@inproceedings{3b498f7a201741448d29f2108090b716,
title = "Supercritical Tradeoff Between Size and Depth for Resolution over Parities",
abstract = "Alekseev and Itsykson (STOC 2025) proved the existence of an unsatisfiable CNF formula such that any resolution over parities (Res()) refutation must either have exponential size (in the formula size) or superlinear depth (in the number of variables). In this paper, we extend this result by constructing a formula with the same hardness properties, but which additionally admits a resolution refutation of quasi-polynomial size. This establishes a supercritical tradeoff between size and depth for resolution over parities. The proof builds on the framework of Alekseev and Itsykson and relies on a lifting argument applied to the supercritical tradeoff between width and depth in resolution, proposed by Buss and Thapen (IPL 2026).",
keywords = "lifting theorems, resolution depth, resolution over parities, resolution width, supercritical tradeoff",
author = "Dmitry Itsykson and Alexander Knop",
note = "Publisher Copyright: {\textcopyright} Dmitry Itsykson and Alexander Knop.; 17th Innovations in Theoretical Computer Science Conference, ITCS 2026 ; Conference date: 27-01-2026 Through 30-01-2026",
year = "2026",
month = jan,
day = "1",
doi = "10.4230/LIPIcs.ITCS.2026.81",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Shubhangi Saraf",
booktitle = "17th Innovations in Theoretical Computer Science Conference,ITCS 2026",
address = "Germany",
}