What exactly is the halting problem?

Question

Whenever people ask about the halting problem as it pertains to programming, people respond with \"If you just add one loop, you\'ve got the halting program and therefore yo

Answer 1

Here is a program that the halting problem will never be able to solve.

Assume that you have your magical program/method to determine that a program halts.

public bool DeterminesHalt(string filename, string[] args){
    //runs whatever program you tell it do, passing any args
    //returns true if the program halts, false if it doesn't
}

Now lets say we write a small piece of code such as...

public static void Main(string[] args){
    string filename = Console.ReadLine(); //read in file to run from user
    if(DeterminesHalt(filename, args))
        for(;;);
    else
        return;
}

So for this example, we can write a program to do the exact opposite of our magical halting method does. If we somehow determine that a given program will halt, we just hop into an infinite loop; otherwise if we determine that the program is in an infinite loop, we end the program.

No matter how many input checks you do, there is no possible solution to determine whether EVERY program written halts or not.