Abstract
The maximum depth of recursion refers to the number of levels of activation of a procedure which exist during the deepest call of the procedure. A re-examination of the maximum depth of recursion of the Ackermann function results in a new formula which takes a full account of the dependence of this property on the parameters. It is shown that the recursive use parameter of the Ackermann function contributes to the depth of recursion, and that this contribution may be reduced by rearranging the order of the parameters. The stack required by the Ackermann function was investigated using ALGOL 68-R.
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