标题：Bi-decomposition of multi-valued logical functions and its applications
作者：Daizhan Cheng;Xiangru Xu
作者机构：[Cheng, D] School of Control Science and Engineering, Shandong University, Jinan 250061, China, Academy of Mathematics and Systems Science, Chinese Ac 更多
通讯作者地址：[Cheng, DZ]Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China.
关键词：Multi-valued logical function;Bi-decomposition;Implicit function theorem;Dynamic-algebraic Boolean network;Semi-tensor product of matrices
摘要：The bi-decomposition of multi-valued logical (MVL) functions, including disjoint and non-disjoint cases, is considered. Using a semi-tensor product, an MVL function can be expressed in its algebraic form. Based on this form, straightforward verifiable necessary and sufficient conditions are provided for each case, respectively. The constructive proofs also lead to constructing corresponding decompositions. Using these results, the implicit function theorem (IFT) of k-valued functions, as a special bi-decomposition, is obtained. Finally, as an application, the normalization of dynamic-algebraic (D-A) Boolean networks is investigated using IFT of k-valued functions.