{"paper":{"title":"The \\mu-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.FL"],"primary_cat":"cs.LO","authors_text":"Felix Klaedtke (ETH Zurich, Germany), Julian Gutierrez (University of Cambridge, Martin Lange (University of Kassel, Switzerland), United Kingdom)","submitted_at":"2012-10-09T00:54:03Z","abstract_excerpt":"It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict.  However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures.  A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus.  Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited.  This paper makes progress in answering these questions by showing that the alternation hierarchy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2455","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"}