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Lower bounds for the polynomial calculus and the Gröbner basis algorithm

Authors:

Russell Impagliazzo,

Pavel Pudlák,

Jiří SgallAuthors Info & Claims

Computational Complexity, Volume 8, Issue 2

Pages 127 - 144

https://doi.org/10.1007/s000370050024

Published: 01 November 1999 Publication History

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Torán JWörz F(2024)Cutting Planes Width and the Complexity of Graph Isomorphism RefutationsACM Transactions on Computational Logic10.1145/367712125:4(1-25)Online publication date: 18-Jul-2024
https://dl.acm.org/doi/10.1145/3677121
Mikša MNordström J(2024)A Generalized Method for Proving Polynomial Calculus Degree Lower BoundsJournal of the ACM10.1145/367566871:6(1-43)Online publication date: 4-Jul-2024
https://dl.acm.org/doi/10.1145/3675668
Hakoniemi TLimaye NTzameret IMohar BShinkar IO'Donnell R(2024)Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and BarriersProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649616(1396-1404)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649616
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Index Terms

Lower bounds for the polynomial calculus and the Gröbner basis algorithm
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation

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Published In

Computational Complexity Volume 8, Issue 2

Nov. 1999

103 pages

ISSN:1016-3328

Editor:
Joachim von zur Gathen
Univ.-GH Paderborn, Paderborn, Germany

Issue’s Table of Contents

Publisher

Birkhauser Verlag

Switzerland

Publication History

Published: 01 November 1999

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Torán JWörz F(2024)Cutting Planes Width and the Complexity of Graph Isomorphism RefutationsACM Transactions on Computational Logic10.1145/367712125:4(1-25)Online publication date: 18-Jul-2024
https://dl.acm.org/doi/10.1145/3677121
Mikša MNordström J(2024)A Generalized Method for Proving Polynomial Calculus Degree Lower BoundsJournal of the ACM10.1145/367566871:6(1-43)Online publication date: 4-Jul-2024
https://dl.acm.org/doi/10.1145/3675668
Hakoniemi TLimaye NTzameret IMohar BShinkar IO'Donnell R(2024)Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and BarriersProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649616(1396-1404)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649616
Kaufmann DFleury MBiere AKauers M(2024)Practical algebraic calculus and Nullstellensatz with the checkers Pacheck and Pastèque and Nuss-CheckerFormal Methods in System Design10.1007/s10703-022-00391-x64:1(73-107)Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s10703-022-00391-x
Impagliazzo RMouli SPitassi T(2023)Lower Bounds for Polynomial Calculus with Extension Variables over Finite FieldsProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.7(1-24)Online publication date: 17-Jul-2023
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Sokolov D(2022)Pseudorandom generators, resolution and heavy widthProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.15(1-22)Online publication date: 20-Jul-2022
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Andrews RForbes MLeonardi SGupta A(2022)Ideals, determinants, and straightening: proving and using lower bounds for polynomial idealsProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520025(389-402)Online publication date: 9-Jun-2022
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de Rezende SLauria MNordström JSokolov D(2021)The power of negative reasoningProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.40Online publication date: 20-Jul-2021
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2021.40
Alekseev Y(2021)A lower bound for polynomial calculus with extension ruleProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.21Online publication date: 20-Jul-2021
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Itsykson DOkhotin AOparin V(2021)Computational and Proof Complexity of Partial String AvoidabilityACM Transactions on Computation Theory10.1145/344236513:1(1-25)Online publication date: 21-Jan-2021
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Recommendations

Relation between the XL Algorithm and Gröbner Basis Algorithms

An Algorithm to Check Whether a Basis of a Parametric Polynomial System is a Comprehensive Gröbner Basis and the Associated Completion Algorithm

Conditional GrÖbner Basis: GrÖbner Basis Detection with Parameters

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