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 REco-RE.

References

Complexity Zoo: Class R


Prefix: a b c d e f g h i j k l m n o p q r s t u v w x y z 0 1 2 3 4 5 6 7 8 9

Portal di Ensiklopedia Dunia

Kembali kehalaman sebelumnya