{"paper":{"title":"On the Generative Power of Omega-Grammars and Omega-Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.FL","authors_text":"Zhe Chen","submitted_at":"2013-08-21T08:57:05Z","abstract_excerpt":"An \\omega-grammar is a formal grammar used to generate \\omega-words (i.e. infinite length words), while an \\omega-automaton is an automaton used to recognize \\omega-words. This paper gives clean and uniform definitions for \\omega-grammars and \\omega-automata, provides a systematic study of the generative power of \\omega-grammars with respect to \\omega-automata, and presents a complete set of results for various types of \\omega-grammars and acceptance modes. We use the tuple (\\sigma,\\rho,\\pi) to denote various acceptance modes, where \\sigma denotes that some designated elements should appear at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4516","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"}