Turing's Halting Problem

Turing's Halting Problem asks whether it’s possible to create a program that can correctly determine, for any other program and its input, whether that program will eventually stop running or continue forever. Alan Turing proved that such a universal method cannot exist; there’s no way to know in advance for every case. This means some programs are inherently unpredictable: they may halt or run endlessly, and no validator can always tell which is which. The Halting Problem thus highlights fundamental limits in what machines can precisely foresee about computational processes.