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 equal to the set of all total computable functions.

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.


  • Blum, Lenore, Mike Shub, and Steve Smale. "On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines." Bulletin (New Series) of the American Mathematical Society 21.1 (1989): 1-46.

Complexity Zoo: Class R

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