Abstract

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.

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