pysähtymisongelma
The halting problem, known in Finnish as the pysähtymisongelma, is a fundamental decision problem in computability theory. It asks whether it is possible to determine, for an arbitrary program and an arbitrary input, whether the program will eventually finish running (halt) or continue to run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. This is a landmark result in computer science, demonstrating inherent limitations of computation.
The proof of the halting problem's undecidability typically involves a self-referential argument. Imagine a hypothetical program,
The undecidability of the halting problem has profound implications. It implies that there are problems that