{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KIU7IGOK3JGMGV6DGMYWJM364X","short_pith_number":"pith:KIU7IGOK","schema_version":"1.0","canonical_sha256":"5229f419cada4cc357c3333164b37ee5f559598b3b78de2d63cf69d705c207c9","source":{"kind":"arxiv","id":"1308.4516","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.4516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-08-21T08:57:05Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"f018e34057c29a7d9dde4af9e24ff606ec30a62daebad317d78f6815de8131eb","abstract_canon_sha256":"75bc95c4e736c9b1cdd82ab6d4109bf83296b127e599a77594a6dcd67793c79c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.871340Z","signature_b64":"5Amc8JD/J86MH+ttV7OibcWpQFYKz/dOrj501vJXhVUH6KD2l2pNaOtyFsSUyCvftXD7R8CyezWtt9ZLayJICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5229f419cada4cc357c3333164b37ee5f559598b3b78de2d63cf69d705c207c9","last_reissued_at":"2026-05-18T03:15:21.870729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.870729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1308.4516","created_at":"2026-05-18T03:15:21.870838+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.4516v1","created_at":"2026-05-18T03:15:21.870838+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4516","created_at":"2026-05-18T03:15:21.870838+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIU7IGOK3JGM","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIU7IGOK3JGMGV6D","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIU7IGOK","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X","json":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X.json","graph_json":"https://pith.science/api/pith-number/KIU7IGOK3JGMGV6DGMYWJM364X/graph.json","events_json":"https://pith.science/api/pith-number/KIU7IGOK3JGMGV6DGMYWJM364X/events.json","paper":"https://pith.science/paper/KIU7IGOK"},"agent_actions":{"view_html":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X","download_json":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X.json","view_paper":"https://pith.science/paper/KIU7IGOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.4516&json=true","fetch_graph":"https://pith.science/api/pith-number/KIU7IGOK3JGMGV6DGMYWJM364X/graph.json","fetch_events":"https://pith.science/api/pith-number/KIU7IGOK3JGMGV6DGMYWJM364X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X/action/storage_attestation","attest_author":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X/action/author_attestation","sign_citation":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X/action/citation_signature","submit_replication":"https://pith.science/pith/KIU7IGOK3JGMGV6DGMYWJM364X/action/replication_record"}},"created_at":"2026-05-18T03:15:21.870838+00:00","updated_at":"2026-05-18T03:15:21.870838+00:00"}