{"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"}