We give a “regularity lemma” for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1, 1}n . Roughly speaking, this result shows that every degree-d PTF ...
Ilias Diakonikolas, Rocco A. Servedio, Li-Yang Tan...
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algeb...
In this paper we derive aggregate separation bounds, named after Davenport-MahlerMignotte (DMM), on the isolated roots of polynomial systems, specifically on the minimum distance ...
Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsig...
We present algorithms that compute the linear and quadratic factors of supersparse (lacunary) bivariate polynomials over the rational numbers in polynomial-time in the input size....
We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n×n matrix of degree d over ...