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›› 2012, Vol. ›› Issue (6): 743-749.DOI: 10.7523/j.issn.2095-6134.2012.6.004

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

ZHAO Yin1, GAO Xu2, CHENG Dai-Zhan1   

  1. 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:2011-06-28 Revised:2011-09-27 Online:2012-11-15
  • Supported by:
    Supported by National Natural Science Foundation of China(61074114,60821091) 

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.

Key words: Boolean function, semi-tensor product, truth table, polynomial form, linear structure

CLC Number: