{"paper":{"title":"Constructing small tree grammars and small circuits for formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.FL"],"primary_cat":"cs.DS","authors_text":"Artur Jez, Danny Hucke, Eric Noeth, Markus Lohrey, Moses Ganardi","submitted_at":"2014-07-16T12:48:48Z","abstract_excerpt":"It is shown that every tree of size $n$ over a fixed set of $\\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\\big(\\frac{n}{\\log_\\sigma n}\\big) = O\\big(\\frac{n \\log \\sigma}{\\log n}\\big)$ many hierarchically defined pieces. Formally, such a hierarchical decomposition has the form of a straight-line linear context-free tree grammar of size $O\\big(\\frac{n}{\\log_\\sigma n}\\big)$, which can be used as a compressed representation of the input tree. This generalizes an analogous result for strings. Previous grammar-based tree compressors were not analyz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4286","kind":"arxiv","version":3},"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"}