In computer science this is known as the halting problem.

One of the best known examples is the Halting problem.

The Halting problem was the first such set to be constructed.

As an example, consider the following variant of the halting problem.

Even undecidable problems, like the halting problem, can be used.

Even more difficult are the undecidable problems, such as the halting problem.

But, many of these index sets are even more complicated than the halting problem.

These numbers have the same Turing degree as the halting problem.

So for the moment we will act like there really is a program that solves the halting problem.

Much of computability theory builds on the halting problem result.

We have previously shown, however, that the halting problem is undecidable.

This was the first question, even before the halting problem, for which undecidability could be proved.

Often the new problem is reduced to solving the halting problem.

The domain is always Turing equivalent to the halting problem.

The Halting problem is a problem in computer science.

The following example shows how to use reduction from the halting problem to prove that a language is undecidable.

We can now show that H decides the halting problem:

Is there a program that solves the halting problem?

Halting problem: Whether a program given a finite input finishes running or will run forever.

Specific instances cannot be given but this follows from the undecidability of the halting problem.

A lot of confusion revolves around the halting problem.

The halting problem is historically important because it was one of the first problems to be proved undecidable.

Let the program for which the halting problem is to be solved be N bits long.

Thus, the halting problem would be solved for .

Because the halting problem is undecidable, termination analysis cannot work correctly in all cases.