{"paper":{"title":"Compaction of Church Numerals for Higher-Order Compression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Isamu Furuya, Takuya Kida","submitted_at":"2017-06-30T08:36:57Z","abstract_excerpt":"In this study, we address the problem of compacting Church numerals. Church numerals appear as a representation of the repetitive part of data in higher-order compression. We propose a novel decomposition scheme for a natural number using tetration, which leads to a compact representation of $\\lambda$-terms equivalent to the original Church numerals. For natural number $n$, we prove that the size of the $\\lambda$-term obtained by the proposed method is $O(({\\rm slog}_{2}n)^{\\log n/ \\log \\log n})$. Moreover, we quantitatively confirmed experimentally that the proposed method outperforms a binar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10061","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"}