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 (also called decidable 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.

References

Complexity Zoo: Class R


P ≟ NP 

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