Undecidable decision problem
= Undecidable decision problem
= Undecidable
{synonym}
A decision problem for which no <algorithm> terminates with the correct yes-or-no answer on every input. For example, if the <diagonal halting set> had a decision algorithm, a program could halt on its own code exactly when that algorithm says it does not halt, producing a contradiction. An <undecidable decision problem> may still admit a partial procedure that terminates on every yes-instance.