{"paper":{"title":"Lower Bounds for Unambiguous Automata via Communication Complexity","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.FL","authors_text":"Mika G\\\"o\\\"os, Stefan Kiefer, Weiqiang Yuan","submitted_at":"2021-09-19T16:16:23Z","abstract_excerpt":"We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results.\n  $\\textit{Complement:}$ There is a language $L$ recognised by an $n$-state UFA such that the complement language $\\overline{L}$ requires NFAs with $n^{\\tilde{\\Omega}(\\log n)}$ states. This improves on a lower bound by Raskin.\n  $\\textit{Union:}$ There are languages $L_1$, $L_2$ recognised by $n$-state UFAs such that the union $L_1\\cup L_2$ requires UFAs with $n^{\\tilde{\\Omega}(\\log n)}$ states.\n  $\\textit{Separation:}$ There is a language $L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.09155","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.09155/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}