The structure of canalizing functions  

作　　者：Zhiqiang LI Daizhan CHENG 

机构地区：[1]Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou Henan 450002, China [2]Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《控制理论与应用（英文版）》2010年第3期375-381,共7页

基　　金：supported by the National Natural Science Foundation of China (No.60674022,60736022,60821091)

摘　　要：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.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.

关 键 词：Canalizing function Boolean function Seminested canalizing function 

分 类 号：TN791[电子电信—电路与系统] O413.1[理学—理论物理]