Non-deterministic Turing Machine

We can expand our definition of the transition function to provide a set of possible instructions which we can choose from, thus defining a non-deterministic Turing Machine:

$$\begin{array}{rl}& \delta :(Q\times \Sigma \times \{\bigsqcup \})\to \mathcal{P}(Q\times \Sigma \cup \{\bigsqcup \}\times \{\leftarrow ,\to \})\\ & \delta :(\text{current state},\text{read})\to \left\{\begin{array}{c}\text{possible instructions}\\ \text{state},\text{write},\text{move}\end{array}\right\}\end{array}$$