Year: 2025
Type: article
Abstract: . We study Frege proofs using depth-[Formula: see text] Boolean formulas for the Tseitin contradiction on [Formula: see text] grids. We prove that if each line in the proof is of size [Formula: see text], then the number of lines is exponential in [Formula: see text]. This strengthens a recent result of Pitassi, Ramakrishman, and Tan [2022 IEEE 62 nd Annual Symposium on Foundations of Computer Science, 2022, pp. 445–456]. The key technical step is a multiswitching lemma extending the switching lemma of Håstad [ J. ACM, 68 (2021), 1] for a space of restrictions related to the Tseitin contradiction. The strengthened lemma also allows us to improve the lower bound for standard proof size of bounded depth Frege refutations from exponential in [Formula: see text] to exponential in [Formula: see text]. This strengthens the bounds given in the preliminary version of this paper [J. Håstad and K. Risse, 2022 IEEE 63 rd Annual Symposium on Foundations of Computer Science, 2022, pp. 1138–1149].
Source: SIAM Journal on Computing
DOI: 10.1137/22m153851x
Authors: Johan Håstad, Kilian Risse
Institutions: KTH Royal Institute of Technology, Lund University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415267733