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Completeness and normal form of multi-valued logical functions

文献类型：期刊论文

作者Cheng, Daizhan2; Liu, Zequn1,2; Qi, Hongsheng1,2
刊名JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
出版日期2020-09-01
卷号357期号:14页码:9871-9884
ISSN号0016-0032
DOI10.1016/j.jfranklin.2020.06.026
英文摘要Theory of completeness is essential for multi-valued logical functions. Using semi-tensor product (STP) of matrices, the algebraic form of k-valued logical functions is presented. Using algebraic form, a method is proposed to construct an adequate set of connectives (ASC), consisting of unary operators with conjunction/disjunction for k-valued logical functions, which can be used to express any k-valued logical functions. Based on it, two normal forms of k-valued logical functions are presented, which are extensions of the disjunctive normal form and conjunctive normal form of Boolean functions respectively. The ASC is then simplified to a condensed set. Finally, the normal forms are further extended to mix-valued logical functions. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
资助项目National Natural Science Foundation of China (NSFC)[61773371] ; National Natural Science Foundation of China (NSFC)[61873262] ; National Natural Science Foundation of China (NSFC)[61733018] ; Youth Innovation Promotion Association of the CAS
WOS研究方向Automation & Control Systems ; Engineering ; Mathematics
语种英语
WOS记录号WOS:000577481300035
出版者PERGAMON-ELSEVIER SCIENCE LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/52340]  
专题中国科学院数学与系统科学研究院
通讯作者Cheng, Daizhan
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Cheng, Daizhan,Liu, Zequn,Qi, Hongsheng. Completeness and normal form of multi-valued logical functions[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,2020,357(14):9871-9884.
APA Cheng, Daizhan,Liu, Zequn,&Qi, Hongsheng.(2020).Completeness and normal form of multi-valued logical functions.JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,357(14),9871-9884.
MLA Cheng, Daizhan,et al."Completeness and normal form of multi-valued logical functions".JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 357.14(2020):9871-9884.

入库方式： OAI收割

来源：数学与系统科学研究院

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