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数学与物理学

基于半张量积方法的布尔函数矩阵表示的一些应用

  • 赵寅 ,
  • 高旭 ,
  • 程代展
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  • 1. 中国科学院数学与系统科学研究院系统控制重点实验室, 北京 100190;
    2. 伊利诺伊大学芝加哥分校数学、统计与计算机科学系, 芝加哥 60607

收稿日期: 2011-06-28

  修回日期: 2011-09-27

  网络出版日期: 2012-11-15

Some applications of the matrix expression of Boolean function via semi-tensor product

  • ZHAO Yin ,
  • GAO Xu ,
  • CHENG Dai-Zhan
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  • 1. Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
    2. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago 60607, USA

Received date: 2011-06-28

  Revised date: 2011-09-27

  Online published: 2012-11-15

Supported by

Supported by National Natural Science Foundation of China(61074114,60821091) 

摘要

利用矩阵的半张量积, 布尔函数可以被表示为矩阵形式. 通过这个方法, 我们给出了布尔函数从真值表到多项式形式转换的一个简洁的证明, 并研究了布尔函数的线性结构.

本文引用格式

赵寅 , 高旭 , 程代展 . 基于半张量积方法的布尔函数矩阵表示的一些应用[J]. 中国科学院大学学报, 2012 , (6) : 743 -749 . DOI: 10.7523/j.issn.2095-6134.2012.6.004

Abstract

Boolean function can be expressed in matrix form using semi-tensor product of matrices. Using this approach, we give a neat proof of the conversion of a Boolean function from the truth table to the polynomial form. The linear structure of Boolean functions is also investigated.

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