Compaction of Church Numerals

Furuya, Isamu; Kida, Takuya

Algorithms, 2019, 12(8), 159

Permalink : https://hdl.handle.net/2115/75613

このアイテムのアクセス数:620件（2026-08-20 09:25 集計）

ファイル	フォーマット	サイズ	閲覧回数	説明
https://doi.org/10.3390/a12080159			38

アクセス権	open access
URI	https://hdl.handle.net/2115/75613
タイトル	Compaction of Church Numerals
著者	著者名 Furuya, Isamu
著者	e-Rad_Researcher 70343316 著者名 Kida, Takuya
言語	英語
キーワード	loss-less compression
	lambda term
	higher-order compression
発行日	2019-08
出版者	MDPI
収録物名	Algorithms
巻(号)	12(8)
ページ	159
抄録	In this study, we address the problem of compaction of Church numerals. Church numerals are unary representations of natural numbers on the scheme of lambda terms. We propose a novel decomposition scheme from a given natural number into an arithmetic expression using tetration, which enables us to obtain a compact representation of lambda terms that leads to the Church numeral of the natural number. For natural number n, we prove that the size of the lambda term obtained by the proposed method is O ( ( slog 2 n ) ( log n / log log n ) ) . Moreover, we experimentally confirmed that the proposed method outperforms binary representation of Church numerals on average, when n is less than approximately 10,000.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	Creative Commons Attribution 4.0 International
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.3390/a12080159