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From: grunwald@uiucdcsb.UUCP
Newsgroups: net.math
Subject: Re: Beyond Exponentiation
Message-ID: <9700033@uiucdcsb.UUCP>
Date: Mon, 4-Feb-85 18:46:00 EST
Article-I.D.: uiucdcsb.9700033
Posted: Mon Feb  4 18:46:00 1985
Date-Received: Wed, 6-Feb-85 04:15:27 EST
References: <186@ihnet.UUCP>
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Nf-ID: #R:ihnet:-18600:uiucdcsb:9700033:000:377
Nf-From: uiucdcsb!grunwald    Feb  4 17:46:00 1985

You can define ackermanns function as:

S[1] := m;
S[2] := n;
i := 2;
while (i != 1) do
	if (S[i-1] == 0) {
		S[i-1] := S[i] + 1;
		i := i -1;
	}
	else if ( S[i] == 0 ) {
		S[i-1] := S[i-1] - 1;
		S[i] := 1;
	}
	else {
		S[i+1] := S[i] - 1;
		S[i] := S[i+1];
		S[i-1] := S[i-1] - 1;
		i := i + 1;
	}
}
z := S[1];

As in "Mathematical Theory of Computation" by Manna, Page 235.