{"paper":{"title":"Lower bounds for Combinatorial Algorithms for Boolean Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Debarati Das, Michael Saks, Michal Kouck\\'y","submitted_at":"2018-01-16T10:49:10Z","abstract_excerpt":"In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (BMM), and prove lower bounds on computing BMM in these models. First, we give a relatively relaxed combinatorial model which is an extension of the model by Angluin (1976), and we prove that the time required by any algorithm for the BMM is at least $\\Omega(n^3 / 2^{O( \\sqrt{ \\log n })})$. Subsequently, we propose a more general model capable of simulating the \"Four Russians Algorithm\". We prove a lower bound of $\\Omega(n^{7/3} / 2^{O(\\sqrt{ \\log n })})$ for the BMM under this model. We use a spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05202","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}