Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Standard

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. ed. / Shubhangi Saraf. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. p. 1-24 28 (Leibniz International Proceedings in Informatics, LIPIcs, Vol. 169).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Harvard

de Rezende, SF, Nordström, J, Risse, K & Sokolov, D 2020, Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs. in S Saraf (ed.), 35th Computational Complexity Conference, CCC 2020., 28, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Leibniz International Proceedings in Informatics, LIPIcs, vol. 169, pp. 1-24, 35th Computational Complexity Conference, CCC 2020, Virtual, Online, Germany, 28/07/2020. https://doi.org/10.4230/LIPIcs.CCC.2020.28

APA

de Rezende, S. F., Nordström, J., Risse, K., & Sokolov, D. (2020). Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs. In S. Saraf (Ed.), 35th Computational Complexity Conference, CCC 2020 (pp. 1-24). [28] Schloss Dagstuhl - Leibniz-Zentrum für Informatik. Leibniz International Proceedings in Informatics, LIPIcs Vol. 169 https://doi.org/10.4230/LIPIcs.CCC.2020.28

Vancouver

de Rezende SF, Nordström J, Risse K, Sokolov D. Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs. In Saraf S, editor, 35th Computational Complexity Conference, CCC 2020. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. 2020. p. 1-24. 28. (Leibniz International Proceedings in Informatics, LIPIcs, Vol. 169). https://doi.org/10.4230/LIPIcs.CCC.2020.28

Author

de Rezende, Susanna F. ; Nordström, Jakob ; Risse, Kilian ; Sokolov, Dmitry. / Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs. 35th Computational Complexity Conference, CCC 2020. editor / Shubhangi Saraf. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. pp. 1-24 (Leibniz International Proceedings in Informatics, LIPIcs, Vol. 169).

Bibtex

@inproceedings{03240730b51743f1adeac78320d15e30,
title = "Exponential resolution lower bounds for weak pigeonhole principle and perfect matching formulas over sparse graphs",
abstract = "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.",
keywords = "Perfect matching, Proof complexity, Resolution, Sparse graphs, Weak pigeonhole principle",
author = "{de Rezende}, {Susanna F.} and Jakob Nordstr{\"o}m and Kilian Risse and Dmitry Sokolov",
year = "2020",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.CCC.2020.28",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik",
pages = "1--24",
editor = "Shubhangi Saraf",
booktitle = "35th Computational Complexity Conference, CCC 2020",
note = "35th Computational Complexity Conference, CCC 2020 ; Conference date: 28-07-2020 Through 31-07-2020",

}

RIS

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

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 - Article in proceedings

AN - SCOPUS:85089398484

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 1

EP - 24

BT - 35th Computational Complexity Conference, CCC 2020

A2 - Saraf, Shubhangi

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

T2 - 35th Computational Complexity Conference, CCC 2020

Y2 - 28 July 2020 through 31 July 2020

ER -

ID: 251867082