Testing and Realization of Three-Valued Majority Functions by Complete Monotonicity

Kazuharu YAMATO; Kyoichi NAKASHIMA; Yutaka HATA

Testing and Realization of Three-Valued Majority Functions by Complete Monotonicity

Kazuharu YAMATO, Kyoichi NAKASHIMA, Yutaka HATA

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This paper presents a method for implementing the testing and realization of three-valued majority functions by using properties of 02-complete monotonicity which is an extended concept of complete monotonicity in binary logic. It is shown that reduced functions of three-valued majority functions are 02-completely monotonic, and all 7 or less variable three-valued logical functions satisfying the M(1) majority condition are three-valued majority functions if two-valued input three-valued output functions obtained by taking out only output values for 02-input vectors are 02-completely monotonic. For the realization of majority functions, m-variable inequalities are defined from 02-complete monotonicity. The weight vector is determined by solving weight inequalities derived from m-variable inequalities, and then thresholds are obtained. The overall algorithm of the method is given along with an example.

Publication: IEICE TRANSACTIONS on transactions Vol.E69-E No.8 pp.852-858

Publication Date: 1986/08/25

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Type of Manuscript: PAPER

Category: Computer System

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Kazuharu YAMATO
Kyoichi NAKASHIMA
Yutaka HATA

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Kazuharu YAMATO, Kyoichi NAKASHIMA, Yutaka HATA, "Testing and Realization of Three-Valued Majority Functions by Complete Monotonicity" in IEICE TRANSACTIONS on transactions, vol. E69-E, no. 8, pp. 852-858, August 1986, doi: .
Abstract: This paper presents a method for implementing the testing and realization of three-valued majority functions by using properties of 02-complete monotonicity which is an extended concept of complete monotonicity in binary logic. It is shown that reduced functions of three-valued majority functions are 02-completely monotonic, and all 7 or less variable three-valued logical functions satisfying the M(1) majority condition are three-valued majority functions if two-valued input three-valued output functions obtained by taking out only output values for 02-input vectors are 02-completely monotonic. For the realization of majority functions, m-variable inequalities are defined from 02-complete monotonicity. The weight vector is determined by solving weight inequalities derived from m-variable inequalities, and then thresholds are obtained. The overall algorithm of the method is given along with an example.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e69-e_8_852/_p

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@ARTICLE{e69-e_8_852,
author={Kazuharu YAMATO, Kyoichi NAKASHIMA, Yutaka HATA, },
journal={IEICE TRANSACTIONS on transactions},
title={Testing and Realization of Three-Valued Majority Functions by Complete Monotonicity},
year={1986},
volume={E69-E},
number={8},
pages={852-858},
abstract={This paper presents a method for implementing the testing and realization of three-valued majority functions by using properties of 02-complete monotonicity which is an extended concept of complete monotonicity in binary logic. It is shown that reduced functions of three-valued majority functions are 02-completely monotonic, and all 7 or less variable three-valued logical functions satisfying the M(1) majority condition are three-valued majority functions if two-valued input three-valued output functions obtained by taking out only output values for 02-input vectors are 02-completely monotonic. For the realization of majority functions, m-variable inequalities are defined from 02-complete monotonicity. The weight vector is determined by solving weight inequalities derived from m-variable inequalities, and then thresholds are obtained. The overall algorithm of the method is given along with an example.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Testing and Realization of Three-Valued Majority Functions by Complete Monotonicity
T2 - IEICE TRANSACTIONS on transactions
SP - 852
EP - 858
AU - Kazuharu YAMATO
AU - Kyoichi NAKASHIMA
AU - Yutaka HATA
PY - 1986
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E69-E
IS - 8
JA - IEICE TRANSACTIONS on transactions
Y1 - August 1986
AB - This paper presents a method for implementing the testing and realization of three-valued majority functions by using properties of 02-complete monotonicity which is an extended concept of complete monotonicity in binary logic. It is shown that reduced functions of three-valued majority functions are 02-completely monotonic, and all 7 or less variable three-valued logical functions satisfying the M(1) majority condition are three-valued majority functions if two-valued input three-valued output functions obtained by taking out only output values for 02-input vectors are 02-completely monotonic. For the realization of majority functions, m-variable inequalities are defined from 02-complete monotonicity. The weight vector is determined by solving weight inequalities derived from m-variable inequalities, and then thresholds are obtained. The overall algorithm of the method is given along with an example.
ER -