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.
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页码：3695 / 3704
页数：10
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