Primitive Recursive

Some articles on primitive recursive, recursive, primitive:

Random-access Machine - The "indirect" Operation - Bounded Indirection and The Primitive Recursive Functions
... this problem of indirection if we are to compute the recursive functions (also called the μ-recursive functions ) – both total and partial varieties ... form of indirection – and thereby compute the sub-class of primitive recursive functions – by using a primitive recursive "operator" called "definition by cases" (defined in ... will not allow us to compute the partial recursive functions – for those we need unbounded indirection aka the μ operator ...
Course-of-values Recursion - Application To Primitive Recursive Functions
... In the context of primitive recursive functions, it is convenient to have a means to represent finite sequences of natural numbers as single natural numbers ... It can be shown that, with this representation, the ordinary operations on sequences are all primitive recursive ... of sequences, it can be seen that if h(m) is primitive recursive then the function ...
Mc Carthy Formalism - Introduction - Expansion of IF-THEN-ELSE To The CASE Operator
... a definition of what it means to be a primitive recursive function "A function φ is primitive recursive in ψ1...ψl (briefly Ψ), if there is a finite ... a "basis" function (it can be a constant such as 0), primitive recursion uses either the base or the previous value of the function to produce the value of the function primitive recursion is ... IF-THEN-ELSE—the "case statement" (or "switch statement")--is primitive recursive can be found in Kleene 1952229 at "#F ('mutually-exclusive predicates')" ...
PR (complexity)
... PR is the complexity class of all primitive recursive functions – or, equivalently, the set of all formal languages that can be decided by such a function ... Ackermann function is an example of a function that is not primitive recursive, showing that PR is strictly contained in R ... 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 ...
Counter Machine - The Partial Recursive Functions: Building "convenience Instructions" Using Recursion
... And in fact the following is summary of how the primitive recursive functions such as ADD, MULtiply and EXPonent can come about (see Boolos-Burgess-Jeffrey (2002) p ... CLR, J, DEC, INC, JZ, H } In general, we can build any partial- or total- primitive recursive function that we wish, by using the same methods ... (2002) give demonstrations of how to form the five primitive recursive function "operators" (1-5 below) from the base set (1) ...

Famous quotes containing the word primitive:

    How far men go for the material of their houses! The inhabitants of the most civilized cities, in all ages, send into far, primitive forests, beyond the bounds of their civilization, where the moose and bear and savage dwell, for their pine boards for ordinary use. And, on the other hand, the savage soon receives from cities iron arrow-points, hatchets, and guns, to point his savageness with.
    Henry David Thoreau (1817–1862)