{"paper":{"title":"Piecewise Testable Languages and Nondeterministic Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Tom\\'a\\v{s} Masopust","submitted_at":"2016-03-01T17:11:05Z","abstract_excerpt":"A regular language is $k$-piecewise testable if it is a finite boolean combination of languages of the form $\\Sigma^* a_1 \\Sigma^* \\cdots \\Sigma^* a_n \\Sigma^*$, where $a_i\\in\\Sigma$ and $0\\le n \\le k$. Given a DFA $A$ and $k\\ge 0$, it is an NL-complete problem to decide whether the language $L(A)$ is piecewise testable and, for $k\\ge 4$, it is coNP-complete to decide whether the language $L(A)$ is $k$-piecewise testable. It is known that the depth of the minimal DFA serves as an upper bound on $k$. Namely, if $L(A)$ is piecewise testable, then it is $k$-piecewise testable for $k$ equal to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00361","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"}