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Ackermann function

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive…

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Ackermann function

Nodes71
Edges70
Triples126
Avg. degree1.97
Density0.028169
Components1

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Ackermann function

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related to External links · 58
Ackermann function → Ackermann, Ackermann's, Ackermann's Function, Ady, Algorithms, An, An Easy-Sounding Problem Yields, Archived, August, Ben, BF02187894, Bigger Number, Black, Brubaker, Computational Geometry, Data Structures, Davenport, December, Dictionary, Discrete
related to General remarks · 12
Ackermann function → Ackermann, An, Each, Expressed, For, However, In, It, Its, Knuth's, This, Turing
related to Table of values · 9
Ackermann function → Ackermann, Computing, First, Here, If, Knuth, The, Then, To
related to As a benchmark · 8
Ackermann function → Ackermann's, Brian Wichmann, Dragoș Vaida, Sundblad's, The, The Ackermann, Whetstone, Yngve Sundblad
related to In discrete geometry · 6
Ackermann function → Ackermann, Certain, Davenport, For, Omega, Schinzel
related to Inverse · 6
Ackermann function → Ackermann, Chazelle's, In, Since, Sometimes Ackermann's, This
related to In computational complexity · 5
Ackermann function → Ackermann, For, Petri, The, The Ackermann
related to Computation by TRS, based on hyperoperators · 4
Ackermann function → Ackermann, As Sundblad, Matos, Porto
related to Computation by term rewriting system, based on 2-ary function · 3
Ackermann function → Ackermann, The, TRS
related to Computation by TRS, based on iterated 1-ary function · 2
Ackermann function → Ackermann, The

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function displaystyle ackermann recursive operatorname primitive inverse functions reduction rules time one begin end number sequence stack computation complexity recursion

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the exponential functioninstance ofincluding very fast-growing functions0.80text
the factorial functioninstance ofincluding very fast-growing functions0.80text
multi-instance ofincluding very fast-growing functions0.80text
superfactorial functionsinstance ofincluding very fast-growing functions0.80text
and even functions defined using Knuth's up-arrow notationinstance ofincluding very fast-growing functions0.80text
a Turing machineinstance ofwhich is obviously computable on a machine with infinite memory0.80text
so is a computable functioninstance ofwhich is obviously computable on a machine with infinite memory0.80text
grows faster than any primitive recursive functioninstance ofwhich is obviously computable on a machine with infinite memory0.80text
is therefore not primitive recursive.Not primitive recursiveThe Ackermann function grows faster than any primitive recursive functioninstance ofwhich is obviously computable on a machine with infinite memory0.80text
therefore is not itself primitive recursive.Proof sketchinstance ofwhich is obviously computable on a machine with infinite memory0.80text
is therefore not primitive recursiveinstance ofwhich is obviously computable on a machine with infinite memory0.80text
Ackermann functionrelated to As a benchmarkThe Ackermann0.60section

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