We consider the problem of solving systems of multivariate polynomial equations of degree
k over a finite field. For every integer k≤ 2 and finite field q where q= pd for a prime p, we …

Hardness magnification reduces major complexity separations (such as EXP⊈ NC 1) to
proving lower bounds for some natural problem Q against weak circuit models. Several …

We consider a notion of probabilistic rank and probabilistic sign-rank of a matrix, which
measure the extent to which a matrix can be probabilistically represented by low-rank …

We study a simple and general template for constructing affine extractors by composing a
linear transformation with resilient functions. Using this we show that good affine extractors …

Given a Boolean function f:{-1, 1}^{n}→{-1, 1, define the Fourier distribution to be the
distribution on subsets of [n], where each S⊆[n] is sampled with probability f ˆ (S) 2. The …

We give new quantum algorithms for evaluating composed functions whose inputs may be
shared between bottom-level gates. Let $ f $ be an $ m $-bit Boolean function and consider …

A natural model of read-once linear branching programs is a branching program where
queries are $\mathbb {F} _2 $ linear forms, and along each path, the queries are linearly …

We show that over the field of complex numbers, every homogeneous polynomial of degree
d can be approximated (in the border complexity sense) by a depth-3 arithmetic circuit of top …

Approximate Degree in Classical and Quantum Computing Page 1 Approximate Degree in
Classical and Quantum Computing Page 2 Other titles in Foundations and Trends® in …

The border, or the approximative, model of algebraic computation (VP) is quite popular due
to the Geometric Complexity Theory (GCT) approach to P≠ NP conjecture, and its complex …