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Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields Impagliazzo, Russell Mouli, Sasank Pitassi, Toniann Proof complexity Algebraic proof systems Polynomial Calculus Extension variables AC⁰[p]-Frege For every prime p > 0, every n > 0 and κ = O(log n), we show the existence of an unsatisfiable system of polynomial equations over O(n log n) variables of degree O(log n) such that any Polynomial Calculus refutation over 𝔽_p with M extension variables, each depending on at most κ original variables requires size exp(Ω(n²)/10^κ(M + n log n)) Schloss Dagstuhl – Leibniz-Zentrum für Informatik Russell Impagliazzo and Sasank Mouli and Toniann Pitassi 2023 Is Part Of LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2023.7 urn:nbn:de:0030-drops-182774 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.7 eng https://creativecommons.org/licenses/by/4.0/legalcode