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Electronic Colloquium on Computational Complexity

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All reports by Author Vince Grolmusz:

TR03-074 | 24th June 2003
Vince Grolmusz

Sixtors and Mod 6 Computations

We consider the following phenomenon: with just one multiplication
we can compute (3u+2v)(3x+2y)= 3ux+4vy mod 6, while computing the same polynomial modulo 5 needs 2 multiplications. We generalize this observation and we define some vectors, called sixtors, with remarkable zero-divisor properties. Using sixtors, we also generalize our earlier result ... more >>>

TR03-058 | 22nd July 2003
Vince Grolmusz

Defying Dimensions Modulo 6

Revisions: 2

We show that a certain representation of the matrix-product can be computed with $n^{o(1)}$ multiplications. We also show, that similar representations of matrices can be compressed enormously with the help of simple linear transforms.

more >>>

TR03-001 | 8th January 2003
Vince Grolmusz

Near Quadratic Matrix Multiplication Modulo Composites

Comments: 1

We show how one can use non-prime-power, composite moduli for
computing representations of the product of two $n\times n$ matrices
using only $n^{2+o(1)}$ multiplications.

more >>>

TR02-052 | 3rd September 2002
Vince Grolmusz

Computing Elementary Symmetric Polynomials with a Sub-Polynomial Number of Multiplications

Revisions: 1

Elementary symmetric polynomials $S_n^k$ are used as a
benchmark for the bounded-depth arithmetic circuit model of computation.
In this work we prove that $S_n^k$ modulo composite numbers $m=p_1p_2$
can be computed with much fewer multiplications than over any field, if
the coefficients of monomials $x_{i_1}x_{i_2}\cdots x_{i_k}$ ... more >>>

TR98-036 | 11th June 1998
Vince Grolmusz, Gábor Tardos

Lower Bounds for (MOD p -- MOD m) Circuits

Modular gates are known to be immune for the random
restriction techniques of Ajtai; Furst, Saxe, Sipser; and Yao and
Hastad. We demonstrate here a random clustering technique which
overcomes this difficulty and is capable to prove generalizations of
several known modular circuit lower bounds of Barrington, Straubing,
Therien; Krause ... more >>>

TR95-046 | 4th August 1995
Vince Grolmusz

On the Power of Circuits with Gates of Low L_1 Norms

We examine the power of Boolean functions with low L_1 norms in several
settings. In large part of the recent literature, the degree of a polynomial
which represents a Boolean function in some way was chosen to be the measure of the complexity of the Boolean function.
However, some functions ... more >>>

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