 The transition function for the machine T is a function from computation states to computation states. If \(\delta(q_i,S_j) = (S_{i,j},D,q_{i,j})\), then when the machine’s state is \(q_j\), reading the symbol \(S_j\), \(T\) replaces \(S_j\) by \(S_{i,j}\), moves in direction \(D \in \{L,R\}\) and goes to state \(q_{i,j}\).