Singular Boolean networks： Semi-tensor product approach

• Published in: Science China. Information sciences Vol. 56; no. 11; pp. 261 - 274
• Main Authors: Feng, JunE, Yao, Juan, Cui, Peng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2013; Springer Nature B.V
• Subjects: Algebra; Boolean algebra; Boolean functions; Computer Science; Fixed points (mathematics); Information Systems and Communication Service; Mathematical analysis; Networks; Research Paper; Tensors; 代数表达式; 充分必要条件; 奇异; 布尔网络; 张量积; 标准化问题; 矩阵表达式; 逻辑功能; singular Boolean network; normalization problem; admissible initial value; semi-tensor product
• ISSN: 1674-733X; 1869-1919
• DOI: 10.1007/s11432-012-4666-8

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.