{"paper":{"title":"Direct and dual laws for automata with multiplicities","license":"","headline":"","cross_cats":["cs.DM","cs.SC"],"primary_cat":"math.CO","authors_text":"Eric Laugerotte (LIFAR EA2655), G\\'erard Duchamp (LIPN), Jean-Gabriel Luque (IGM-LabInfo), Marianne Flouret (LIH EA3219)","submitted_at":"2006-07-18T07:08:35Z","abstract_excerpt":"We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal, characterize the dual laws preserving rationality and also relators that are compatible with these laws."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607412","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"}