Manuals/calci/ACKERMANN

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ACKERMANN(m,n)


  • and are the positive integers.

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A(m,n) = \begin{cases} n+1 \mbox {if} \mbox {m=0} \\ A(m-1,1) & \mbox {if} \mbox {m>0} and \mbox {n=0} \\ A(m-1,A(m,n-1))& \mbox {if} \mbox {m>0} and \mbox {n>0} \end{cases} } for nonnegative integers m and n.

  • Its value grows rapidly, even for small inputs.