An Extension of Logic Functions on the Quaternary Boolean Ring<SUP>*</SUP>

Zensho NAKAO

An Extension of Logic Functions on the Quaternary Boolean Ring^*

Zensho NAKAO

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A quaternary Boolean ring structure is introduced to the four-element set L={0,,,1}, which is the only Boolean ring structure possible on it; the set of logic functions on L and L² expressible over the ring is extended from the Boolean polynomials to the entire logic functions; the extension becomes possible after inclusion of two non-Boolean polynomials in the basis, where the number is the smallest possible one. A one-to-one mapping between L and {0,1,2,3} is made, and resulting arithmetic operations on L are make explicit in the form of monadic or dyadic functions.

Publication: IEICE TRANSACTIONS on transactions Vol.E69-E No.11 pp.1169-1172

Publication Date: 1986/11/25

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Type of Manuscript: LETTER

Category: Computer System

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Zensho NAKAO

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Zensho NAKAO, "An Extension of Logic Functions on the Quaternary Boolean Ring*" in IEICE TRANSACTIONS on transactions, vol. E69-E, no. 11, pp. 1169-1172, November 1986, doi: .
Abstract: A quaternary Boolean ring structure is introduced to the four-element set L={0,,,1}, which is the only Boolean ring structure possible on it; the set of logic functions on L and L² expressible over the ring is extended from the Boolean polynomials to the entire logic functions; the extension becomes possible after inclusion of two non-Boolean polynomials in the basis, where the number is the smallest possible one. A one-to-one mapping between L and {0,1,2,3} is made, and resulting arithmetic operations on L are make explicit in the form of monadic or dyadic functions.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e69-e_11_1169/_p

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@ARTICLE{e69-e_11_1169,
author={Zensho NAKAO, },
journal={IEICE TRANSACTIONS on transactions},
title={An Extension of Logic Functions on the Quaternary Boolean Ring*},
year={1986},
volume={E69-E},
number={11},
pages={1169-1172},
abstract={A quaternary Boolean ring structure is introduced to the four-element set L={0,,,1}, which is the only Boolean ring structure possible on it; the set of logic functions on L and L² expressible over the ring is extended from the Boolean polynomials to the entire logic functions; the extension becomes possible after inclusion of two non-Boolean polynomials in the basis, where the number is the smallest possible one. A one-to-one mapping between L and {0,1,2,3} is made, and resulting arithmetic operations on L are make explicit in the form of monadic or dyadic functions.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - An Extension of Logic Functions on the Quaternary Boolean Ring*
T2 - IEICE TRANSACTIONS on transactions
SP - 1169
EP - 1172
AU - Zensho NAKAO
PY - 1986
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E69-E
IS - 11
JA - IEICE TRANSACTIONS on transactions
Y1 - November 1986
AB - A quaternary Boolean ring structure is introduced to the four-element set L={0,,,1}, which is the only Boolean ring structure possible on it; the set of logic functions on L and L² expressible over the ring is extended from the Boolean polynomials to the entire logic functions; the extension becomes possible after inclusion of two non-Boolean polynomials in the basis, where the number is the smallest possible one. A one-to-one mapping between L and {0,1,2,3} is made, and resulting arithmetic operations on L are make explicit in the form of monadic or dyadic functions.
ER -