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

Grzegorczyk Hierarchy - Relation To

... The definition of is the same as that of the

**Primitive Recursive Functions**... The definition of is the same as that of the

**primitive recursive functions**, RP, except that recursion is limited ( for some j in ) and the**functions**are ... 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 ...Algorithm Characterizations - 1943, 1952 Stephen Kleene's Characterization - 1943 "Thesis I", 1952 "Church's Thesis"

... Every effectively calculable

... 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, formally) are ... definition of the notion of a calculation (decision) procedure or algorithm, for the case of a**function**(predicate) of natural numbers" (p ...Primitive Recursive Function

... The

... The

**primitive recursive functions**are defined using**primitive**recursion and composition as central operations and are a strict subset of the total µ-**recursive functions**(µ-rec ... 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 ...Primitive Recursive Function - Examples - Subtraction

... Because

... Because

**primitive recursive functions**use natural numbers rather than integers, and the natural numbers are not closed under subtraction, a limited subtraction ... 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 ...μ-recursive Function - Definition

... The μ-

... 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 ...### Famous quotes containing the words functions and/or primitive:

“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity *functions* in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”

—Terri Apter (20th century)

“The sight of a Black nun strikes their sentimentality; and, as I am unalterably rooted in native ground, they consider me a work of *primitive* art, housed in a magical color; the incarnation of civilized, anti-heathenism, and the fruit of a triumphing idea.”

—Alice Walker (b. 1944)

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