Wikipedia:Today's featured article/September 24, 2004

From Wikipedia, the free encyclopedia
Defintion of the Akermann function
Defintion of the Akermann function

The Ackermann function is an important example encountered by mathematicians in the theory of computation. It is a recursive function which takes two natural numbers as arguments and returns a natural number as its value. In 1928, Wilhelm Ackermann considered a function A (mnp) of three variables, the p-fold iterated exponentiation of m with n or m → n → p in Conway's notation. He proved that it is a recursive function which is not primitive recursive. This definition was later simplified by Rozsa Peter and Raphael Robinson to the two-variable definition given above. It grows extremely quickly, and this extreme growth can be exploited to show that the computable function f (n) = A(nn) grows faster than any primitive-recursive function and is therefore not primitive-recursive. Due to its definition in terms of extremely deep recursion, it can be used as a benchmark of a compiler's ability to optimize recursion. (more...)

Recently featured: Black holeIrish theatreCoronation of the British monarch