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

Michael S. Paterson*, Nicholas Pippenger, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

11 Scopus citations

Abstract

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 n1/p+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.

Original languageEnglish
Pages (from-to)642-650
Number of pages9
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
Volume2
StatePublished - 1990
Externally publishedYes
EventProceedings of the 31st Annual Symposium on Foundations of Computer Science - St. Louis, MO, USA
Duration: 22 Oct 199024 Oct 1990

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