{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:3SEWFX5KXVTS2RR6NGHWDOD2XE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"46abdd2e80b9b58d19ae50e63f9dcdca3d67a0a0e0cc53a075862978436bb7fc","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-02-12T17:29:08Z","title_canon_sha256":"07b40c06ec0b6bf4edf98faf56a729a49ca8c5ab13d75f7b28c6b9371bc1fe1f"},"schema_version":"1.0","source":{"id":"quant-ph/0202066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0202066","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0202066v1","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0202066","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"3SEWFX5KXVTS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"3SEWFX5KXVTS2RR6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"3SEWFX5K","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:2f786014faf47991d847ce041a97bc1f52000974af9b569e37fb7fc62dbdde91","target":"graph","created_at":"2026-05-18T04:11:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\\tilde{O}(s^{3}/\\epsilon + s^{2}/\\epsilon^{2})$, where $s$ is the size of DNF formula and $\\epsilon$ is the PAC error accuracy. If $s$ and $1/\\epsilon$ are comparable, this gives a modest improvement over a previously known classical query complexity of $\\tilde{O}(ns^{2}/\\epsilon^{2})$. We also show a lower bound of $\\Omega(s\\log n/n)$ on the query complexity of any quantum PAC algorithm for learning a DNF of size $s$ with $n$ inputs under the uniform distribution.","authors_text":"Christino Tamon, Jeffrey C. Jackson, Tomoyuki Yamakami","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2002-02-12T17:29:08Z","title":"Quantum DNF Learnability Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0202066","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fcbf0a8eb97b4d0f252f2bd0ea8c148208a8f8d152ffa362a5bae0459bf2113e","target":"record","created_at":"2026-05-18T04:11:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"46abdd2e80b9b58d19ae50e63f9dcdca3d67a0a0e0cc53a075862978436bb7fc","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-02-12T17:29:08Z","title_canon_sha256":"07b40c06ec0b6bf4edf98faf56a729a49ca8c5ab13d75f7b28c6b9371bc1fe1f"},"schema_version":"1.0","source":{"id":"quant-ph/0202066","kind":"arxiv","version":1}},"canonical_sha256":"dc8962dfaabd672d463e698f61b87ab9142abc62d363f524bcb1446b0f3afdd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc8962dfaabd672d463e698f61b87ab9142abc62d363f524bcb1446b0f3afdd9","first_computed_at":"2026-05-18T04:11:18.205164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:18.205164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IiZ819kwkWzvmqSctV/qDAeeB4EUneTAAoGL5qva6RyfzD+tQ4OtKgCXqwkb7jcKJZ4j/eVxnxqtPJUFsu4WAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:18.205751Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0202066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcbf0a8eb97b4d0f252f2bd0ea8c148208a8f8d152ffa362a5bae0459bf2113e","sha256:2f786014faf47991d847ce041a97bc1f52000974af9b569e37fb7fc62dbdde91"],"state_sha256":"2869b9e76a831462b33a974d832815cf8045da4077b9d1e547c0e3c86de9c930"}