2026-07-20T14:45:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8877 2024-03-06T10:42:51Z ddc:004 open_access

Hardness Amplification for Non-Commutative Arithmetic Circuits Carmosino, Marco L. Impagliazzo, Russell Lovett, Shachar Mihajlin, Ivan arithmetic circuits hardness amplification circuit lower bounds non-commutative computation We show that proving mildly super-linear lower bounds on non-commutative arithmetic circuits implies exponential lower bounds on non-commutative circuits. That is, non-commutative circuit complexity is a threshold phenomenon: an apparently weak lower bound actually suffices to show the strongest lower bounds we could desire. This is part of a recent line of inquiry into why arithmetic circuit complexity, despite being a heavily restricted version of Boolean complexity, still cannot prove super-linear lower bounds on general devices. One can view our work as positive news (it suffices to prove weak lower bounds to get strong ones) or negative news (it is as hard to prove weak lower bounds as it is to prove strong ones). We leave it to the reader to determine their own level of optimism. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marco L. Carmosino and Russell Impagliazzo and Shachar Lovett and Ivan Mihajlin 2018 Is Part Of LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2018.12 urn:nbn:de:0030-drops-88772 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.12 eng https://creativecommons.org/licenses/by/3.0/legalcode