标题：Explicit formula of logical algebraic equations and singular Boolean networks with probability
作者：Yu, Yongyuan ;Feng, Jun-E. ;Wang, Sen
作者机构：[Yu, Yongyuan ;Feng, Jun-E. ;Wang, Sen ] School of Mathematics, Shandong University, Jinan; 250100, China
会议名称：35th Chinese Control Conference, CCC 2016
会议日期：27 July 2016 through 29 July 2016
来源：Chinese Control Conference, CCC
关键词：Implicit Function Theorem; Logical Algebraic Equations; Semi-tensor Product; Singular Boolean Networks
摘要：The implicit function theorem (IFT) of logical algebraic equations (LAEs) and a class of more generalized singular Boolean networks (SBNs) are considered. Using matrix semi-tensor product (STP), three equivalent expressions of LAEs and their relationship are presented. LAEs have equivalent explicit formula, if and only if data submatrix has distinct rows. An algorithm is provided to find all the explicit formulas of LAEs. Combined with the derived results about minimum independent variables, a class of SBNs is normalizable. Furthermore, the SBNs with probability is investigated and some results such as the reachability and attractors are obtained. © 2016 TCCT.