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		Zhiqiang LI,Daizhan CHENG.[en_title][J].Control Theory and Technology,2010,8(3):375~381.[Copy]

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ZhiqiangLI,DaizhanCHENG
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DOI：10.1007/s11768-010-0018-7

Received:January 19, 2010Revised:January 19, 2010

基金项目:This work was supported by the National Natural Science Foundation of China (No.60674022, 60736022, 60821091).

The structure of canalizing functions

Zhiqiang LI,Daizhan CHENG

(Department of Mathematics and Information Science, Henan University of Economics and Law;Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences)

Abstract:

The structure of a canalizing function is discussed. Using a new matrix product, namely semitensor product, the logical function is expressed in its matrix form. From its matrix expression, a criterion is obtained to test whether a logical function is a canalizing function. Then a formula is obtained to calculate the number of canalizing functions. Moreover, an algorithm is presented to generate canalizing functions. Finally, some results obtained are extended to seminested canalizing functions.

Key words: Canalizing function Boolean function Seminested canalizing function