{"paper":{"title":"Dynamic Membership for Regular Tree Languages","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.FL","authors_text":"Antoine Amarilli, Charles Paperman, Corentin Barloy, Louis Jachiet","submitted_at":"2025-04-24T13:26:08Z","abstract_excerpt":"We study the dynamic membership problem for regular tree languages under relabeling updates: we fix an alphabet $\\Sigma$ and a regular tree language $L$ over $\\Sigma$ (expressed, e.g., as a tree automaton), we are given a tree $T$ with labels in $\\Sigma$, and we must maintain the information of whether the tree $T$ belongs to $L$ while handling relabeling updates that change the labels of individual nodes in $T$.\n  Our first contribution is to show that this problem admits an $O(\\log n / \\log \\log n)$ algorithm for any fixed regular tree language, improving over known $O(\\log n)$ algorithms. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17536","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/2504.17536/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"}