Pumping lemma condition 3

  1. It says that |xy| < p. But I don't understand why even after reading the proof. If I have a four state DFA, whose last state is the one that is gonna repeat for a given input string of length p, |x| is already gonna be four, since it represents the states necessary to reach the repetition state. So in this worst case scenery, |x| is already equal to p, so with |y|>0 we already have |xy|>p. SO what's wrong with my line of thought
     
  2. jcsd
  3. If I understand correctly, the pumping lemma gives you a number, p, such that a bunch of stuff happens. Can you reference the exact pumping lemma you are talking about?
     
  4. verty

    verty 1,854
    Homework Helper

    And show us the proof so we can understand.
     
  5. I am sorry, I forgot that there is more than one pumping lemma so I aborted the copy that I was doing. Very clever from my part. Anyway I attached a screenshot of the proof:
     

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