或-符合代数系统中的对称变量检测算法

Xiao-hua LI; Ji-zhong SHEN

doi:10.1631/jzus.C1400093

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或-符合代数系统中的对称变量检测算法

电子工程 | Updated：2022-05-19

- 或-符合代数系统中的对称变量检测算法
- An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system
- 信息与电子工程前沿（英文） 2014年15卷第12期页码：1174-1182
- Affiliations：
  
  1.Campus Information Center, Zhejiang University, Hangzhou 310027, China
  2.Department of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  Ji-zhong SHEN, E-mail: jzshen@zju.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61471314 and 61271124), the National Social Science Foundation of China (No. 12AZD121), the Zhejiang Provincial Natural Science Foundation of China (No. LY13F010001), and the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Nos. 2013BAH27F01 and 2013BAH27F02)
- DOI：10.1631/jzus.C1400093
  中图分类号： TN431
- 收稿：2014-03-16，
  
  修回：2014-11-13，
  
  纸质出版：2014-12
- Accepted：
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或-符合代数系统中的对称变量检测算法[J]. 信息与电子工程前沿（英文）, 2014,15(12):1174-1182.

Xiao-hua LI, Ji-zhong SHEN. An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(12): 1174-1182.
或-符合代数系统中的对称变量检测算法[J]. 信息与电子工程前沿（英文）, 2014,15(12):1174-1182. DOI： 10.1631/jzus.C1400093.

Xiao-hua LI, Ji-zhong SHEN. An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(12): 1174-1182. DOI： 10.1631/jzus.C1400093.

摘要

研究目的

逻辑变量对称性在逻辑综合、OBDD化简、故障检测、电路分析及密码学函数构造等领域具有广泛的应用。为简化或-符合代数系统中12类对称变量的检测过程，提出一种新的检测算法。

创新要点

提出新的基于或-符合展开系数对称性检测算法。该算法可实现12类对称变量的完备性检测，同样适用于与-或-非代数系统和与-异或代数系统。

研究方法

首先，分析基于或-符合展开布尔函数的子函数系数矩阵和有序子系数矩阵之间的关系（公式5），提出基于有序子系数矩阵的12类对称形式的约束条件（表3）。根据该约束条件，通过判别

图的有序特征格值，提出逻辑变量12类对称形式的快速检测算法（图4）。与其他方法相比（表7），该方法有效避免或-符合展开系数和与-异或展开系数及与-或-非展开系数之间的转换，同时解决了

图方法中的完备性问题。算法用C语言实现并用MCNC91 benchmarks（表6）进行测试。

重要结论

提出或-符合代数系统中12类对称变量的检测算法。与其他方法相比，该算法在适用的检测变量数、检测类型、检测过程的复杂度方面最优。

Abstract

To simplify the process for identifying 12 types of symmetric variables in the canonical OR-coincidence (COC) algebra system

we propose a new symmetry detection algorithm based on OR-NXOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on OR-NXOR expansion around two arbitrary logical variables

the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints

the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the transformation process from OR-NXOR expansion to AND-OR-NOT expansion

or to AND-XOR expansion

and solves the problem of completeness in the

-map method. The application results show that

compared with traditional methods

the new algorithm is an optimal detection method in terms of applicability of the number of logical variables

detection type

and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.

关键词

Keywords

references

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