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From: brent@maine.bitnet.UUCP
Newsgroups: comp.misc
Subject: Re: The Ackermann function
Message-ID: <123BRENT@MAINE>
Date: Fri, 4-Dec-87 21:04:25 EST
Article-I.D.: MAINE.123BRENT
Posted: Fri Dec  4 21:04:25 1987
Date-Received: Thu, 10-Dec-87 00:54:11 EST
References: <2093@umd5.umd.edu>
Organization: University of Maine System
Lines: 44

In article <2093@umd5.umd.edu>, cgs@umd5.umd.edu (Chris Sylvain) writes:
>
>Would someone please explain to me what it (Ackermann's function)
>is good for/what it models ?
>...
>I keep getting 'introduced' to it, but never any history of it is provided.
     
Ackermann's function was one of the first functions developed which is
not a Primitive Recursive function.
     
These are the initial functions:
     
    a) The 0-place zero function given by: Z() = 0
     
    b) The i'th k-place projection function given by:
     
          k
         P (n ,...,n ) = n
          i  1      k     i
     
    c) The successor function given by: S(n) = n+1
     
A function is a Primitive Recursive function if it is one of the initial
functions above, or if it can be generated by compositions of initial
functions by Primitive Recursion.  (If you want to know what Primitive
Recursion is, I'd be happy to show you.)
     
ANYHOW, Ackermann's Function is not a Primitive Recursive function, and
I believe it was the first one ever shown not to be.  This makes Ackermann's
function special, because most everything else -- essentially all useful,
computable functions -- is Primative Recursive.
     
HOWEVER, you probably keep getting "introduced" to Ackermann's function
because of the interesting way it behaves when it's first parameter is
large.  Good way to show CS students how recursion can cause problems.
-------
  ..  Sine here...
 .  .         Brent C.J. Britton 
              Computer and Data Processing Services
.    .    .   University of Maine System
              Orono, ME 04469
      .  .    207/581-3557
       ..