the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is...

work in mathematical logic and the Ackermann function, an important example in the theory of computation. Ackermann was born in Herscheid, Germany, and...

recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other...

rule part of the definition, as in Knuth's up-arrow version of the Ackermann function: a [ n ] b = a [ n − 1 ] ( a [ n ] ( b − 1 ) ) , n ≥ 1 {\displaystyle...

same function within a definition be to arguments that are smaller in some well-partial-order on the function's domain. For instance, for the Ackermann function...

Lamé function Mathieu function Mittag-Leffler function Painlevé transcendents Parabolic cylinder function Arithmetic–geometric mean Ackermann function: in...

grows phenomenally fast as a function of n, far faster than any primitive recursive function or the Ackermann function, for example.[citation needed]...

3=g_{3}(2)=g_{2}^{2}(1)=g_{2}(g_{2}(1))=f^{f(1)}(1)=f^{a^{b}}(1)} The Ackermann function can be expressed using Conway chained arrow notation: A ( m , n )...

faster than exponential functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow faster. See Big...

recursive function that computes their score (computes σ), thus providing a lower bound for Σ. This function's growth is comparable to that of Ackermann's function...

required is O(mα(n)), where α(n) is the extremely slow-growing inverse Ackermann function. Although disjoint-set forests do not guarantee this time per operation...

tetration in Wiktionary, the free dictionary. Ackermann function Big O notation Double exponential function Hyperoperation Iterated logarithm Symmetric...

Sudan function is an example of a function that is recursive, but not primitive recursive. This is also true of the better-known Ackermann function. In...

Wilhelm Ackermann Ackermann function Ackermann ordinal Ackermann set theory Ackermann steering geometry, in mechanical engineering Ackermann's formula...

Turing-complete language and can express all computable functions. For example, it can express the Ackermann function, which (not being primitive recursive) cannot...

primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known...

α(V)) for this loop, where α is the extremely slowly growing inverse Ackermann function. This part of the time bound is much smaller than the time for the...

increasing) function; in particular, Ackermann function. Simple function: a real-valued function over a subset of the real line, similar to a step function. Measurable...

the Ackermann function. Raphael M. Robinson called functions of two natural number variables G(n, x) double recursive with respect to given functions, if...

by a function involving the first four hyperoperators;. Then, f ω ( x ) {\displaystyle f_{\omega }(x)} is comparable to the Ackermann function, f ω +...

extremely large numbers: Knuth's up-arrow notation/hyperoperators/Ackermann function, including tetration Conway chained arrow notation Steinhaus-Moser...

tetration, and A ( n , n ) {\displaystyle A(n,n)} , the diagonal of the Ackermann function. In reality, initial exponential growth is often not sustained forever...

named hyperoperation. This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation. Just as exponentiation grows faster...

the pentation function may also be obtained from the values in the fourth row of the table of values of a variant of the Ackermann function: if A ( n ,...

enormously large – bounds that grow exponentially, or even as fast as the Ackermann function are not uncommon. In some small niche cases, upper and lower bounds...

ISBN 978-3-319-68397-3. Halmos, Chapter 11 Rubtsov, C.A.; Romerio, G.F. (2004). "Ackermann's Function and New Arithmetical Operations" (PDF). Paul R. Halmos (1968). Naive...

mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function. A Latin square...

as μ-operator or mu-operator) because Ackermann (1925) produced a hugely growing function—the Ackermann function—and Rózsa Péter (1935) produced a general...

the rapidly growing Ackermann function A(n, n). (In fact, f ( n ) > A ( n , n ) {\displaystyle f(n)>A(n,n)} for all n.) The function f can also be expressed...

recursive functions such as the Ackermann function. It dominates every computable function provably total in Peano arithmetic, which includes functions such...