Article

Notes on Resolution over Linear Equations

Author:

Svyatoslav GryaznovAuthors Info & Claims

Computer Science – Theory and Applications: 14th International Computer Science Symposium in Russia, CSR 2019, Novosibirsk, Russia, July 1–5, 2019, Proceedings

Pages 168 - 179

https://doi.org/10.1007/978-3-030-19955-5_15

Published: 01 July 2019 Publication History

Abstract

We consider the proof system

Res (\oplus)

introduced by Itsykson and Sokolov [8] which is an extension of Resolution proof system and operates with disjunctions of linear equations over

F_{2}

. In this paper we prove exponential lower bounds on tree-like

Res (\oplus)

refutations for Ordering and Dense Linear Ordering principles by Prover-Delayer games.

We also consider the following problem: given two disjunctions of linear equations over ring R decide whether all Boolean satisfying assignments of one of them satisfy another. Part and Tzameret conjectured that for rings

R \neq F_{2}

this problem is

coNP

-hard, but proved it only for rings with

char (R) = 0

and

char (R) \geq 5

[10]. We completely prove the conjecture.

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Cited By

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Gryaznov SOvcharov SRiazanov A(2024)Resolution Over Linear Equations: Combinatorial Games for Tree-like Size and SpaceACM Transactions on Computation Theory10.1145/367541516:3(1-15)Online publication date: 11-Jul-2024
https://dl.acm.org/doi/10.1145/3675415
Efremenko KGarlík MItsykson DMohar BShinkar IO'Donnell R(2024)Lower Bounds for Regular Resolution over ParitiesProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649652(640-651)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649652

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Resolution Over Linear Equations: Combinatorial Games for Tree-like Size and Space
We consider the proof system Res \((\oplus)\) introduced by Itsykson and Sokolov (Ann. Pure Appl. Log.’20), which is an extension of the resolution proof system and operates with disjunctions of linear equations over \({\mathbb {F}}_2\) .

We study ...
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Published In

Computer Science – Theory and Applications: 14th International Computer Science Symposium in Russia, CSR 2019, Novosibirsk, Russia, July 1–5, 2019, Proceedings

Jul 2019

396 pages

ISBN:978-3-030-19954-8

DOI:10.1007/978-3-030-19955-5

Editors:
René van Bevern
Novosibirsk State University, Novosibirsk, Russia
,
Gregory Kucherov
Laboratoire d'Informatique Gaspard-Monge, Marne-la-Vallée, France

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 July 2019

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Gryaznov SOvcharov SRiazanov A(2024)Resolution Over Linear Equations: Combinatorial Games for Tree-like Size and SpaceACM Transactions on Computation Theory10.1145/367541516:3(1-15)Online publication date: 11-Jul-2024
https://dl.acm.org/doi/10.1145/3675415
Efremenko KGarlík MItsykson DMohar BShinkar IO'Donnell R(2024)Lower Bounds for Regular Resolution over ParitiesProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649652(640-651)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649652

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Recommendations

A new PCP outer verifier with applications to homogeneous linear equations and max-bisection

Resolution Over Linear Equations: Combinatorial Games for Tree-like Size and Space

Random resolution refutations

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