Primitive Recursive Functions

Some articles on primitive recursive functions, function, recursive, recursive functions, functions, primitive:

Primitive Recursive Function - Examples - Subtraction
... Because primitive recursive functions use natural numbers rather than integers, and the natural numbers are not closed under subtraction, a limited subtraction function is ... This limited subtraction function sub(a,b) returns if this is nonnegative and returns 0 otherwise ... The predecessor function acts as the opposite of the successor function and is recursively defined by the rules pred(0)=0, pred(n+1)=n ...
Algorithm Characterizations - 1943, 1952 Stephen Kleene's Characterization - 1943 "Thesis I", 1952 "Church's Thesis"
... Every effectively calculable function (effectively decidable predicate) is general recursive" (First stated by Kleene in 1943 (reprinted page 274 in Davis, ed ... The Undecidable appears also verbatim in Kleene (1952) p.300) In a nutshell to calculate any function the only operations a person needs (technically ... or algorithm, for the case of a function (predicate) of natural numbers" (p ...
μ-recursive Function - Definition
... The μ-recursive functions (or partial μ-recursive functions) are partial functions that take finite tuples of natural numbers and return a single natural number ... They are the smallest class of partial functions that includes the initial functions and is closed under composition, primitive recursion, and the μ operator ... The smallest class of functions including the initial functions and closed under composition and primitive recursion (i.e ...
Primitive Recursive Function
... The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive ... In computability theory, primitive recursive functions are a class of functions that form an important building block on the way to a full formalization of computability ... These functions are also important in proof theory ...
Grzegorczyk Hierarchy - Relation To Primitive Recursive Functions
... hierarchy can be seen as a way to limit the power of primitive recursion to different levels ... It is clear from this fact that all functions in any level of the Grzegorczyk hierarchy are primitive recursive functions (i.e ... and thus It can also be shown that all primitive recursive functions are in some level of the hierarchy (Rose 1984 Gakwaya 1997), thus and the sets partition the set of ...

Famous quotes containing the words functions and/or primitive:

    Empirical science is apt to cloud the sight, and, by the very knowledge of functions and processes, to bereave the student of the manly contemplation of the whole.
    Ralph Waldo Emerson (1803–1882)

    The primitive wood is always and everywhere damp and mossy, so that I traveled constantly with the impression that I was in a swamp; and only when it was remarked that this or that tract, judging from the quality of the timber on it, would make a profitable clearing, was I reminded, that if the sun were let in it would make a dry field, like the few I had seen, at once.
    Henry David Thoreau (1817–1862)