{"paper":{"title":"State Complexity of Pattern Matching in Regular Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Abhishek Madan, Janusz A. Brzozowski, Sylvie Davies","submitted_at":"2018-06-12T16:59:13Z","abstract_excerpt":"In a simple pattern matching problem one has a pattern $w$ and a text $t$, which are words over a finite alphabet $\\Sigma$. One may ask whether $w$ occurs in $t$, and if so, where? More generally, we may have a set $P$ of patterns and a set $T$ of texts, where $P$ and $T$ are regular languages. We are interested whether any word of $T$ begins with a word of $P$, ends with a word of $P$, has a word of $P$ as a factor, or has a word of $P$ as a subsequence. Thus we are interested in the languages $(P\\Sigma^*)\\cap T$, $(\\Sigma^*P)\\cap T$, $(\\Sigma^* P\\Sigma^*)\\cap T$, and $(\\Sigma^* \\mathbin{\\ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04645","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"}