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A minimum adequate set of multi-valued logic
DaizhanCheng,Jun-eFeng,JianliZhao,ShihuaFu
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(1 Research Center of Semi?tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng, China 2 Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing 100190, China;3 School of Mathematics, Shandong University, Jinan, China)
摘要:
An adequate set of k-valued logic is provided, which contains only two operators. It is also proved that this adequate set is of minimum size.
关键词:  k-valued logic · Normal form · Adequate set (ADS) · Structure matrix of logical functions · Semi-tensor product of matrices
DOI:https://doi.org/10.1007/s11768-021-00064-w
基金项目:This work was supported partly by the National Natural Science Foundation of China (Nos.61773371, 61733018, 61877036) and the Natural Science Fund of Shandong Province (No. ZR2019MF002).
A minimum adequate set of multi-valued logic
Daizhan Cheng,Jun-e Feng,Jianli Zhao,Shihua Fu
(1 Research Center of Semi?tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng, China 2 Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing 100190, China;3 School of Mathematics, Shandong University, Jinan, China)
Abstract:
An adequate set of k-valued logic is provided, which contains only two operators. It is also proved that this adequate set is of minimum size.
Key words:  k-valued logic · Normal form · Adequate set (ADS) · Structure matrix of logical functions · Semi-tensor product of matrices