Decomposition of Logical Mappings and Its Application to Dynamic-algebraic Boolean Networks
Bi-decomposition of Boolean mappings is very important in circuit design, because it saves space and energy. This paper considers two kinds of bi-decompositions: disjoint and non-disjoint. Using semi-tensor product of matrices and the matrix expression of logic, formulas are obtained for both cases. Then the results are extended to the multi-valued and the mix-valued logical functions. Finally, the results obtained are also used to convert the dynamic-algebraic Boolean (control) systems into a normal form, which makes the tools developed for dynamic Boolean (control) networks applicable to dynamic-algebraic Boolean (control) systems.