Results on the realization of Boolean control networks by the vertex partition method  

作　　者：Yifeng LI Jiandong ZHU Xuewen LIU 

机构地区：[1]National Center for Applied Mathematics in Chongqing,Chongqing Normal University,Chongqing 401331,China [2]School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China

出　　处：《Science China(Information Sciences)》2023年第7期206-219,共14页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11991020,11991024,61673012,11971240);Research Project of Chongqing National Center for Applied Mathematics(Grant No.ncamc2022-msxm05);Chongqing Normal University Foundation(Grant No.21XLB045)。

摘　　要：Realization problems,including the minimum realization of Boolean control networks(BCNs),are investigated by the vertex partition method.A general definition of the realization for BCNs that does not involve any subspaces is proposed.For the new and existing realization definitions,by a common concolorous perfect vertex partition(CCP-VP)of vertex-colored state transition graphs,an equivalence relation and a quotient mapping are defined,which induce a quotient system,i.e.,the realization of original BCNs.In addition,if the CCP-VP is an equal partition,a realization induced by a Y-friendly controlled invariant regular subspace is constructed.Finally,an algorithm is designed to construct the minimum realization of BCNs for different realization definitions,and three examples are given to illustrate the obtained results.

关 键 词：Boolean control networks REALIZATION semi-tensor product of matrices vertex partition state transition graph 

分 类 号：O231[理学—运筹学与控制论]