Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 4F / b / Solution

Use the same program as $N$, replacing only its first line by a test for a final $1$:If the input ends in $1$, the $q_3$ loop erases it and eventually appends output $1$. Every other input, including the empty word, follows the $q_0$ loop and produces $0$. This is the characteristic function of $\{w1:w\in \mathbb{B}\}$.