# Pumping lemma for context-free languages

## Type of pumping lemma / From Wikipedia, the free encyclopedia

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In computer science, in particular in formal language theory, the **pumping lemma for context-free languages**, also known as the **Bar-Hillel lemma**,[1] is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages.

Type of pumping lemma

The pumping lemma can be used to construct a proof by contradiction that a specific language is *not* context-free. Conversely, the pumping lemma does not suffice to guarantee that a language *is* context-free; there are other necessary conditions, such as Ogden's lemma, or the Interchange lemma.