- PR (complexity)
PR is the complexity class of all
primitive recursive function s – or, equivalently, the set of allformal language s that can be decided by such a function. This includes addition, multiplication, exponentiation, tetration, etc.The
Ackermann function is an example of a function that is "not" primitive recursive, showing that PR is strictly contained in R.PR functions can be explicitly enumerated, whereas functions in R cannot be (since otherwise the
halting problem would be decidable). That is, PR is a "syntactic" class whereas R is "semantic."On the other hand, we can "enumerate" any
recursively enumerable set (see also its complexity class RE) by a primitive-recursive function in the following sense: given an input ("M", "k"), where "M" is a Turing machine and "k" is an integer, if "M" halts within "k" steps then output "M"; otherwise output nothing. Then the union of the outputs, over all possible inputs ("M", "k"), is exactly the set of "M" that halt.PR strictly contains
ELEMENTARY .ee also
*
Primitive recursive function
Wikimedia Foundation. 2010.