Classification and Enumeration of Linearly Separable Boolean Functions Based on Optimal Separation System

被引：0
|
作者：
Jin, Wei [1 ]
Chen, Fangyue [1 ]
He, Qinbin [2 ]
机构：
[1] Hangzhou Dianzi Univ, Sch Comp Sci & Technol, Hangzhou 310018, Zhejiang, Peoples R China
[2] Taizhou Univ, Sch Elect & Informat Engn, Taizhou 318000, Zhejiang, Peoples R China
来源：
NEURAL PROCESSING LETTERS | 2022年 / 54卷 / 05期
关键词：
Linearly separable Boolean function (LSBF); Balanced LSBF (BLSBF); Self-dual (SD) class; Optimal separation system; Classification enumeration formula; THRESHOLD FUNCTIONS; GRAPH;
D O I：
10.1007/s11063-022-10781-1
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, some profound mathematical properties of linearly separable Boolean functions (LSBF) are revealed based on the optimal separation system derived from support vector machine, and a novel approach is proposed for the classification and enumeration of this kind of function. Completely different the existing linear program method, the method presented now can be used not only to enumerate the number of self-dual function classes and the total number of LSBFs, but also to calculate the optimal separation system of any balanced LSBF accurately.
引用
收藏
页码：3695 / 3704
页数：10
相关论文
共 50 条
  • [21] RRAM-based Adaptive Neural Logic Block for Implementing Non-Linearly Separable Functions In a Single Layer
    Soltiz, Michael
    Merkel, Cory
    Kudithipudi, Dhireesha
    Rose, Garrett S.
    PROCEEDINGS OF THE 2012 IEEE/ACM INTERNATIONAL SYMPOSIUM ON NANOSCALE ARCHITECTURES (NANOARCH), 2012, : 218 - 225
  • [22] Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions
    Shen, Bingsheng
    Yu, Tao
    Zhou, Zhengchun
    Yang, Yang
    DESIGNS CODES AND CRYPTOGRAPHY, 2024, 92 (12) : 4213 - 4230
  • [23] Constructing Boolean Functions With (Potentially) Optimal Algebraic Immunity Based on Multiplicative Decompositions of Finite Fields
    Wu, Baofeng
    Zheng, Jia
    Lin, Dongdai
    2015 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2015, : 491 - 495
  • [24] Optimal Discriminant Functions Based on Sampled Distribution Distance for Modulation Classification
    Urriza, Paulo
    Rebeiz, Eric
    Cabric, Danijela
    IEEE COMMUNICATIONS LETTERS, 2013, 17 (10) : 1885 - 1888
  • [25] Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields
    Liu Zhuojun
    Wu Baofeng
    JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2019, 32 (01) : 356 - 374
  • [26] Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields
    Zhuojun Liu
    Baofeng Wu
    Journal of Systems Science and Complexity, 2019, 32 : 356 - 374
  • [27] Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields
    LIU Zhuojun
    WU Baofeng
    JournalofSystemsScience&Complexity, 2019, 32 (01) : 356 - 374
  • [28] Detection of the Cardiovascular Diseases by using a Linearly Modeling System with the PSO-based Classification Scheme
    Shen, Meng-Cheng
    Chen, Heng-Chou
    Chen, Chih-Hui
    ISDA 2008: EIGHTH INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS DESIGN AND APPLICATIONS, VOL 1, PROCEEDINGS, 2008, : 531 - +
  • [29] Detection of the cardiovascular diseases by using a linearly modeling system with the PSO-based classification scheme
    Shen, Meng-Cheng
    Tsai, Yeong-Shyeong
    Chen, Heng-Chou
    PROCEEDINGS OF THE 11TH WSEAS INTERNATIONAL CONFERENCE ON SYSTEMS, VOL 2: SYSTEMS THEORY AND APPLICATIONS, 2007, : 378 - +
  • [30] A systematic method of constructing Boolean functions with optimal algebraic immunity based on the generator matrix of the Reed–Muller code
    Sihong Su
    Xiaohu Tang
    Xiangyong Zeng
    Designs, Codes and Cryptography, 2014, 72 : 653 - 673
12345