{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:BGAAF7SNJ65WDFMKBJ7MU5SWQ2","short_pith_number":"pith:BGAAF7SN","schema_version":"1.0","canonical_sha256":"098002fe4d4fbb61958a0a7eca765686ae819a44d88929bd9481ed17b8ca3786","source":{"kind":"arxiv","id":"2306.00135","version":1},"attestation_state":"computed","paper":{"title":"Optimal Approximate Minimization of One-Letter Weighted Finite Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Borja Balle, Clara Lacroce, Guillaume Rabusseau, Prakash Panangaden","submitted_at":"2023-05-31T19:23:38Z","abstract_excerpt":"In this paper, we study the approximate minimization problem of weighted finite automata (WFAs): to compute the best possible approximation of a WFA given a bound on the number of states. By reformulating the problem in terms of Hankel matrices, we leverage classical results on the approximation of Hankel operators, namely the celebrated Adamyan-Arov-Krein (AAK) theory.\n  We solve the optimal spectral-norm approximate minimization problem for irredundant WFAs with real weights, defined over a one-letter alphabet. We present a theoretical analysis based on AAK theory, and bounds on the quality "},"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":"2306.00135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2023-05-31T19:23:38Z","cross_cats_sorted":[],"title_canon_sha256":"2b8991d3374348d65a904bd4fbe39a22382b6f133c1eba168c2b9832dcfa1870","abstract_canon_sha256":"e002ce190b3e139e777b0211c0a8dbdb395e0e16ac37ef4bd09144464cf9cf3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:46.213222Z","signature_b64":"alGHa60v5qWtS6olp6j0rQfbvmpROFofp89nV4eN+Wi3et1sb6rrKrLdj1u8B2hO45wQlYKnFcPPo4vPq3W8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"098002fe4d4fbb61958a0a7eca765686ae819a44d88929bd9481ed17b8ca3786","last_reissued_at":"2026-07-05T10:12:46.212707Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:46.212707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Approximate Minimization of One-Letter Weighted Finite Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Borja Balle, Clara Lacroce, Guillaume Rabusseau, Prakash Panangaden","submitted_at":"2023-05-31T19:23:38Z","abstract_excerpt":"In this paper, we study the approximate minimization problem of weighted finite automata (WFAs): to compute the best possible approximation of a WFA given a bound on the number of states. By reformulating the problem in terms of Hankel matrices, we leverage classical results on the approximation of Hankel operators, namely the celebrated Adamyan-Arov-Krein (AAK) theory.\n  We solve the optimal spectral-norm approximate minimization problem for irredundant WFAs with real weights, defined over a one-letter alphabet. We present a theoretical analysis based on AAK theory, and bounds on the quality "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.00135","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.00135/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2306.00135","created_at":"2026-07-05T10:12:46.212766+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.00135v1","created_at":"2026-07-05T10:12:46.212766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.00135","created_at":"2026-07-05T10:12:46.212766+00:00"},{"alias_kind":"pith_short_12","alias_value":"BGAAF7SNJ65W","created_at":"2026-07-05T10:12:46.212766+00:00"},{"alias_kind":"pith_short_16","alias_value":"BGAAF7SNJ65WDFMK","created_at":"2026-07-05T10:12:46.212766+00:00"},{"alias_kind":"pith_short_8","alias_value":"BGAAF7SN","created_at":"2026-07-05T10:12:46.212766+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/BGAAF7SNJ65WDFMKBJ7MU5SWQ2","json":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2.json","graph_json":"https://pith.science/api/pith-number/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/graph.json","events_json":"https://pith.science/api/pith-number/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/events.json","paper":"https://pith.science/paper/BGAAF7SN"},"agent_actions":{"view_html":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2","download_json":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2.json","view_paper":"https://pith.science/paper/BGAAF7SN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.00135&json=true","fetch_graph":"https://pith.science/api/pith-number/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/action/storage_attestation","attest_author":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/action/author_attestation","sign_citation":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/action/citation_signature","submit_replication":"https://pith.science/pith/BGAAF7SNJ65WDFMKBJ7MU5SWQ2/action/replication_record"}},"created_at":"2026-07-05T10:12:46.212766+00:00","updated_at":"2026-07-05T10:12:46.212766+00:00"}