{"paper":{"title":"Computing convolution on grammar-compressed text","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hideo Bannai, Masayuki Takeda, Shunsuke Inenaga, Tomohiro I, Toshiya Tanaka","submitted_at":"2013-03-16T05:07:24Z","abstract_excerpt":"The convolution between a text string $S$ of length $N$ and a pattern string $P$ of length $m$ can be computed in $O(N \\log m)$ time by FFT. It is known that various types of approximate string matching problems are reducible to convolution. In this paper, we assume that the input text string is given in a compressed form, as a \\emph{straight-line program (SLP)}, which is a context free grammar in the Chomsky normal form that derives a single string. Given an SLP $\\mathcal{S}$ of size $n$ describing a text $S$ of length $N$, and an uncompressed pattern $P$ of length $m$, we present a simple $O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3945","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"}