{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IZ7DFJNVGWK3G3LDMSXHSRJJJ5","short_pith_number":"pith:IZ7DFJNV","schema_version":"1.0","canonical_sha256":"467e32a5b53595b36d6364ae7945294f693b5bc39015a303c270466e984fd281","source":{"kind":"arxiv","id":"1606.01199","version":2},"attestation_state":"computed","paper":{"title":"On the Complexity and Decidability of Some Problems Involving Shuffle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Ian McQuillan, Joey Eremondi, Oscar H. Ibarra","submitted_at":"2016-06-03T17:40:47Z","abstract_excerpt":"The complexity and decidability of various decision problems involving the shuffle operation are studied. The following three problems are all shown to be $NP$-complete: given a nondeterministic finite automaton (NFA) $M$, and two words $u$ and $v$, is $L(M)$ not a subset of $u$ shuffled with $v$, is $u$ shuffled with $v$ not a subset of $L(M)$, and is $L(M)$ not equal to $u$ shuffled with $v$? It is also shown that there is a polynomial-time algorithm to determine, for $NFA$s $M_1, M_2$ and a deterministic pushdown automaton $M_3$, whether $L(M_1)$ shuffled with $L(M_2)$ is a subset of $L(M_3"},"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":"1606.01199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-06-03T17:40:47Z","cross_cats_sorted":[],"title_canon_sha256":"cb59422d81d247996d5f9ec565ab17fd96c53b424e24a221d5979bd6b83338a5","abstract_canon_sha256":"e4bf4ae167865eb726195bb812b35dee30749065b8c63e4e938cbe4c402a14d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:55.033481Z","signature_b64":"3CRK5LIPTWUX9bm1pILSfJetmSSId2lyzwkrgmRr665q2gKqU99DoRbPHiYtk1cQiciCHftnSjLpMoHtEtuFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"467e32a5b53595b36d6364ae7945294f693b5bc39015a303c270466e984fd281","last_reissued_at":"2026-05-17T23:51:55.032974Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:55.032974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Complexity and Decidability of Some Problems Involving Shuffle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Ian McQuillan, Joey Eremondi, Oscar H. Ibarra","submitted_at":"2016-06-03T17:40:47Z","abstract_excerpt":"The complexity and decidability of various decision problems involving the shuffle operation are studied. The following three problems are all shown to be $NP$-complete: given a nondeterministic finite automaton (NFA) $M$, and two words $u$ and $v$, is $L(M)$ not a subset of $u$ shuffled with $v$, is $u$ shuffled with $v$ not a subset of $L(M)$, and is $L(M)$ not equal to $u$ shuffled with $v$? It is also shown that there is a polynomial-time algorithm to determine, for $NFA$s $M_1, M_2$ and a deterministic pushdown automaton $M_3$, whether $L(M_1)$ shuffled with $L(M_2)$ is a subset of $L(M_3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01199","kind":"arxiv","version":2},"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":"1606.01199","created_at":"2026-05-17T23:51:55.033057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01199v2","created_at":"2026-05-17T23:51:55.033057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01199","created_at":"2026-05-17T23:51:55.033057+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZ7DFJNVGWK3","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZ7DFJNVGWK3G3LD","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZ7DFJNV","created_at":"2026-05-18T12:30:22.444734+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/IZ7DFJNVGWK3G3LDMSXHSRJJJ5","json":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5.json","graph_json":"https://pith.science/api/pith-number/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/graph.json","events_json":"https://pith.science/api/pith-number/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/events.json","paper":"https://pith.science/paper/IZ7DFJNV"},"agent_actions":{"view_html":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5","download_json":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5.json","view_paper":"https://pith.science/paper/IZ7DFJNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01199&json=true","fetch_graph":"https://pith.science/api/pith-number/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/graph.json","fetch_events":"https://pith.science/api/pith-number/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/action/storage_attestation","attest_author":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/action/author_attestation","sign_citation":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/action/citation_signature","submit_replication":"https://pith.science/pith/IZ7DFJNVGWK3G3LDMSXHSRJJJ5/action/replication_record"}},"created_at":"2026-05-17T23:51:55.033057+00:00","updated_at":"2026-05-17T23:51:55.033057+00:00"}