Publications associées à Polynomial greatest common divisor

The multivariate Serre conjecture ring

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Academic Press Inc Elsevier Science2023

A PCP Theorem for Interactive Proofs and Applications

Alessandro Chiesa

The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Formula Normalizations in Verification

Viktor Kuncak, Simon Guilloud, Mario Bucev, Dragana Milovancevic

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2023

Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap

Florent Gérard Krzakala, Lenka Zdeborová, Luca Pesce, Bruno Loureiro, Bruno Loureiro

A simple model to study subspace clustering is the high-dimensional k -Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction error in this model i ...

2022

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

Lars Rohwedder

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. ...

ASSOC COMPUTING MACHINERY2021

Generalization of the Haldane conjecture to SU(n) chains

Frédéric Mila, Miklos Lajko

Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-psymmetric ones with pnot a multiple of 3, it was argued that the ground state exhibits gap ...

2020

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Francesco Cremonesi, Timothée Ewart, Fabien Jonathan Delalondre

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Computer Algebraic Approach to Verification and Debugging of Galois Field Multipliers

Cunxi Yu, Maciej Jerzy Ciesielski

The paper presents a novel method to verify and debug gate-level arithmetic circuits implemented in Galois Field arithmetic. The method is based on forward reduction of the specification polynomials of the circuit in GF(2(m)) using GF(2) models of its logi ...

IEEE2018