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. Informally, it means that if the answer to a problem instance is 'yes', then there is some procedure which takes finite time to determine this, and this procedure never falsely reports 'yes' when the true answer is 'no'. 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.