Asymptotically Optimal Circuit for a Storage Access Function

Authors:
P. Klein;M. S. Paterson
Affiliations:
Department of Mathematics, University of Bielefeld;-
Venue:
IEEE Transactions on Computers
Year:
1980

Citing 0
Cited 2

A well-mixed function with circuit complexity 5n ± o(n): tightness of the Lachish-Raz-type bounds

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A well-mixed function with circuit complexity 5n: Tightness of the Lachish-Raz-type bounds

Theoretical Computer Science

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Abstract

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(vn) gates and a depth asymptotic to k.