R (complexity)

In computational complexity theory, R is the class of decision problems solvable by a Turing machine, which is the set of all recursive languages.

Equivalent formulations

R is equivalent to the set of all total computable functions in the sense that:

a decision problem is in R if and only if its indicator function is computable,
a total function is computable if and only if its graph is in R.

Relationship with other classes

Since 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, the class is equal to RE ∩ co-RE.