Semidecided

Semidecided is an English adjective used primarily in theoretical computer science and logic to describe a proposition, problem, or statement that has been addressed by a semidecision procedure, but has not been fully decided. In computability theory, a problem is semidecidable if there exists a Turing machine that halts with a positive answer for every yes-instance and may run forever on no-instances. A problem described as semidecided would be one for which a semidecision procedure can confirm membership (the statement is true) in finite time, but does not guarantee rejection of non-membership; the negation may be non-semi-decidable.

The term is uncommon and often replaced by semi-decidable or recursively enumerable. Semidecided can be used informally to emphasize the process or state of partial verification, as in “the property is semidecided for this set” meaning that some instances have been verified via semidecision. It is distinct from decidable, where both yes and no answers are guaranteed to be produced by an algorithm in finite time, and from non-semidecidable cases, where neither membership nor non-membership can be confirmed by such a procedure.

In usage, semidecided appears mainly in informal expositions, discussions of undecidability, or as a pedagogical shorthand when contrasting with full decidability. See also semi-decidable, recursively enumerable, co-recursively enumerable, Turing machine.