{"paper":{"title":"On $k$-piecewise testability (preliminary report)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Micha\\\"el Thomazo, Tom\\'a\\v{s} Masopust","submitted_at":"2014-12-04T12:27:07Z","abstract_excerpt":"For a non-negative integer $k$, a language is $k$-piecewise test\\-able ($k$-PT) if it is a finite boolean combination of languages of the form $\\Sigma^* a_1 \\Sigma^* \\cdots \\Sigma^* a_n \\Sigma^*$ for $a_i\\in\\Sigma$ and $0\\le n \\le k$. We study the following problem: Given a DFA recognizing a piecewise testable language, decide whether the language is $k$-PT. We provide a complexity bound and a detailed analysis for small $k$'s. The result can be used to find the minimal $k$ for which the language is $k$-PT. We show that the upper bound on $k$ given by the depth of the minimal DFA can be expone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1641","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"}