Wikipedia on the Halting Problem: “In computability theory, the halting problem is a decision problem which can be stated as follows: given a description of a program and a finite input, decide whether the program finishes running or will run forever, given that input.” Alan Turing proved that, at least for his own purely abstract-but-nonetheless-computer-like Turing Machine, the halting problem cannot be solved. See also: Busy Beavers, Watchdog Timers, and a Dead Man’s Switch.