Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!utgpu!water!watmath!clyde!rutgers!ukma!psuvm.bitnet!cunyvm!maine.bitnet!brent 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. BrittonComputer and Data Processing Services . . . University of Maine System Orono, ME 04469 . . 207/581-3557 ..