{"paper":{"title":"Compact Labelings For Efficient First-Order Model-Checking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.DS","authors_text":"Bruno Courcelle (LaBRI, Cyril Gavoille (LaBRI, INRIA Futurs), IUF), Mamadou Moustapha Kant\\'e (LaBRI)","submitted_at":"2008-11-28T13:29:15Z","abstract_excerpt":"We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \\emph{nicely locally cwd-decomposable}. This notion generalizes that of a \\emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \\emph{clique-width} with limited overlaps. We also consider such labelings for \\emph{bounded} first-order formulas on graph classes of \\emph{bounded e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4713","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":""},"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"}