Question

Consider the computational problem T.MPRINTSGin20, defined as follows. The input is an ASCII description of a Turing machine M. If M prints a G within its first 20 steps on input I, then I is a solution. If there is no such string I, the solution is "no". Is TMPrintsGin20 computable? Briefly justify your answer, without necessarily giving a rigorous mathematical proof.

Answer 1

The computational problem TMPrintsGin20 is computable. A Turing machine can be simulated to determine if it will print a 'G' within its first 20 steps on a given input.

Step-by-step explanation:

The computational problem TMPrintsGin20 is computable. A Turing machine is a mathematical model that can perform computation, and therefore it is possible to determine whether it will print a 'G' within its first 20 steps on a given input.

To determine if M prints a 'G' within its first 20 steps, we can simulate the steps of the Turing machine on the input I until either a 'G' is printed or 20 steps have been reached. If a 'G' is printed, then I is a solution. Otherwise, if no 'G' is printed within the first 20 steps, the solution is 'no'.

For example, let's say the Turing machine M reads the input I character by character and prints a 'G' if it encounters a specific character. We can simulate the steps of M on I, and if a 'G' is printed within the first 20 steps, we know that I is a solution.