Question

Describe how Turing machines are used to recognize sets.

Short answer

Set A is recognized by a Turing machine T when the input x moves T from the start state \({s_0}\) to the last state for all \(x \in A\).

Step-by-step solution

General form

Turing machine\(T = \left( {S,\,I,\,f,\,{s_0}} \right)\):A four-tuple consisting of a finite set \(S\) of states, an alphabet \(I\) containing the space symbol B, a sub-function \(f\) from \(S \times I\) to \(S \times I \times \left\{ {R,\,L} \right\}\) and an initial state \({s_0}\)

Step 2: Describe the Turing machine used to recognize set

Referring to the Turing machine:

A four-tuple consisting of a finite set \(S\) of states, an alphabet \(I\) containing the blank symbol B, a sub-function \(f\) from \(S \times I\) to \(S \times I \times \left\{ {R,\,L} \right\}\), and an initial state \({s_0}\).

Then, it is set A is recognized by a Turing machine T when the input x moves T from the start state \({s_0}\) to the last state for all \(x \in A\).

Hence, the result is founded.