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

Kazuharu YAMATO  Kyoichi NAKASHIMA  Yutaka HATA  

IEICE TRANSACTIONS (1976-1990)   Vol.E69   No.8   pp.852-858
Publication Date: 1986/08/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Computer System

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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.