Definition: A function of two parameters whose value grows very fast.
See also inverse Ackermann function.
Note: Many people have defined other similar functions which are not simply a restating of this one.
In 1928, Wilhelm Ackermann observed that A(x,y,z), the z-fold iterated exponentiation of x with y, is a recursive function that is not primitive recursive. A(x,y,z) was simplified to a function of 2 variables by Rózsa Péter in 1935. Raphael M. Robinson simplified the initial condition in 1948.
Robert Munafo's Versions of Ackermann's Function and analysis. Cowles and Bailey Several Versions of Ackermann's function.
Wilhelm Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Mathematische Annalen 99(1):118-133, December 1928.
The formal definition given here is Gnx in the first page of
Raphael M. Robinson, Recursion and Double Recursion, Bulletin of the American Mathematical Society 54:987-993, October 1948.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 4 October 2010.
HTML page formatted Mon Jul 16 11:56:53 2012.
Cite this as:
Paul E. Black, "Ackermann's function", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 4 October 2010. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/ackermann.html