Ackermann function
See also Ackermann benchmark, Ackermann
Ackermann function - “The *function A defined inductively on pairs of nonnegative integers. The highly recursive nature of the function makes it a popular choice for testing the ability of *compilers or computers to handle *recursion. It provides an example of a function that is general *recursive but not *primitive recursive because of the exceedingly rapid growth in its value as m increases.” (Fair Use ODCS)
- Snippet from Wikipedia: 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 recursive.
After Ackermann's publication of his function (which had three non-negative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version is the two-argument Ackermann–Péter function developed by Rózsa Péter and Raphael Robinson. Its value grows very rapidly; for example, results in , an integer of 19,729 decimal digits.