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09/18/2023
Deterministic Algorithms for Low Degree Factors of Constant Depth Circuits
For every constant d, we design a subexponential time deterministic algo...
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08/08/2023
Determinants vs. Algebraic Branching Programs
We show that for every homogeneous polynomial of degree d, if it has det...
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04/03/2023
Fast Numerical Multivariate Multipoint Evaluation
We design nearly-linear time numerical algorithms for the problem of mul...
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04/30/2022
Fast Multivariate Multipoint Evaluation Over All Finite Fields
Multivariate multipoint evaluation is the problem of evaluating a multiv...
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11/15/2021
Fast, Algebraic Multivariate Multipoint Evaluation in Small Characteristic and Applications
Multipoint evaluation is the computational task of evaluating a polynomi...
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03/14/2021
Ideal-theoretic Explanation of Capacity-achieving Decoding
In this work, we present an abstract framework for some algebraic error-...
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12/13/2020
If VNP is hard, then so are equations for it
Assuming that the Permanent polynomial requires algebraic circuits of ex...
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12/07/2020
Monotone Circuit Lower Bounds from Robust Sunflowers
Robust sunflowers are a generalization of combinatorial sunflowers that ...
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12/02/2020
Decoding Multivariate Multiplicity Codes on Product Sets
The multiplicity Schwartz-Zippel lemma bounds the total multiplicity of ...
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09/05/2020
A Lower Bound on Determinantal Complexity
The determinantal complexity of a polynomial P ∈𝔽[x_1, …, x_n] over a fi...
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04/29/2020
On the Existence of Algebraically Natural Proofs
For every constant c > 0, we show that there is a family {P_N, c} of pol...
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03/29/2020
A Polynomial Degree Bound on Defining Equations of Non-rigid Matrices and Small Linear Circuits
We show that there is a defining equation of degree at most 𝗉𝗈𝗅𝗒(n) for ...
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11/28/2019
Schur Polynomials do not have small formulas if the Determinant doesn't!
Schur Polynomials are families of symmetric polynomials that have been c...
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11/26/2019
A Quadratic Lower Bound for Algebraic Branching Programs and Formulas
We show that any Algebraic Branching Program (ABP) computing the polynom...
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11/26/2019
A Quadratic Lower Bound for Algebraic Branching Programs
We show that any Algebraic Branching Program (ABP) computing the polynom...
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04/30/2019
Derandomization from Algebraic Hardness
A hitting-set generator (HSG) is a polynomial map G:F^k →F^n such that f...
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04/30/2019
Derandomization from Algebraic Hardness: Treading the Borders
A hitting-set generator (HSG) is a polynomial map Gen:F^k →F^n such that...
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04/02/2019
Lower Bounds for Matrix Factorization
We study the problem of constructing explicit families of matrices which...
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03/06/2019
Closure of VP under taking factors: a short and simple proof
In this note, we give a short, simple and almost completely self contain...
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02/19/2019
Towards Optimal Depth Reductions for Syntactically Multilinear Circuits
We show that any n-variate polynomial computable by a syntactically mult...
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07/17/2018
Near-optimal Bootstrapping of Hitting Sets for Algebraic Models
The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel [Ore22,DL78,Zi...
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07/17/2018
Near-optimal Bootstrapping of Hitting Sets for Algebraic Circuits
The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel states that an...
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06/15/2018
Arithmetic Circuits with Locally Low Algebraic Rank
In recent years, there has been a flurry of activity towards proving low...
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04/24/2018
On Multilinear Forms: Bias, Correlation, and Tensor Rank
In this paper, we prove new relations between the bias of multilinear fo...
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04/10/2018
On top fan-in vs formal degree for depth-3 arithmetic circuits
We show that over the field of complex numbers, every homogeneous polyno...
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03/15/2018
Some Closure Results for Polynomial Factorization and Applications
In a sequence of seminal results in the 80's, Kaltofen showed that the c...
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08/07/2017
