Super-Critical Trade-Offs in Resolution over Parities via Lifting

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10515158" target="_blank" >RIV/00216208:11320/25:10515158 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.CCC.2025.24" target="_blank" >https://doi.org/10.4230/LIPIcs.CCC.2025.24</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2025.24" target="_blank" >10.4230/LIPIcs.CCC.2025.24</a>

Result language

angličtina

Original language name

Super-Critical Trade-Offs in Resolution over Parities via Lifting

Original language description

Razborov [24] exhibited the following surprisingly strong trade-off phenomenon in propositional proof complexity: for a parameter k = k(n), there exists k-CNF formulas over n variables, having resolution refutations of O(k) width, but every tree-like refutation of width n(1-epsilon)/k needs size exp (n(Omega(k))). We extend this result to tree-like Resolution over parities, commonly denoted by Res(circle plus), with parameters essentially unchanged. To obtain our result, we extend the lifting theorem of Chattopadhyay, Mande, Sanyal and Sherif [11] to handle tree-like affine DAGs. We introduce additional ideas from linear algebra to handle forget nodes along long paths.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GN22-14872O" target="_blank" >GN22-14872O: Combinatorial Methods in Information Theory</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-379-9

ISSN

1868-8969

e-ISSN

—

Number of pages

19

Pages from-to

1-19

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Wadern

Event location

Toronto

Event date

Aug 5, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001589513400024