{"paper":{"title":"Low rank MSO","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Giannos Stamoulis, Marek Soko{\\l}owski, Micha{\\l} Pilipczuk, Miko{\\l}aj Boja\\'nczyk, Wojciech Przybyszewski","submitted_at":"2025-02-12T15:10:18Z","abstract_excerpt":"We introduce a new logic for describing properties of graphs, which we call low rank MSO. This is the fragment of monadic second-order logic in which set quantification is restricted to vertex sets of bounded cutrank. We prove the following statements about the expressive power of low rank MSO.\n  - Over any class of graphs that is weakly sparse, low rank MSO has the same expressive power as separator logic. This equivalence does not hold over all graphs.\n  - Over any class of graphs that has bounded VC dimension, low rank MSO has the same expressive power as flip-connectivity logic. This equiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08476","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.08476/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"}