Undecidable problem
DECISION PROBLEM FOR WHICH IT IS IMPOSSIBLE TO CONSTRUCT AN ALGORITHM THAT ALWAYS LEADS TO A CORRECT YES-OR-NO ANSWER
Undecidable language; Semi-decidable; Undecidable set; Uncomputable problem; Unsolvable problem; Algorithmically insoluble; Algorithmic insolubility; Recursively undecidable; Algorithmically unsolvable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run.