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I have studied Pumping Lemma carefully and have solved many exercises about it but I can't get an idea on how to solve this one: can anyone help me?

Let L = { w#x | x is a substring of w }. Prove that L is not regular.

I have tried setting the Pumping length to |w| and to |x| but I just don't find words that are not in L..

Thx in advance

Raphael
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  • What is # in the language? Does it belong to language L? – Alwyn Mathew Jun 05 '16 at 13:45
  • Welcome to Computer Science! What have you tried? Where did you get stuck? We do not want to just do your (home-)work for you; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for a relevant discussion. If you are uncertain how to improve your question, why not ask around in [chat]? You may also want to check out our reference questions. – Raphael Jun 05 '16 at 14:03
  • Note that you don't get to "set" the Pumping length! – Raphael Jun 05 '16 at 14:03
  • @AlwynMathew andy doesn't give the alphabet; I'd guess that $L \in {0,1,#}$ and $x,w \in {0,1}^*$ are reasonable assumptions. "#" is a separator. – Raphael Jun 05 '16 at 14:04
  • Hint: The Pumping lemma does not characterise REG! It's perfectly possible that a non-regular language has the Pumping property. Try another method! (In fact, I think this one has if we assume a binary alphabet. For larger alphabets, set $w=x$ to a "long" square-free word.) – Raphael Jun 05 '16 at 14:07

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