2026-07-22T21:50:38Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19624 2024-03-06T11:04:30Z ddc:004 open_access

Matrix Multiplication in Quadratic Time and Energy? Towards a Fine-Grained Energy-Centric Church-Turing Thesis Valiant, Gregory Physics based computing matrix multiplication low-energy computing We describe two algorithms for multiplying n × n matrices using time and energy Õ(n²) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different algorithm, is for Boolean matrix multiplication. We hope this work inspires a deeper consideration of physically plausible/realizable models of computing that might allow for algorithms which improve upon the runtimes and energy usages suggested by the parallel RAM model in which each operation requires one unit of time and one unit of energy. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Gregory Valiant 2024 Is Part Of LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2024.96 urn:nbn:de:0030-drops-196248 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.96 eng https://creativecommons.org/licenses/by/4.0/legalcode