Recall that a deterministic Turing machine \(T \in \mathfrak{T}\) can be represented as a tuple \(\langle Q,\Sigma,\delta,s \rangle\) where \(Q\) is a finite set of internal states, \(\Sigma\) is a finite tape alphabet, \(s \in Q\) is \(T\)’s start state, and \(\delta\) is a transition function mapping state-symbol pairs \(\langle q,\sigma \rangle\) into state-action pairs \(\langle q,a \rangle\). Here \(a\) is chosen from the set of actions \(\{\sigma,\Leftarrow,\Rightarrow \}\) – i.e. write the symbol \(\sigma \in \Sigma\) on the current square, move the head left, or move the head right. Such a function is hence of type \(\delta: Q \times \Sigma \rightarrow Q \times \alpha\). On the other hand, a non-deterministic Turing machine \(N \in \mathfrak{N}\) is of the form \(\langle Q,\Sigma,\Delta,s \rangle\) where \(Q,\Sigma\), and \(s\) are as before but \(\Delta\) is now only required to be a relation – i.e. \(\Delta \subseteq (Q \times \Sigma) \times (Q \times \alpha)\). As a consequence, a machine configuration in which \(N\) is in state \(q\) and reading symbol \(\sigma\) can lead to finitely many distinct successor configurations – e.g. it is possible that \(\Delta\) relates \(\langle q,\sigma \rangle\) to both \(\langle q',a' \rangle\) and \(\langle q'',a'' \rangle\) for distinct states \(q'\) and \(q''\) and actions \(a'\) and   \(a''\).[11]