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The pumping lemma, which gives a pretty good test to see if a language is regular or show that some languages are not regular. (There are also more general pumping lemmas that use pigeonhole for their proofs, but I don't know them.)

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The pumping lemma, which gives a pretty good test to see if a language is regular or not. (There are also more general pumping lemmas that use pigeonhole for their proofs, but I don't know them.)