Singular Boolean networks:Semi-tensor product approach  

作　　者：FENG JunE YAO Juan CUI Peng 

机构地区：[1]School of Mathematics, Shandong University [2]School of Control Science and Engineering, Shandong University

出　　处：《Science China(Information Sciences)》2013年第11期261-274,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.60974137,61174092,61174141);Research Awards Young and Middle-Aged Scientists of Shandong Province(Grant Nos.BS2011SF009,BS2011DX019);Outstanding Young Fund of Shandong Province(Grant No.JQ201219);Independent Innovation Foundation of Shandong University(Grant No.2010TS007)

摘　　要：Singular Boolean networks are introduced in this paper. Via semi-tensor product of matrices and the matrix expression of logical functions, two kinds of the condensed algebraic expressions of singular Boolean networks are obtained. The normalization problem of singular Boolean networks is addressed; that is, under what condition singular Boolean networks can be converted into normal Boolean networks with algebraic restric- tions. Then one sufficient condition and one necessary and sufficient condition are derived for the normalization problem. Furthermore, the solvability of singular Boolean networks is discussed and the concept of admissible initial values of singular Boolean networks is presented. Finally, fixed points and cycles of singular Boolean networks are also investigated.Singular Boolean networks are introduced in this paper. Via semi-tensor product of matrices and the matrix expression of logical functions, two kinds of the condensed algebraic expressions of singular Boolean networks are obtained. The normalization problem of singular Boolean networks is addressed; that is, under what condition singular Boolean networks can be converted into normal Boolean networks with algebraic restric- tions. Then one sufficient condition and one necessary and sufficient condition are derived for the normalization problem. Furthermore, the solvability of singular Boolean networks is discussed and the concept of admissible initial values of singular Boolean networks is presented. Finally, fixed points and cycles of singular Boolean networks are also investigated.

关 键 词：admissible initial value normalization problem semi-tensor product singular Boolean network 

分 类 号：O151.21[理学—数学] TN47[理学—基础数学]