Computability theory

study of computable functions and Turing degrees

Computability theory is part of computer science. Scientists want to know what can be computed, and what can not.

There is a model of a computer that is used for this. It is called the Turing machine. A Turing machine basically is a special typewriter with an endless ribbon. The machine is named after the mathematician Alan Turing.

A problem is computable if it can be expressed in such a way that a Turing machine can solve it.

One of the best known examples is the Halting problem. The task is to write a program which says for all programs whether they will finally stop. This is impossible to decide. Mathematicians say the problem is undecidable.