AbstractWe give a method, based on algebraic geometry, to show lower bounds for the complexity of polynomials with algebraic coefficients. Typical examples are polynomials with coefficients which are roots of unity, such as Σj=1de2πiiXi and Σj=ide2πipiXj where pj is the jth prime number.We apply the method also to systems of linear equations
We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formula...
We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degre...
In circuit complexity, the polynomial method is a general approach to proving circuit lower bounds i...
AbstractWe present a very simple method to prove lower bounds for the nonscalar complexity of polyno...
AbstractWe generalize several methods for obtaining lower bounds for the complexity of polynomials, ...
AbstractWe prove new lower bounds for the complexity of polynomials, e.g., for polynomials with 0–1-...
In recent years a number of algorithms have been designed for the "inverse" computational ...
AbstractThis paper gives nearly optimal lower bounds on the minimum degree of polynomial calculus re...
La complexité algorithmique est l'étude des ressources nécessaires — le temps, la mémoire, … — pour ...
AbstractWe present a new method to obtain lower bounds for the time complexity of polynomial evaluat...
AbstractFor given f1,…,fm ϵ K[x] which are relatively prime we present degree bounds on the ai neede...
What is the smallest formula computing a given multivariate polynomial f(x)= In this talk I will pr...
In this paper we review the existing linear and quadratic complexity (upper) bounds on the values of...
AbstractFor each wϵN we establish polynomials Rw,jjϵN with (w+1)(w+2)2 variables and deg Rw,j⩽2wj+1 ...
The doctoral dissertation deals with mathematical problems related to various heights of polynomials...
We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formula...
We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degre...
In circuit complexity, the polynomial method is a general approach to proving circuit lower bounds i...
AbstractWe present a very simple method to prove lower bounds for the nonscalar complexity of polyno...
AbstractWe generalize several methods for obtaining lower bounds for the complexity of polynomials, ...
AbstractWe prove new lower bounds for the complexity of polynomials, e.g., for polynomials with 0–1-...
In recent years a number of algorithms have been designed for the "inverse" computational ...
AbstractThis paper gives nearly optimal lower bounds on the minimum degree of polynomial calculus re...
La complexité algorithmique est l'étude des ressources nécessaires — le temps, la mémoire, … — pour ...
AbstractWe present a new method to obtain lower bounds for the time complexity of polynomial evaluat...
AbstractFor given f1,…,fm ϵ K[x] which are relatively prime we present degree bounds on the ai neede...
What is the smallest formula computing a given multivariate polynomial f(x)= In this talk I will pr...
In this paper we review the existing linear and quadratic complexity (upper) bounds on the values of...
AbstractFor each wϵN we establish polynomials Rw,jjϵN with (w+1)(w+2)2 variables and deg Rw,j⩽2wj+1 ...
The doctoral dissertation deals with mathematical problems related to various heights of polynomials...
We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formula...
We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degre...
In circuit complexity, the polynomial method is a general approach to proving circuit lower bounds i...
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