THE TURING MACHINE OF ACKERMANN' S FUNCTIO N M . A . Mc BETH , Computer Centre, Goldsmith's College, London . 1 Introduction ACKERMANN's arithmetic function : 211( x , y) = x + y; 2t +i( x , 1 ) = x ; 2t,l+i( x , y + 1 ) = Zan{ x , 2tn-f-1( x > y ) } although of more potent growth than any primitive recursive function, is nonetheless de fined effectively by double recursion, and so Qt E 7., the (non-constructive) class of genera l recursive functions . Therefore, since any f E R has among its equivalent formulations , representability in first-order arithmetic, and computability by a TURING machine (o r flow-chart), it may be of interest to the reader to see that the flow-chart of 2t is easily given . To complement this, the feather diagram of the calculation of %,,, (x, y) is sketched, wit h application to a characterization of 2i due to G . MILLS . 2 Initial Cases The special case 2t1 (x,1) = x + 1 (defying 21,E + 1 (x,1) = x) necessitates flow-charts especiall y for addition of y = z(l) to x =
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The Turing machine of Ackermann's function
McBeth, M. A.
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, Volume 23 (1)
Association for Computing Machinery – Jan 25, 1992
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