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Compaction of Church Numerals

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Title: Compaction of Church Numerals
Authors: Furuya, Isamu Browse this author
Kida, Takuya Browse this author →KAKEN DB
Keywords: loss-less compression
lambda term
higher-order compression
Issue Date: Aug-2019
Publisher: MDPI
Journal Title: Algorithms
Volume: 12
Issue: 8
Start Page: 159
Publisher DOI: 10.3390/a12080159
Abstract: 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.
Rights: https://creativecommons.org/licenses/by/4.0/
Type: article
URI: http://hdl.handle.net/2115/75613
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

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