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Faster circuits and shorter formulae for multiple addition, multiplication and symmetric Boolean functions

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3 Author(s)
Paterson, M.S. ; Dept. of Comput. Sci., Warwick Univ., Coventry, UK ; Pippenger, N. ; Zwick, U.

A general theory is developed for constructing the shallowest possible circuits and the shortest possible formulas for the carry-save addition of n numbers using any given basic addition unit. More precisely, it is shown that if BA is a basic addition unit with occurrence matrix N, then the shortest multiple carry-save addition formulas that could be obtained by composing BA units are of size n1p+o(1)/, where p is the unique real number for which the Lp norm of the matrix N equals 1. An analogous result connects the delay matrix M of the basic addition unit BA and the minimal q such that multiple carry-save addition circuits of depth (q+o(1)) log n could be constructed by combining BA units. On the basis of these optimal constructions of multiple carry-save adders, the shallowest known multiplication circuits are constructed

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990