 Pumping lemma for regular languages

For a deterministic finite automaton with $N$ states, every accepted word $w$ with $|w|\ge N$ has a decomposition $w=xyz$ such that $|xy|\le N$, $|y|\ge 1$, and $x{y}^{i}z$ is accepted for every integer $i\ge 0$.

The Pumping Lemma for regular languages is a fundamental property used to prove that certain languages are not regular.