{"paper":{"title":"A finer reparameterisation theorem for MSO and FO queries on strings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.LO","authors_text":"L\\^e Th\\`anh D\\~ung Nguy\\^en, Pawe{\\l} Parys","submitted_at":"2025-12-06T15:06:23Z","abstract_excerpt":"We show a theorem on monadic second-order k-ary queries on finite words. It may be illustrated by the following example: if the number of results of a query on binary strings is O(number of 0s $\\times$ number of 1s), then each result can be MSO-definably identified from a 0-position, a 1-position and some finite data.\n  Our proofs also handle the case of first-order logic / aperiodic monoids. Thus we can state and prove the folklore theorem that dimension minimisation holds for first-order string-to-string interpretations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.06466","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/2512.06466/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"}