What is Ackermann's Function?

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive. See the article "A function to end all functions" by GŁnter Dotzel, Algorithm 2.4, Oct 1991, Pg 16. The function f(x) = A(x, x) grows much faster than polynomials or exponentials. The definition is:

	1. If x = 0 then  A(x, y) = y + 1
	2. If y = 0 then  A(x, y) = A(x-1, 1)
	3. Otherwise,     A(x, y) = A(x-1, A(x, y-1))

See: Ackermann Function -- From MathWorld
See: Ackermann Function -- From Wikipedia, the free encyclopedia

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