An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system  

作　　者：Xiao-hua LI Ji-zhong SHEN 

机构地区：[1]Campus Information Center, Zhejiang University [2]Department of Information Science & Electronic Engineering, Zhejiang University

出　　处：《Journal of Zhejiang University-Science C(Computers and Electronics)》2014年第12期1174-1182,共9页浙江大学学报C辑（计算机与电子（英文版）

基　　金：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);the National Key Technology Research and Development Program of the Ministry of Science and Technology of China(Nos.2013BAH27F01 and 2013BAH27F02)

摘　　要：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 dj-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.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 dj-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：Symmetric variable dj-map Canonical OR-coincidence algebra system Boolean function 

分 类 号：O153.2[理学—数学]