{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KDKV5BU26ICLJJBOVMWTWSHKGY","short_pith_number":"pith:KDKV5BU2","schema_version":"1.0","canonical_sha256":"50d55e869af204b4a42eab2d3b48ea361ed27c1cf05c8bb1f8d66e07b44f518a","source":{"kind":"arxiv","id":"1503.02840","version":2},"attestation_state":"computed","paper":{"title":"An Upper Bound on the Complexity of Recognizable Tree Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"cs.FL","authors_text":"Dominique Lecomte (IMJ), IMJ), Olivier Finkel (ELM, Pierre Simonnet (SPE)","submitted_at":"2015-03-10T10:02:21Z","abstract_excerpt":"The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\\Game (D\\_n({\\bf\\Sigma}^0\\_2))$ for some natural number $n\\geq 1$, where $\\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\\omega$ into the class ${\\bf\\Delta}^1\\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\\bf\\"},"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":"1503.02840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-03-10T10:02:21Z","cross_cats_sorted":["math.GN","math.LO"],"title_canon_sha256":"ad57212fcb105c1079a28f6cc66a51c226553a3ba61834f33ced218aefe7baf4","abstract_canon_sha256":"4f21c12be6b2a72f20ff32c55afae982e59ef9d18d9a2f2e2ec8600a4d136239"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:04.326998Z","signature_b64":"vb/4gFZr0g05y/bws4yMAnNUr15PSkGnCEYCL0p+2KzUFmP5W9RRrSL7HAOpcTu0rp/6H+Dz/yn0mQViJVzxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50d55e869af204b4a42eab2d3b48ea361ed27c1cf05c8bb1f8d66e07b44f518a","last_reissued_at":"2026-05-18T02:25:04.326638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:04.326638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Upper Bound on the Complexity of Recognizable Tree Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"cs.FL","authors_text":"Dominique Lecomte (IMJ), IMJ), Olivier Finkel (ELM, Pierre Simonnet (SPE)","submitted_at":"2015-03-10T10:02:21Z","abstract_excerpt":"The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\\Game (D\\_n({\\bf\\Sigma}^0\\_2))$ for some natural number $n\\geq 1$, where $\\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\\omega$ into the class ${\\bf\\Delta}^1\\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\\bf\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02840","kind":"arxiv","version":2},"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":"1503.02840","created_at":"2026-05-18T02:25:04.326697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02840v2","created_at":"2026-05-18T02:25:04.326697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02840","created_at":"2026-05-18T02:25:04.326697+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDKV5BU26ICL","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDKV5BU26ICLJJBO","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDKV5BU2","created_at":"2026-05-18T12:29:27.538025+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/KDKV5BU26ICLJJBOVMWTWSHKGY","json":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY.json","graph_json":"https://pith.science/api/pith-number/KDKV5BU26ICLJJBOVMWTWSHKGY/graph.json","events_json":"https://pith.science/api/pith-number/KDKV5BU26ICLJJBOVMWTWSHKGY/events.json","paper":"https://pith.science/paper/KDKV5BU2"},"agent_actions":{"view_html":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY","download_json":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY.json","view_paper":"https://pith.science/paper/KDKV5BU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02840&json=true","fetch_graph":"https://pith.science/api/pith-number/KDKV5BU26ICLJJBOVMWTWSHKGY/graph.json","fetch_events":"https://pith.science/api/pith-number/KDKV5BU26ICLJJBOVMWTWSHKGY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY/action/storage_attestation","attest_author":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY/action/author_attestation","sign_citation":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY/action/citation_signature","submit_replication":"https://pith.science/pith/KDKV5BU26ICLJJBOVMWTWSHKGY/action/replication_record"}},"created_at":"2026-05-18T02:25:04.326697+00:00","updated_at":"2026-05-18T02:25:04.326697+00:00"}