{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:O5PE3MQJCFBSBLGFQU2TW3TMQ7","short_pith_number":"pith:O5PE3MQJ","schema_version":"1.0","canonical_sha256":"775e4db209114320acc585353b6e6c87da0189d305e82193c276695e721ed21b","source":{"kind":"arxiv","id":"1503.01068","version":2},"attestation_state":"computed","paper":{"title":"An approach to computing downward closures","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Georg Zetzsche","submitted_at":"2015-03-03T19:19:56Z","abstract_excerpt":"The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes.\n  This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be redu"},"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":"1503.01068","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.FL","submitted_at":"2015-03-03T19:19:56Z","cross_cats_sorted":[],"title_canon_sha256":"27f1327c47676f8bf4163d5ebbc1be582a427a5af1b7d2c3c09e18da13840d40","abstract_canon_sha256":"d3a172124da604c8ae835ee8305daf14ff8f5612ff95e470edbe3b1820908eb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:57.662880Z","signature_b64":"SXzQYU5eA4b9XTSSjeJ2Nt0Rh+5Asv6j9eD3XEESVcmZA2XDg4G1hMV3I4Xkk/hTqad5uJw253jOyZRRoXizBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"775e4db209114320acc585353b6e6c87da0189d305e82193c276695e721ed21b","last_reissued_at":"2026-05-18T01:59:57.662482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:57.662482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An approach to computing downward closures","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Georg Zetzsche","submitted_at":"2015-03-03T19:19:56Z","abstract_excerpt":"The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes.\n  This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be redu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01068","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":"1503.01068","created_at":"2026-05-18T01:59:57.662543+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01068v2","created_at":"2026-05-18T01:59:57.662543+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01068","created_at":"2026-05-18T01:59:57.662543+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5PE3MQJCFBS","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5PE3MQJCFBSBLGF","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5PE3MQJ","created_at":"2026-05-18T12:29:34.919912+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/O5PE3MQJCFBSBLGFQU2TW3TMQ7","json":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7.json","graph_json":"https://pith.science/api/pith-number/O5PE3MQJCFBSBLGFQU2TW3TMQ7/graph.json","events_json":"https://pith.science/api/pith-number/O5PE3MQJCFBSBLGFQU2TW3TMQ7/events.json","paper":"https://pith.science/paper/O5PE3MQJ"},"agent_actions":{"view_html":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7","download_json":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7.json","view_paper":"https://pith.science/paper/O5PE3MQJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01068&json=true","fetch_graph":"https://pith.science/api/pith-number/O5PE3MQJCFBSBLGFQU2TW3TMQ7/graph.json","fetch_events":"https://pith.science/api/pith-number/O5PE3MQJCFBSBLGFQU2TW3TMQ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7/action/storage_attestation","attest_author":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7/action/author_attestation","sign_citation":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7/action/citation_signature","submit_replication":"https://pith.science/pith/O5PE3MQJCFBSBLGFQU2TW3TMQ7/action/replication_record"}},"created_at":"2026-05-18T01:59:57.662543+00:00","updated_at":"2026-05-18T01:59:57.662543+00:00"}