{"paper":{"title":"Reducing CMSO Model Checking to Highly Connected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LO"],"primary_cat":"cs.DS","authors_text":"Daniel Lokshtanov, Meirav Zehavi, M. S. Ramanujan, Saket Saurabh","submitted_at":"2018-02-05T15:06:32Z","abstract_excerpt":"Given a Counting Monadic Second Order (CMSO) sentence $\\psi$, the CMSO$[\\psi]$ problem is defined as follows. The input to CMSO$[\\psi]$ is a graph $G$, and the objective is to determine whether $G\\models \\psi$. Our main theorem states that for every CMSO sentence $\\psi$, if CMSO$[\\psi]$ is solvable in polynomial time on \"globally highly connected graphs\", then CMSO$[\\psi]$ is solvable in polynomial time (on general graphs). We demonstrate the utility of our theorem in the design of parameterized algorithms. Specifically we show that technical problem-specific ingredients of a powerful method f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01453","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":""},"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"}