Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.