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Abstract: Elementary symmetric polynomials S n are used as a benchmark for the boundeddepth arithmetic circuit model of computation. In this work we prove that for constant k's, S n modulo composite numbers m = p 1 p 2 can be computed by homogeneous circuits with much fewer multiplications than over any field, if the coefficients of monomials x i 1 x i 2 \Delta \Delta \Delta x i k are allowed to be 1 either mod p 1 or mod p 2 but not necessarily both. More exactly, we prove that for any constant k ... (Update)
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BibTeX entry: (Update)
Vince Grolmusz. Computing elementary symmetric polynomials with a subpolynomial number of multiplications. Technical Report TR02-052, ECCC, 2002. ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/2002/TR02-052/index.html. http://citeseer.ist.psu.edu/grolmusz02computing.html More
@misc{ grolmusz02computing,
author = "V. Grolmusz",
title = "Computing elementary symmetric polynomials with a subpolynomial number
of multiplications",
text = "Vince Grolmusz. Computing elementary symmetric polynomials with a subpolynomial
number of multiplications. Technical Report TR02-052, ECCC, 2002. ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/2002/TR02-052/index.html.",
year = "2002",
url = "citeseer.ist.psu.edu/grolmusz02computing.html" }
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Documents on the same site (ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/2002/TR02-052/index.html):
Computing Elementary Symmetric Polynomials with a Sub-Polynomial .. - Grolmusz (2002) (Correct)
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