{"paper":{"title":"The Power of the Weak","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alessandro Facchini, Fabio Zanasi, Facundo Carreiro, Yde Venema","submitted_at":"2018-09-10T12:05:05Z","abstract_excerpt":"A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal $\\mu$-calculus ($\\mu\\mathrm{ML}$) is equivalent modulo bisimilarity to standard monadic second-order logic (here abbreviated as $\\mathrm{smso}$), over the class of labelled transition systems (LTSs for short). Our work proves two results of the same kind, one for the alternation-free fragment of $\\mu\\mathrm{ML}$ ($\\mu_D\\mathrm{ML}$) and one for weak $\\mathrm{mso}$ ($\\mathrm{wmso}$). Whereas it was known that $\\mu_D\\mathrm{ML}$ and $\\mathrm{wmso}$ are equivalent modulo bisim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03896","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"}