Examples of using Primitive recursive in English and their translations into Serbian
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Is also primitive recursive.
Exponentiation and primality testing are primitive recursive.
However, all primitive recursive functions halt.
For every e, the function h(n)= f(e, n)is primitive recursive.
Primitive recursive arithmetic was first proposed by Thoralf Skolem in 1923.
Course-of-values recursion defines primitive recursive functions.
The set of primitive recursive functions is known as PR in computational complexity theory.
For example, if g andh are 2-ary primitive recursive functions then.
Some additional forms of recursion also define functions that are in fact primitive recursive.
To fit this into a strict primitive recursive definition, define.
This argument provides a computable function which is not primitive recursive.
In the following we observe that primitive recursive functions can be of four types.
Most of the functions normally studied in number theory are primitive recursive.
Let fn denote the unary primitive recursive function given by this definition.
This argument provides a total computable function that is not primitive recursive.
In order to fit this into a strict primitive recursive definition, we define.
The primitive recursive functions of one argument(i.e., unary functions) can be computably enumerated.
Some forms of mutual recursion also define primitive recursive functions.
Most notably, there are primitive recursive problems that are not in ELEMENTARY.
The Paris- Harrington theorem involves a total recursive function that is not primitive recursive.
More complex primitive recursive functions can be obtained by applying the operations given by these axioms.
Other examples of total recursive but not primitive recursive functions are known.
However, the primitive recursive functions are not the largest recursively enumerable set of total computable functions.
Most number-theoretic functions definable using recursion on a single variable are primitive recursive.
This means that the n-th definition of a primitive recursive function in this enumeration can be effectively determined from n.
In the late 19th century, Leopold Kronecker formulated notions of computability,defining primitive recursive functions.
Primitive recursive functions tend to correspond very closely with our intuition of what a computable function must be.
In fact, it is difficult to devise a function that is"not" primitive recursive, although some are known(see the section on Limitations below).
The primitive recursive functions are the basic functions and those obtained from the basic functions by applying these operations a finite number of times.
It follows that it is difficult to devise a computable function that is not primitive recursive, although some are known(see the section on Limitations below).