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I've had multiple lectures on the pumping lemma but still can't grasp exactly what it is...my main questions are as follows

  1. What is the pumping lemma for?

  2. How do you use it to prove a language is not regular (with an example please)

    e.g. if L is in sigma and L is regular, prove that sigma*-L is regular

    It doesn't need to be this exact example in case you think I'm trying to cheat for homework or something.

In lectures we've been doing this by using contradictions but I seem to only understand the answer and nothing else

user40945
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    The pumping lemma is for proving that languages are not regular; there are examples in our reference question. Beyond that, it's hard to answer your question. You say that you've had the pumping lemma explained to you multiple times but you're asking for another explanation. Since we don't know what you didn't understand the previous times it was explained to you, it's very likely that your reaction to a new explanation would be, "I don't understand that, either!" – David Richerby Oct 12 '15 at 18:02
  • You write "L is in sigma$ and "sigma^*-L" but neither of those things really makes sense. At least part of your misunderstanding is because you haven't mastered the basic definitions. Help with that kind of thing really needs to be interactive but Stack Exchange just isn't set up for interactivity. I think the best thing for you to do would be to arrange a meeting with your instructor (or even a fellow student) so you can both go through this together. – David Richerby Oct 12 '15 at 18:04
  • This is also a same-time cross-posted dupe of http://cstheory.stackexchange.com/q/32794/8067 – Zsbán Ambrus Oct 12 '15 at 20:10
  • @ZsbanAmbrus : $:$ I pointed the OP here. $;;;;$ –  Oct 12 '15 at 20:44
  • @RickyDemer you should've directed the OP to use the search engine here (: – Ran G. Oct 13 '15 at 00:33

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