Difference between revisions of "Manuals/calci/ACKERMANN"

Revision as of 14:03, 21 September 2016

ACKERMANN(m,n)

The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function.
All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
Its arguments are never negative and it always terminates.
One common version, the two-argument Ackermann–Péter function, is defined as follows:

$A(m,n)={\begin{cases}n+1ifm=0\\A(m-1,1)&{\mbox{if}}m>0andn=0\\A(m-1,A(m,n-1))&{\mbox{if}}m>0andn>0\end{cases}}$ for nonnegative integers m and n.

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-<div style="font-size:30px">'''BETADIST(x,alpha,beta,a,b)'''</div><br/>
+<div style="font-size:30px">'''ACKERMANN(m,n)'''</div><br/>
-*<math>x</math> is the value between <math>a</math> and <math>b</math>
+*<math>m</math>  and <math>n</math> are the positive integers.
-*alpha and beta are the value of the shape parameter
-*<math>a</math> & <math>b</math> the lower and upper limit to the interval of <math>x</math>.
 ==Description==
+*The   Ackermann function   is a classic example of a recursive function, notable especially because it is not a   primitive recursive function.
+*All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
+*Its arguments are never negative and it always terminates.
+*One common version, the two-argument Ackermann–Péter function, is defined as follows:
+<math>A(m,n) = \begin{cases} n+1 if m=0 \\
+A(m-1,1) & \mbox {if} m>0 and n=0 \\
+A(m-1,A(m,n-1))& \mbox {if} m>0 and n>0
+\end{cases}</math>
+for nonnegative integers m and n.
+*Its value grows rapidly, even for small inputs.