{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MW4LCIP2BLW5WZJCWIO66UETCJ","short_pith_number":"pith:MW4LCIP2","schema_version":"1.0","canonical_sha256":"65b8b121fa0aeddb6522b21def5093127d33a543eb69da2b517a18407548d07b","source":{"kind":"arxiv","id":"1101.3443","version":1},"attestation_state":"computed","paper":{"title":"Borel Hierarchy and Omega Context Free Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Olivier Finkel (ELM)","submitted_at":"2011-01-18T12:40:06Z","abstract_excerpt":"We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:\"A Decade of Concurrency\", Springer LNCS 803 (1994), 583-621], proving new topological properties of omega context free languages : there exist some omega-CFL which are non Borel sets. And one cannot decide whether an omega-CFL is a Borel set. We give also an answer to questions of Niwinski and Simonnet about omega powers of finitary languages, giving an example of a finitary context free language L such that L^omega is not a Borel set. Then we prove some recursive an"},"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":"1101.3443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-01-18T12:40:06Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"23f97f3693e37c725dabc6943106bda19c775327167c86b494d2196fc5b19bdd","abstract_canon_sha256":"c7283893f5b5f69cfad348388b2ab5096dcc7960822ef1951cd8a8d8f4d5a079"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:21.972152Z","signature_b64":"4CJ99rKzWq34NDsGELuG5CYINqvQD+pXv0W15XKam4nxZp588BAWxTURLNdqzdzcksI4IlZiDYH5bhpFYLCUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65b8b121fa0aeddb6522b21def5093127d33a543eb69da2b517a18407548d07b","last_reissued_at":"2026-05-18T04:31:21.971688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:21.971688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Borel Hierarchy and Omega Context Free Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Olivier Finkel (ELM)","submitted_at":"2011-01-18T12:40:06Z","abstract_excerpt":"We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:\"A Decade of Concurrency\", Springer LNCS 803 (1994), 583-621], proving new topological properties of omega context free languages : there exist some omega-CFL which are non Borel sets. And one cannot decide whether an omega-CFL is a Borel set. We give also an answer to questions of Niwinski and Simonnet about omega powers of finitary languages, giving an example of a finitary context free language L such that L^omega is not a Borel set. Then we prove some recursive an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3443","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":"1101.3443","created_at":"2026-05-18T04:31:21.971755+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3443v1","created_at":"2026-05-18T04:31:21.971755+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3443","created_at":"2026-05-18T04:31:21.971755+00:00"},{"alias_kind":"pith_short_12","alias_value":"MW4LCIP2BLW5","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"MW4LCIP2BLW5WZJC","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"MW4LCIP2","created_at":"2026-05-18T12:26:37.096874+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/MW4LCIP2BLW5WZJCWIO66UETCJ","json":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ.json","graph_json":"https://pith.science/api/pith-number/MW4LCIP2BLW5WZJCWIO66UETCJ/graph.json","events_json":"https://pith.science/api/pith-number/MW4LCIP2BLW5WZJCWIO66UETCJ/events.json","paper":"https://pith.science/paper/MW4LCIP2"},"agent_actions":{"view_html":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ","download_json":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ.json","view_paper":"https://pith.science/paper/MW4LCIP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3443&json=true","fetch_graph":"https://pith.science/api/pith-number/MW4LCIP2BLW5WZJCWIO66UETCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/MW4LCIP2BLW5WZJCWIO66UETCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ/action/storage_attestation","attest_author":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ/action/author_attestation","sign_citation":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ/action/citation_signature","submit_replication":"https://pith.science/pith/MW4LCIP2BLW5WZJCWIO66UETCJ/action/replication_record"}},"created_at":"2026-05-18T04:31:21.971755+00:00","updated_at":"2026-05-18T04:31:21.971755+00:00"}