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139
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FOCS
2007
IEEE
15 years 11 months ago
A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits
We construct an explicit polynomial f(x1, . . . , xn), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least ...
Ran Raz, Amir Shpilka, Amir Yehudayoff
ICTAC
2007
Springer
15 years 11 months ago
Discovering Non-linear Ranking Functions by Solving Semi-algebraic Systems
Abstract. Differing from [6] this paper reduces non-linear ranking function discovering for polynomial programs to semi-algebraic system solving, and demonstrates how to apply the...
Yinghua Chen, Bican Xia, Lu Yang, Naijun Zhan, Cha...
122
Voted
ARITH
2003
IEEE
15 years 10 months ago
"Partially Rounded" Small-Order Approximations for Accurate, Hardware-Oriented, Table-Based Methods
We aim at evaluating elementary and special functions using small tables and small, rectangular, multipliers. To do that, we show how accurate polynomial approximations whose orde...
Jean-Michel Muller
ISAAC
2007
Springer
158views Algorithms» more  ISAAC 2007»
15 years 11 months ago
On the Expressive Power of Planar Perfect Matching and Permanents of Bounded Treewidth Matrices
Valiant introduced some 25 years ago an algebraic model of computation along with the complexity classes VP and VNP, which can be viewed as analogues of the classical classes P and...
Uffe Flarup, Pascal Koiran, Laurent Lyaudet
CORR
2006
Springer
87views Education» more  CORR 2006»
15 years 5 months ago
Low Complexity Algorithms for Linear Recurrences
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; ind...
Alin Bostan, Frédéric Chyzak, Bruno ...