{"paper":{"title":"Detecting regularities on grammar-compressed strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ayumi Shinohara, Hideo Bannai, Kazuyuki Narisawa, Kouji Shimohira, Masayuki Takeda, Shunsuke Inenaga, Tomohiro I, Wataru Matsubara","submitted_at":"2013-04-26T04:55:07Z","abstract_excerpt":"We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size $n$ that represents a string $s$ of length $N$, our algorithm compute all runs and squares in $s$ in $O(n^3h)$ time and $O(n^2)$ space, where $h$ is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in $O(n^3h + gnh\\log N)$ time and $O(n^2)$ space, where $g$ is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7067","kind":"arxiv","version":1},"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"}