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On Small-depth Frege Proofs for Tseitin for Grids

Published: 17 November 2020 Publication History

Abstract

We prove that a small-depth Frege refutation of the Tseitin contradiction on the grid requires subexponential size. We conclude that polynomial size Frege refutations of the Tseitin contradiction must use formulas of almost logarithmic depth.

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  1. On Small-depth Frege Proofs for Tseitin for Grids

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    cover image Journal of the ACM
    Journal of the ACM  Volume 68, Issue 1
    February 2021
    215 pages
    ISSN:0004-5411
    EISSN:1557-735X
    DOI:10.1145/3437069
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    New York, NY, United States

    Publication History

    Published: 17 November 2020
    Accepted: 01 September 2020
    Revised: 01 February 2020
    Received: 01 September 2017
    Published in JACM Volume 68, Issue 1

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    Author Tags

    1. Frege proofs
    2. Small-depth formulas
    3. switching lemma

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    Cited By

    View all
    • (2023)Near-optimal Lower Bounds on Quantifier Depth and Weisfeiler–Leman Refinement StepsJournal of the ACM10.1145/319525770:5(1-32)Online publication date: 11-Oct-2023
    • (2023)On small-depth Frege proofs for PHP2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00010(37-49)Online publication date: 6-Nov-2023
    • (2022)Linear branching programs and directional affine extractorsProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.4(1-16)Online publication date: 20-Jul-2022
    • (2022)On Bounded Depth Proofs for Tseitin Formulas on the Grid; Revisited2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00110(1138-1149)Online publication date: Oct-2022
    • (2022)Tradeoffs for small-depth Frege proofs2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00052(445-456)Online publication date: Feb-2022
    • (2021)A lower bound for polynomial calculus with extension ruleProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.21Online publication date: 20-Jul-2021

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