{"paper":{"title":"Solving random equations in Garside groups using length functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.AG"],"primary_cat":"math.GR","authors_text":"Boaz Tsaban, Martin Hock","submitted_at":"2006-11-29T16:34:43Z","abstract_excerpt":"We give a systematic exposition of memory-length algorithms for solving equations in noncommutative groups. This exposition clarifies some points untouched in earlier expositions. We then focus on the main ingredient in these attacks: Length functions.\n  After a self-contained introduction to Garside groups, we describe length functions induced by the greedy normal form and by the rational normal form in these groups, and compare their worst-case performances.\n  Our main concern is Artin's braid groups, with their two known Garside presentations, due to Artin and due to Birman-Ko-Lee (BKL). We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611918","kind":"arxiv","version":4},"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"}