{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:G26Q2CN3PQNMRSIMP7MGPPVDXG","short_pith_number":"pith:G26Q2CN3","schema_version":"1.0","canonical_sha256":"36bd0d09bb7c1ac8c90c7fd867bea3b9b5c11b5cf599f48bb1a4bcbfbd2c11af","source":{"kind":"arxiv","id":"1812.04219","version":3},"attestation_state":"computed","paper":{"title":"A Quantum Query Complexity Trichotomy for Regular Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Daniel Grier, Luke Schaeffer, Scott Aaronson","submitted_at":"2018-12-11T05:00:52Z","abstract_excerpt":"We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from taking any other asymptotic complexity. This is in contrast to even the context-free languages, which we show can have query complexity Theta(n^c) for all computable c in [1/2,1]. Our result implies an equivalent trichotomy for the approximate degree of regular languages, and a dichotomy---either Theta(1) or Theta(n)---for sensitivity, block sensitivity, ce"},"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":"1812.04219","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-12-11T05:00:52Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"cd3e1915a03542d1f8c9119b03c50dde22ca7704de51df74a1851eeca7fb3aaa","abstract_canon_sha256":"1e819fc4c2f3d19e048115aa477cc5805dbe5c8e5c3b99317164ff18a5549e82"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:31.260296Z","signature_b64":"OGz7ZL42pu3se6G2yPd876MNbozrLPRmHL9Af/L1jrsyg4bHn7+lrbjp6bjhwSV3uP+C+oxfHsfzY+OqOLaOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36bd0d09bb7c1ac8c90c7fd867bea3b9b5c11b5cf599f48bb1a4bcbfbd2c11af","last_reissued_at":"2026-05-17T23:48:31.259753Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:31.259753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Quantum Query Complexity Trichotomy for Regular Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Daniel Grier, Luke Schaeffer, Scott Aaronson","submitted_at":"2018-12-11T05:00:52Z","abstract_excerpt":"We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from taking any other asymptotic complexity. This is in contrast to even the context-free languages, which we show can have query complexity Theta(n^c) for all computable c in [1/2,1]. Our result implies an equivalent trichotomy for the approximate degree of regular languages, and a dichotomy---either Theta(1) or Theta(n)---for sensitivity, block sensitivity, ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04219","kind":"arxiv","version":3},"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":"1812.04219","created_at":"2026-05-17T23:48:31.259829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04219v3","created_at":"2026-05-17T23:48:31.259829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04219","created_at":"2026-05-17T23:48:31.259829+00:00"},{"alias_kind":"pith_short_12","alias_value":"G26Q2CN3PQNM","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"G26Q2CN3PQNMRSIM","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"G26Q2CN3","created_at":"2026-05-18T12:32:25.280505+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/G26Q2CN3PQNMRSIMP7MGPPVDXG","json":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG.json","graph_json":"https://pith.science/api/pith-number/G26Q2CN3PQNMRSIMP7MGPPVDXG/graph.json","events_json":"https://pith.science/api/pith-number/G26Q2CN3PQNMRSIMP7MGPPVDXG/events.json","paper":"https://pith.science/paper/G26Q2CN3"},"agent_actions":{"view_html":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG","download_json":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG.json","view_paper":"https://pith.science/paper/G26Q2CN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04219&json=true","fetch_graph":"https://pith.science/api/pith-number/G26Q2CN3PQNMRSIMP7MGPPVDXG/graph.json","fetch_events":"https://pith.science/api/pith-number/G26Q2CN3PQNMRSIMP7MGPPVDXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG/action/storage_attestation","attest_author":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG/action/author_attestation","sign_citation":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG/action/citation_signature","submit_replication":"https://pith.science/pith/G26Q2CN3PQNMRSIMP7MGPPVDXG/action/replication_record"}},"created_at":"2026-05-17T23:48:31.259829+00:00","updated_at":"2026-05-17T23:48:31.259829+00:00"}