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

被引：59
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
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页码：1979 / 1985
页数：7
相关论文
共 30 条
[1]  
[Anonymous], 1999, SWITCHING THEORY LOG
[2]  
Ashenhurst R. L., 1957, ANN COMPUTATION LAB, V29, P74
[3]   Derivation of vector-valued Boolean functions [J].
Bazsó, F .
ACTA MATHEMATICA HUNGARICA, 2000, 87 (03) :197-203
[4]   Multi-valued logic synthesis [J].
Brayton, RK ;
Khatri, SP .
TWELFTH INTERNATIONAL CONFERENCE ON VLSI DESIGN, PROCEEDINGS, 1999, :196-205
[5]  
Cheng D., 2011, SEMITENSOR PRODUCT A
[6]  
Cheng D., 2012, An Introduction to Semi-Tensor Product of Matrices and Its Applications
[7]   Disturbance Decoupling of Boolean Control Networks [J].
Cheng, Daizhan .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (01) :2-10
[8]   A Linear Representation of Dynamics of Boolean Networks [J].
Cheng, Daizhan ;
Qi, Hongsheng .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (10) :2251-2258
[9]   State-Space Analysis of Boolean Networks [J].
Cheng, Daizhan ;
Qi, Hongsheng .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 2010, 21 (04) :584-594
[10]   Controllability and observability of Boolean control networks [J].
Cheng, Daizhan ;
Qi, Hongsheng .
AUTOMATICA, 2009, 45 (07) :1659-1667
123