Algebraic Thickness of Boolean Functions

ZHOU Yu; WANG Xiao-fen; LUO Yan-feng; XIAO Guo-zhen

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Algebraic Thickness of Boolean Functions

更新时间：2025-07-16

- Algebraic Thickness of Boolean Functions
- Acta Electronica Sinica Vol. 37, Issue 7, Pages: 1412-1415(2009)
- 作者机构：
  
  1. 西安电子科技大学综合业务网理论及关键技术国家重点实验室,陕西,西安,710071
  2. 兰州大学数学与统计学院,甘肃,兰州,730000
  3. 西安电子科技大学综合业务网理论及关键技术国家重点实验室陕西西安,710071
  4. 兰州大学数学与统计学院甘肃兰州,730000
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2009
- 稿件说明：
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ZHOU Yu, WANG Xiao-fen, LUO Yan-feng, et al. Algebraic Thickness of Boolean Functions[J]. Acta Electronica Sinica, 2009, 37(7): 1412-1415.
DOI：

ZHOU Yu, WANG Xiao-fen, LUO Yan-feng, et al. Algebraic Thickness of Boolean Functions[J]. Acta Electronica Sinica, 2009, 37(7): 1412-1415. DOI：

摘要

基于布尔函数的代数次数和代数厚度

给出了布尔函数和其分解函数的代数厚度的关系

利用递归和反证法导出了

n元布尔函数代数厚度的上界是2* *(n-1)

这个上界回答了"是否存在代数厚度大于2* *(n-1)的n元布尔函数"这个公开问题.在此基础上改进了n元k(2≤k≤(n-1)/2)

次基本对称布尔函数的代数厚度的上界

同时也得到了布尔函数的代数厚度的一些性质.

Abstract

Based on the algebraic degree and the algebraic thickness of Boolean functions

the relationship of algebraic thickness between a Boolean function and their decomposing Boolean functions is given

and the upper bound on the algebraic thickness of Boolean functions with

variables is 2* *(

-1) by the recurrence method and the reduction to absurdity.The upper bound answers the open problem:"whether there exists a Boolean function with

variables whose algebraic thickness is strictly greater than 2* *(

-1)".At the end of this paper

according to this fact an upper bound on algebraic thickness of elementary symmetric Boolean functions of

variables with algebraic degree

(2≤

≤(

-1)/2) is improved

and some properties on algebraic thickness of Boolean functions are derived.

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