Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 12G / b / i / Solution

Because $D$ is minimal, every state is accessible. Choose a word $u$ taking the initial state to $p$, and let the nonempty word $v$ label the closed path $\gamma$. If a word $w$ took $p$ to an accept state, thenThese words have strictly increasing lengths because $v\ne ϵ$, contradicting the assumption that $\mathcal{L}(D)$ is finite. Hence no accept state is reachable from $p$.