Completeness and normal form of multi-valued logical functions

doi:10.1016/j.jfranklin.2020.06.026

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	Completeness and normal form of multi-valued logical functions
	Cheng, Daizhan 1; Liu, Zequn 1,2; Qi, Hongsheng 1,2
	2020-09-01
发表期刊	JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
ISSN	0016-0032
卷号	357 期号:14 页码:9871-9884
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.
DOI	10.1016/j.jfranklin.2020.06.026
收录类别	SCI
语种	英语
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
WOS类目	Automation & Control Systems ; Engineering, Multidisciplinary ; Engineering, Electrical & Electronic ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000577481300035
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52341
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.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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.