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http://www.cs.oberlin.edu/~asharp/cs383/handouts/pumping.pdf

I came across this and realized that what some people told me was completely wrong. We get to choose xyz, but the demon choose uvw and uvw = y.

How do we choose a good string for the pumping lemma?

Here, the guy said to me to pick a string and the demon get to choose uvw and uvw = s, to the whole string. He made a mistake, right?

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user539484
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1 Answers1

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So one source tells you to consider strings $xuv^iwz$ and another tells you to consider $uv^iw$. How is $xu$ in the first different from $u$ in the second decomposition?

Karolis Juodelė
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  • so are you saying we can pump y instead of v? and in some case we don't need to decompose to uvw because it would hold for every case? – user539484 Feb 19 '14 at 18:16
  • I'm saying those two are minor variations of the same thing. You're thinking too much about symbol names. The only difference is that first lemma allows you to choose approximately in which region the pumping will happen and the second one tells you that pumping will happen at the beginning of the string. It makes no difference though, considering that the language of suffixes of a regular language is regular. – Karolis Juodelė Feb 19 '14 at 19:27