Some unsolvable problems possess a semidecision procedure, i.e. an algorithm that correctly outputs “true” but fails to terminate in cases where “false” should be output. This is the same as saying that the inputs requiring the output “true” form a set that is recursively enumerable (but need not be recursive). Alternatively one can say that the problem corresponds to a predicate that is semidecidable (but need not be decidable).
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