Bi-decomposition of multi-valued logical functions and its applications

被引：55
|
作者：
Cheng, Daizhan [1 ,2 ]
Xu, Xiangru [2 ]
机构：
[1] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
来源：
AUTOMATICA | 2013年 / 49卷 / 07期
关键词：
Multi-valued logical function; Bi-decomposition; Implicit function theorem; Dynamic algebraic Boolean network; Semi-tensor product of matrices; BOOLEAN CONTROL NETWORKS; MULTIPLE-VALUED LOGIC; CIRCUIT-DESIGN; CONTROLLABILITY; DYNAMICS;
D O I：
10.1016/j.automatica.2013.03.013
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
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. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1979 / 1985
页数：7
相关论文
共 50 条
  • [1] Directional derivatives of multi-valued logical functions
    Liu Zhenbin
    Wang Yuzhen
    2013 32ND CHINESE CONTROL CONFERENCE (CCC), 2013, : 84 - 89
  • [2] Completeness and normal form of multi-valued logical functions
    Cheng, Daizhan
    Liu, Zequn
    Qi, Hongsheng
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2020, 357 (14): : 9871 - 9884
  • [3] Spectral representation of correspondence of multi-valued logical functions
    冯登国
    肖国镇
    ChineseScienceBulletin, 1995, (05) : 439 - 440
  • [4] An algorithm for bi-decomposition of logic functions
    Mishchenko, A
    Steinbach, B
    Perkowski, M
    38TH DESIGN AUTOMATION CONFERENCE PROCEEDINGS 2001, 2001, : 103 - 108
  • [5] Complete bi-decomposition of multiple-valued functions using MIN and MAX gates
    Steinbach, B
    Lang, C
    35TH INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC, PROCEEDINGS, 2005, : 69 - 74
  • [6] Bi-decompositions of multi-valued functions for circuit design and data mining applications
    Steinbach, B
    Perkowski, MA
    Lang, C
    1999 29TH IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC, PROCEEDINGS, 1999, : 50 - 58
  • [7] Bi-decompositions of multi-valued functions for circuit design and data mining applications
    Freiberg Univ of Mining and, Technology, Freiberg, Germany
    Proc Int Symp Mult Valued Logic, (50-58):
  • [8] Study on the spectrums of multi-valued logical functions over finite field
    School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
    不详
    不详
    不详
    Beijing Youdian Daxue Xuebao, 2006, 1 (43-47):
  • [9] A METHOD FOR BI-DECOMPOSITION OF PARTIAL BOOLEAN FUNCTIONS
    Pottosin, Yu, V
    PRIKLADNAYA DISKRETNAYA MATEMATIKA, 2020, (47): : 108 - 116
  • [10] Disturbance Decoupling of Multi-valued Logical Networks
    Liu Zhenbin
    Wang Yuzhen
    Li Haitao
    2011 30TH CHINESE CONTROL CONFERENCE (CCC), 2011, : 93 - 96
12345