多值邏輯函數(shù)與其變元的幾種無關性的譜分析
SPECTRAL ANALYSIS OF SOME INDEPENDENCES OF MULTIPLE-VALUED LOGICAL FUNCTIONS FROM THEIR VARIABLES
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摘要: 多值邏輯函數(shù)與它們的變元之間有許多種特殊關系,單從它們的表達式是較難判斷的。本文給出了多值邏輯函數(shù)與其變元無關和統(tǒng)計無關的一些充分必要條件;給出了多值邏輯函數(shù)與其某些變元代數(shù)無關(也稱為退化)的一些條件和最大程度地退化一個函數(shù)的方法;指出了這些結果在實際中的應用。所有這些結果都是Chrestenson譜方法來研究的。Abstract: There are many kinds of special relationships between multiple-valued logical functions and their variables, and it is difficult to be judged from their expressions . In this paper, some sufficient and necessary conditions of the independence and statistical indepenndence of multiple-valued logical functions from their variables are given. Some conditions of algebraic independence of multi-valued logical functions from some of their variables and the way to degenerate a function to the greatest extent are proposed, and some applications of these results are indicated. All the results are studied by using Chrestenson spectral techniques.
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