What is the purpose of the pumping lemma for context-free languages in automata theory?

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What is the purpose of the pumping lemma for context-free languages in automata theory?

The purpose of the pumping lemma for context-free languages in automata theory is to provide a tool for proving that a language is not context-free. It states that for any context-free language L, there exists a pumping length p such that any string s in L with length greater than or equal to p can be divided into five parts, uvxyz, satisfying certain conditions. By showing that these conditions cannot be met for a given language, we can conclude that the language is not context-free.