Paper Info
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.
Year
DOI
Venue
2019
10.4230/LIPIcs.CCC.2020.28
Electronic Colloquium on Computational Complexity (ECCC)
DocType
Volume
Citations 
Journal
26
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Susanna F. de Rezende1134.35
Jakob Nordström217721.76
Kilian Risse301.01
Dmitry Sokolov477.85