TY - JOUR
T1 - Faster circuits and shorter formulae for multiple addition, multiplication and symmetric Boolean functions
AU - Paterson, Michael S.
AU - Pippenger, Nicholas
AU - Zwick, Uri
PY - 1990
Y1 - 1990
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0025550430&partnerID=8YFLogxK
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AN - SCOPUS:0025550430
SN - 0272-5428
VL - 2
SP - 642
EP - 650
JO - Annual Symposium on Foundations of Computer Science - Proceedings
JF - Annual Symposium on Foundations of Computer Science - Proceedings
T2 - Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Y2 - 22 October 1990 through 24 October 1990
ER -