# Pumping lemma

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In the theory of formal languages, the **pumping lemma** may refer to:

- Pumping lemma for regular languages, the fact that all sufficiently long strings in such a language have a substring that can be repeated arbitrarily many times, usually used to prove that certain languages are not regular
- Pumping lemma for context-free languages, the fact that all sufficiently long strings in such a language have a pair of substrings that can be repeated arbitrarily many times, usually used to prove that certain languages are not context-free
- Pumping lemma for indexed languages
- Pumping lemma for regular tree languages