Exponential Separation Between Powers of Regular and General Resolution over Parities

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493810" target="_blank" >RIV/00216208:11320/24:10493810 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.CCC.2024.23" target="_blank" >https://doi.org/10.4230/LIPIcs.CCC.2024.23</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2024.23" target="_blank" >10.4230/LIPIcs.CCC.2024.23</a>

Result language

angličtina

Original language name

Exponential Separation Between Powers of Regular and General Resolution over Parities

Original language description

Proving super-polynomial lower bounds on the size of proofs of unsatisfiability of Boolean formulas using resolution over parities is an outstanding problem that has received a lot of attention after its introduction by Itsykson and Sokolov [Dmitry Itsykson and Dmitry Sokolov, 2014]. Very recently, Efremenko, Garlík and Itsykson [Klim Efremenko et al., 2023] proved the first exponential lower bounds on the size of ResLin proofs that were additionally restricted to be bottom-regular. We show that there are formulas for which such regular ResLin proofs of unsatisfiability continue to have exponential size even though there exist short proofs of their unsatisfiability in ordinary, non-regular resolution. This is the first super-polynomial separation between the power of general ResLin and that of regular ResLin for any natural notion of regularity.Our argument, while building upon the work of Efremenko et al. [Klim Efremenko et al., 2023], uses additional ideas from the literature on lifting theorems.

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

2024

Confidentiality

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

Article name in the collection

Proceeding of 39th Computational Complexity Conference (CCC 2024)

ISBN

978-3-95977-331-7

ISSN

1868-8969

e-ISSN

—

Number of pages

32

Pages from-to

1-32

Publisher name

Leibniz International Proceedings in Informatics (LIPIcs)

Place of publication

Schloss Dagstuhl

Event location

Ann Arbor

Event date

Jul 22, 2024

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

—