Nonsingularity of Grain-like cascade FSRs via semi-tensor product  

作　　者：Jianquan LU Meilin LI Yang LIU Daniel W.C.HO Jurgen KURTHS 

机构地区：[1]School of Mathematics, Southeast University, Nanjing 210096, China [2]College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China [3]Department of Mathematics, City University of Hong Kong, Hong Kong, China [4]Potsdam Institute for Climate Impact Research, Potsdam 14415, Germany

出　　处：《Science China(Information Sciences)》2018年第1期54-65,共12页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61573102,11671361);Natural Science Foundation of Jiangsu Province of China(Grant No.BK20170019);Jiangsu Provincial Key Laboratory of Networked Collective Intelligence(Grant No.BM2017002);China Postdoctoral Science Foundation(Grant Nos.2014M560377,2015T80483);Jiangsu Province Six Talent Peaks Project(Grant No.2015-ZNDW-002);Fundamental Research Funds for the Central Universities

摘　　要：In this paper, Grain-like cascade feedback shift registers（FSRs） are regarded as two Boolean networks（BNs）, and the semi-tensor product（STP） of the matrices is used to convert the Grain-like cascade FSRs into an equivalent linear equation. Based on the STP, a novel method is proposed herein to investigate the nonsingularity of Grain-like cascade FSRs. First, we investigate the property of the state transition matrix of Grain-like cascade FSRs. We then propose their sufficient and necessary nonsingularity condition. Next,we regard the Grain-like cascade FSRs as Boolean control networks（BCNs） and further provide a sufficient condition of their nonsingularity. Finally, two examples are provided to illustrate the results obtained in this paper.In this paper, Grain-like cascade feedback shift registers（FSRs） are regarded as two Boolean networks（BNs）, and the semi-tensor product（STP） of the matrices is used to convert the Grain-like cascade FSRs into an equivalent linear equation. Based on the STP, a novel method is proposed herein to investigate the nonsingularity of Grain-like cascade FSRs. First, we investigate the property of the state transition matrix of Grain-like cascade FSRs. We then propose their sufficient and necessary nonsingularity condition. Next,we regard the Grain-like cascade FSRs as Boolean control networks（BCNs） and further provide a sufficient condition of their nonsingularity. Finally, two examples are provided to illustrate the results obtained in this paper.

关 键 词：Grain-like cascade FSRs Boolean control networks Boolean networks semi-tensor product NONSINGULARITY 

分 类 号：TP4[自动化与计算机技术]