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Asymptotically Optimal Circuit for a Storage Access Function

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2 Author(s)
Klein, P. ; Department of Mathematics, University of Bielefeld ; Paterson, M.S.

Let gk:{0,1}n+k → {0,1}, where n = 2k, be the binary function defined by gk(a1,···, ak, X0,···, xn-1) = x(a) where (a) is the natural number with binary representation a1,···, ak. This function models the reading operation in a random-access storage. In [1] Paul proved a 2n lower bound to the combinational complexity of gk. This correspondence derives a realization for gk in a circuit with 2n + 0(√n) gates and a depth asymptotic to k.

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Computers, IEEE Transactions on  (Volume:C-29 ,  Issue: 8 )