In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amount of time.
However, when the true answer is 'no', the procedure is not required to halt; it may go into an "infinite loop" for some 'no' cases.
Such a procedure is sometimes called a semi-algorithm, to distinguish it from an algorithm, defined as a complete solution to a decision problem.
Equivalently, RE is the class of decision problems for which a Turing machine can list all the 'yes' instances, one by one (this is what 'enumerable' means).
[3] In fact, it is the intersection of those two classes, because we can decide any problem for which there exists a recogniser and also a co-recogniser by simply interleaving them until one obtains a result.
In January of 2020, a preprint announced a proof that RE was equivalent to the class MIP* (the class where a classical verifier interacts with multiple all-powerful quantum provers who share entanglement);[4] a revised, but not yet fully reviewed, proof was published in Communications of the ACM in November 2021.