Undecidable Problem - The Undecidable Problem in Computability Theory

The Undecidable Problem in Computability Theory

In computability theory, the halting problem is a decision problem which can be stated as follows:

Given the description of an arbitrary program and a finite input, decide whether the program finishes running or will run forever.

Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.