pumping lemma

The pumping lemma is a tool in formal language theory used to determine whether a language (a set of strings) is regular. It states that for any regular language, there exists a length (pumping length), such that any string longer than this can be divided into parts, and the middle part can be "pumped" (repeated) any number of times, and the resulting strings will still belong to the language. If a string cannot be divided this way, or pumping it produces strings outside the language, then the language is not regular. It helps identify complex languages that can't be described by simple regular patterns.