2019
DOI: 10.3390/a12080159
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Compaction of Church Numerals

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) … Show more

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Cited by 2 publications
(1 citation statement)
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“…After several rounds of revisions and reviewing, seven of the submitted articles were accepted for inclusion in the Special Issue. These seven articles present new results for a wide variety of data compression topics: prefix free codes [1], finding patterns using lossy compression [2], compression in PDE solvers [3], compression and embedding of trees [4], compaction of Church numerals [5], compressed sensing [6], time-universal data compression [7]. Combined these results represent some of the current trends in the field.…”
Section: Special Issuementioning
confidence: 93%
“…After several rounds of revisions and reviewing, seven of the submitted articles were accepted for inclusion in the Special Issue. These seven articles present new results for a wide variety of data compression topics: prefix free codes [1], finding patterns using lossy compression [2], compression in PDE solvers [3], compression and embedding of trees [4], compaction of Church numerals [5], compressed sensing [6], time-universal data compression [7]. Combined these results represent some of the current trends in the field.…”
Section: Special Issuementioning
confidence: 93%