Question

Show that the problem of deciding whether a specific program with a specific input halts is solvable.

Short answer

We can decide whether a program with a specific input halts is solvable by running the two programs and the one which halts is solvable.

Step-by-step solution

Step 1:

A = A program

I =Input of the program

Step 2:

We now write a program A' such that A(I) halts if and only if A' does not halt.

Now we will run both the programs.

Any one of the two, A(I) or A'(I) will halt.

Thus the given program with a specific input halts is solvable.