{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TPNWAJYFED2I367I4XMFAK6QSG","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":"54e27681edf65c683cd057fe4207d65c80b44cc9df9a18bcb028b0212b797563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-11-28T17:50:33Z","title_canon_sha256":"5c0bbe95641bca8d32b474f80e6acf68bae6abbabf0190b2c89f4afedef4184c"},"schema_version":"1.0","source":{"id":"1711.10436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10436","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10436v1","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10436","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"TPNWAJYFED2I","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TPNWAJYFED2I367I","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TPNWAJYF","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:cdffe2bf557924aaaf44a44b9e4698c5ddf10a5d013e34a6267c8c635133ea17","target":"graph","created_at":"2026-05-18T00:29:22Z","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 aim at enforcing hard constraints to impose a global structure on sequences generated from Markov models. In this report, we study the complexity of sampling Markov sequences under two classes of constraints: Binary Equalities and Grammar Membership Constraints. First, we give a sketch of proof of #P-completeness for binary equalities and identify three sub-cases where sampling is polynomial. We then give a proof of #P-completeness for grammar membership, and identify two cases where sampling is tractable. The first polynomial sub-case where sampling is tractable is when the grammar is prov","authors_text":"Fran\\c{c}ois Pachet, Stephane Rivaud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-11-28T17:50:33Z","title":"Sampling Markov Models under Constraints: Complexity Results for Binary Equalities and Grammar Membership"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10436","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:a297a8462ff6ffbc767dc042495ed614f42b6206ae13b8ea6c096fc42bb38c07","target":"record","created_at":"2026-05-18T00:29:22Z","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":"54e27681edf65c683cd057fe4207d65c80b44cc9df9a18bcb028b0212b797563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-11-28T17:50:33Z","title_canon_sha256":"5c0bbe95641bca8d32b474f80e6acf68bae6abbabf0190b2c89f4afedef4184c"},"schema_version":"1.0","source":{"id":"1711.10436","kind":"arxiv","version":1}},"canonical_sha256":"9bdb60270520f48dfbe8e5d8502bd091b1b05a04a9895a22abc07fae38536dd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bdb60270520f48dfbe8e5d8502bd091b1b05a04a9895a22abc07fae38536dd9","first_computed_at":"2026-05-18T00:29:22.117910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:22.117910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2StcAoT0gQpScF8ADhtu1y9b0Cdyv3iJbnl/trirZTcWRfkw3711q9obOT8DxbR91FLnmG29jUGZISr4J3oKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:22.118681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a297a8462ff6ffbc767dc042495ed614f42b6206ae13b8ea6c096fc42bb38c07","sha256:cdffe2bf557924aaaf44a44b9e4698c5ddf10a5d013e34a6267c8c635133ea17"],"state_sha256":"8d965a7323a6fbc3ae5a2bccd39d883d8d69865b122fb44c180ca1e655925028"}