the number of states in length?

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▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.