@inproceedings{148653dcb98f4a15977c76e7fb7e2775,
title = "Strong ETH Holds for Bounded-Depth Resolution over Parities",
abstract = "Strong lower bounds of the form 2(1-ϵ)n, where n is the number of variables and ϵ>0 is arbitrarily small (i.e., bounds consistent with the Strong ETH), are exceptionally rare in proof complexity. The seminal work of Beck and Impagliazzo (STOC 2013) achieved such a bound for regular resolution, and the strongest extension known prior to our work was proved for O(ϵ)-regular resolution by Bonacina and Talebanfard (Algorithmica, 2017). We establish similar lower bounds for a significantly stronger proof system - a fragment of resolution over parities (Res(⊕)). This fragment captures Depth-n Res(⊕), and thus our result implies SETH-type lower bounds for both tree-like and regular Res(⊕). The core of our approach is a lossless lifting achieved by assigning distinct, randomly chosen gadgets to each variable. Our result also yields a SETH-type lower bound for Depth-n resolution - a result that was previously unknown. We additionally provide a direct and simplified proof for this special case, which may be of independent interest.",
keywords = "Resolution over parities, SETH lower bound, depth, lifting, lower bounds, proof complexity, resolution width",
author = "Klim Efremenko and Dmitry Itsykson",
note = "Publisher Copyright: {\textcopyright} 2026 Copyright held by the owner/author(s).; 58th Annual ACM Symposium on Theory of Computing, STOC 2026 ; Conference date: 22-06-2026 Through 26-06-2026",
year = "2026",
month = jun,
day = "9",
doi = "10.1145/3798129.3800804",
language = "English",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
publisher = "Association for Computing Machinery",
pages = "898--909",
editor = "Aditya Bhaskara and Artur Czumaj",
booktitle = "STOC 2026 - Proceedings of the 58th Annual ACM Symposium on Theory of Computing",
}