{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SW3TKNNEQOMVDNO5DDE7CHHBTU","short_pith_number":"pith:SW3TKNNE","schema_version":"1.0","canonical_sha256":"95b73535a4839951b5dd18c9f11ce19d08f80036f32060176d51a8cf392195b8","source":{"kind":"arxiv","id":"1806.09660","version":1},"attestation_state":"computed","paper":{"title":"On learning linear functions from subset and its applications in quantum computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, G\\'abor Ivanyos, Miklos Santha","submitted_at":"2018-06-25T18:48:36Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be the finite field of size $q$ and let $\\ell: \\mathbb{F}_q^n \\to \\mathbb{F}_q$ be a linear function. We introduce the {\\em Learning From Subset} problem LFS$(q,n,d)$ of learning $\\ell$, given samples $u \\in \\mathbb{F}_q^n$ from a special distribution depending on $\\ell$: the probability of sampling $u$ is a function of $\\ell(u)$ and is non zero for at most $d$ values of $\\ell(u)$. We provide a randomized algorithm for LFS$(q,n,d)$ with sample complexity $(n+d)^{O(d)}$ and running time polynomial in $\\log q$ and $(n+d)^{O(d)}$. Our algorithm generalizes and improves upon pre"},"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":"1806.09660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-06-25T18:48:36Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"61e1cee1f5201d0f5875ad8a90ef9962532a1d67a3f416c66c928e46b1d29eeb","abstract_canon_sha256":"51d0e3cdd32863af9c4078290e1626b025d8f2277a303d49f9b497369b8c78ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:23.811638Z","signature_b64":"i6bDuc2W5Zh8nlAlQN0OJ5tOrSjT4akwnwaapc7TK8BZekkRj6GPnLLL3V3nOOW5JRY7+YXGCsuZuIFsUhDNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b73535a4839951b5dd18c9f11ce19d08f80036f32060176d51a8cf392195b8","last_reissued_at":"2026-05-18T00:12:23.810896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:23.810896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On learning linear functions from subset and its applications in quantum computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, G\\'abor Ivanyos, Miklos Santha","submitted_at":"2018-06-25T18:48:36Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be the finite field of size $q$ and let $\\ell: \\mathbb{F}_q^n \\to \\mathbb{F}_q$ be a linear function. We introduce the {\\em Learning From Subset} problem LFS$(q,n,d)$ of learning $\\ell$, given samples $u \\in \\mathbb{F}_q^n$ from a special distribution depending on $\\ell$: the probability of sampling $u$ is a function of $\\ell(u)$ and is non zero for at most $d$ values of $\\ell(u)$. We provide a randomized algorithm for LFS$(q,n,d)$ with sample complexity $(n+d)^{O(d)}$ and running time polynomial in $\\log q$ and $(n+d)^{O(d)}$. Our algorithm generalizes and improves upon pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09660","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":"1806.09660","created_at":"2026-05-18T00:12:23.811020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09660v1","created_at":"2026-05-18T00:12:23.811020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09660","created_at":"2026-05-18T00:12:23.811020+00:00"},{"alias_kind":"pith_short_12","alias_value":"SW3TKNNEQOMV","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SW3TKNNEQOMVDNO5","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SW3TKNNE","created_at":"2026-05-18T12:32:53.628368+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/SW3TKNNEQOMVDNO5DDE7CHHBTU","json":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU.json","graph_json":"https://pith.science/api/pith-number/SW3TKNNEQOMVDNO5DDE7CHHBTU/graph.json","events_json":"https://pith.science/api/pith-number/SW3TKNNEQOMVDNO5DDE7CHHBTU/events.json","paper":"https://pith.science/paper/SW3TKNNE"},"agent_actions":{"view_html":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU","download_json":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU.json","view_paper":"https://pith.science/paper/SW3TKNNE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09660&json=true","fetch_graph":"https://pith.science/api/pith-number/SW3TKNNEQOMVDNO5DDE7CHHBTU/graph.json","fetch_events":"https://pith.science/api/pith-number/SW3TKNNEQOMVDNO5DDE7CHHBTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU/action/storage_attestation","attest_author":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU/action/author_attestation","sign_citation":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU/action/citation_signature","submit_replication":"https://pith.science/pith/SW3TKNNEQOMVDNO5DDE7CHHBTU/action/replication_record"}},"created_at":"2026-05-18T00:12:23.811020+00:00","updated_at":"2026-05-18T00:12:23.811020+00:00"}