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I've done a lot of research on this topic, but still don't feel very confident about it. Let's say the example is:

For a language L over an Σ, define N(L)={w∈Σ∗: wk∈L for some k∈Σ∗}. Prove that, if L is regular, so is N(L).

How do I go about proving it?

Raphael
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CSstudent
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    What did you try? Where did you get stuck? – jbapple Mar 03 '16 at 03:17
  • @jbapple I understand that I need to build a finite automata for this and prove that it works for all and only string of N(L), but I'm not sure how exactly to build it and how it would work – CSstudent Mar 03 '16 at 03:26
  • If you can construct a DFA/NFA for such a language and prove the correctness of the automaton, then you are done. (A DFA can only accept a regular language) – Banach Tarski Mar 03 '16 at 06:43
  • @BanachTarski yes, I understand that. But how do I construct a DFA/NFA specifically for the given problem? That's where I'm lost. Thank you!! – CSstudent Mar 03 '16 at 16:13
  • @CSstudent It seems that your question is a duplicate of something that someone has already asked before. See if you get your answer there. – Banach Tarski Mar 03 '16 at 16:28

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