{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:U5BGFYHGHGFRFWQAG7WO7BXQBC","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":"3825f8f312e67bc402276608c6c163d90a4594f217ba0b7517a3d21723b24507","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-06-26T10:13:50Z","title_canon_sha256":"4eb4ddc6ecb6511fd6cd6d12836fec84eee9e36dda1d2bdb957054606beab907"},"schema_version":"1.0","source":{"id":"2406.18224","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.18224","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"2406.18224v3","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.18224","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"U5BGFYHGHGFR","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_16","alias_value":"U5BGFYHGHGFRFWQA","created_at":"2026-05-20T00:00:15Z"},{"alias_kind":"pith_short_8","alias_value":"U5BGFYHG","created_at":"2026-05-20T00:00:15Z"}],"graph_snapshots":[{"event_id":"sha256:79448b985d8ccad4183077529fb5cd7ca2e3eeda011790dac103c0de183d161b","target":"graph","created_at":"2026-05-20T00:00:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.18224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context Free Grammar $G$ over alphabet $\\Sigma$, count the number of words of length exactly $n$ generated by $G$. 2. Given a circuit $\\varphi$ in Decomposable Negation Normal Form (DNNF) over the set of Boolean variables $X$, compute the number of assignments to $X$ such that $\\varphi$ evaluates to 1.\n  Finding polynomial time algorithms for the aforementioned problems has been a longstanding open problem. Prior work could either only obtain a quasi-polynomial runtime","authors_text":"Alexis de Colnet, Kuldeep S. Meel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-06-26T10:13:50Z","title":"#CFG and #DNNF admit FPRAS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.18224","kind":"arxiv","version":3},"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:a0b392d72ccf8c95e4ad78a36e97e9d02d66fa8d4064c9001f3cba6841ee166c","target":"record","created_at":"2026-05-20T00:00:15Z","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":"3825f8f312e67bc402276608c6c163d90a4594f217ba0b7517a3d21723b24507","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-06-26T10:13:50Z","title_canon_sha256":"4eb4ddc6ecb6511fd6cd6d12836fec84eee9e36dda1d2bdb957054606beab907"},"schema_version":"1.0","source":{"id":"2406.18224","kind":"arxiv","version":3}},"canonical_sha256":"a74262e0e6398b12da0037ecef86f008aebc55ea15da826a46db4e00241f7978","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a74262e0e6398b12da0037ecef86f008aebc55ea15da826a46db4e00241f7978","first_computed_at":"2026-05-20T00:00:15.611455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:15.611455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9buqTE+02Uk3zN4nu3y8mClaHO2lQGsahzD2TaNAX/Jw2Jo9839OWSqL0PhHL4OLseqIFRdmOM/k9o/UXUdDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:15.612422Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.18224","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0b392d72ccf8c95e4ad78a36e97e9d02d66fa8d4064c9001f3cba6841ee166c","sha256:79448b985d8ccad4183077529fb5cd7ca2e3eeda011790dac103c0de183d161b"],"state_sha256":"64ac4479f9f7a6cd8bef2ada02816e92727cbdff6275d49eddd3d9cd8b02aad8"}