Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 12J / b / Solution

For machine index $m$, $f_{m,k}$ is the partial $k$-ary function computed by that machine under the fixed coding, and $W_m$ is its halting domain (equivalently the r.e. set enumerated by machine $m$, under the course convention).