Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › Рецензирование
Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs. / de Rezende, Susanna F.; Nordström, Jakob; Risse, Kilian; Sokolov, Dmitry.
35th Computational Complexity Conference, CCC 2020. ред. / Shubhangi Saraf. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. 28 (Leibniz International Proceedings in Informatics, LIPIcs; Том 169).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › Рецензирование
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TY - GEN
T1 - Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs
AU - de Rezende, Susanna F.
AU - Nordström, Jakob
AU - Risse, Kilian
AU - Sokolov, Dmitry
N1 - Funding Information: Funding The authors were funded by the Knut and Alice Wallenberg grant KAW 2016.0066. In addition, the second author was supported by the Swedish Research Council grant 2016-00782 and the Independent Research Fund Denmark (DFF) grant 9040-00389B, and the fourth author by the Knut and Alice Wallenberg grant KAW 2016.0433. Part of this work was carried out while visiting the Simons Institute for the Theory of Computing in association with the DIMACS/Simons Collaboration on Lower Bounds in Computational Complexity, which is conducted with support from the National Science Foundation. Publisher Copyright: © Susanna F. de Rezende, Jakob Nordström, Kilian Risse, and Dmitry Sokolov; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - We show exponential lower bounds on resolution proof length for pigeonhole principle (PHP) formulas and perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge to establish strong lower bounds in the regime between balanced constant-degree expanders as in [Ben-Sasson and Wigderson'01] and highly unbalanced, dense graphs as in [Raz'04] and [Razborov'03,'04]. We obtain our results by revisiting Razborov's pseudo-width method for PHP formulas over dense graphs and extending it to sparse graphs. This further demonstrates the power of the pseudo-width method, and we believe it could potentially be useful for attacking also other longstanding open problems for resolution and other proof systems.
AB - We show exponential lower bounds on resolution proof length for pigeonhole principle (PHP) formulas and perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge to establish strong lower bounds in the regime between balanced constant-degree expanders as in [Ben-Sasson and Wigderson'01] and highly unbalanced, dense graphs as in [Raz'04] and [Razborov'03,'04]. We obtain our results by revisiting Razborov's pseudo-width method for PHP formulas over dense graphs and extending it to sparse graphs. This further demonstrates the power of the pseudo-width method, and we believe it could potentially be useful for attacking also other longstanding open problems for resolution and other proof systems.
KW - Perfect matching
KW - Proof complexity
KW - Resolution
KW - Sparse graphs
KW - Weak pigeonhole principle
UR - http://www.scopus.com/inward/record.url?scp=85089398484&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CCC.2020.28
DO - 10.4230/LIPIcs.CCC.2020.28
M3 - Conference contribution
AN - SCOPUS:85089398484
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 35th Computational Complexity Conference, CCC 2020
A2 - Saraf, Shubhangi
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 35th Computational Complexity Conference, CCC 2020
Y2 - 28 July 2020 through 31 July 2020
ER -
ID: 75310335