Pumping lemma

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

• Ogden's lemma, a stronger version of the pumping lemma for context-free languages

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