Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 12I / ii / Solution

Let $N=|Q|$. The pumping lemma for regular languages states that every $w\in L(D)$ with $|w|\ge N$ can be writtenwithThus one may take the pumping number to be exactly the number $N$ of states of the given automaton, whether or not all of them are accessible.