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| An algorithm for identifying symmetric variables of Boolean function with don't-care-terms |
| ZHANG Yongbo1, LI Xiaohua2 |
1. Campus Information Center, Tourism College of Zhejiang, Hangzhou 311231, China;
2. Campus Information Center of Zhejiang University, Hangzhou 310027, China |
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Abstract To simplify the process for identifying 12 types of symmetric variables in Boolean function, we propose a new symmetry detection algorithm based on minterm expansion of Boolean function with don't-care-terms. By analyzing the constraint conditions of the order eigenvalues matrixes for 12 types of symmetric variables, the algorithm for identifying symmetric variables of Boolean function with don't-care-terms is proposed. The results show that, the new algorithm method is superior than the traditional methods in the applicability of the number of logical variables of Boolean function including don't-care-terms, detection types, and complexity of the identification process.
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Received: 19 May 2016
Published: 08 July 2017
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含无关项布尔函数的对称变量检测算法
为简化布尔函数中12类对称变量的检测过程，提出了含无关项布尔函数基于最小项展开系数的对称变量检测算法.该算法通过判别布尔函数有序特征值矩阵的约束条件以实现对称变量的快速检测.应用结果表明，与现有方法相比，算法在适用的布尔函数变量数、检测类型、检测含无关项布尔函数和检测过程的复杂度方面表现较优.
关键词：
对称变量,
有序特征值矩阵,
布尔函数,
真值表,
任意项
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[1] RICE J, MUZIO J. Antisymmetries in the realization of Boolean functions[C]//IEEE International Symposium on Circuits and Systems. Phoenix, AZ:IEEE,2002:69-72.
[2] BLAIS E, WEINSTEIN A, YOSHIDA Y. Partially symmetric functions are efficiently isomorphism-testable[C]//IEEE 53rd Anual Smposium on Fundation of Computer Science.Washington:IEEE,2012:551-560.
[3] PENG J, WU Q, KAN H. On symmetric Boolean functions with high algebraic immunity on even number of variables[J]. IEEE Transations on Information Theory,2011,57(10):7205-7220.
[4] WANG H, PENG J. On 2k-variable symmetric Boolean functions with maximum algebraic immunity[J]. IEEE Transations on Information Theory,2012,58(8):5612-5624.
[5] MUKHOPADHYAY A. Detection of total or partial symmetry of a switching function with the use of decomposition charts[J]. IEEE Transations on Electronic Computers,1963,EC(12):553-557.
[6] HURST S L. Detection of symmetries in combinatorial functions by spectral means[J]. Electronic Circuits and System,1977,1(5):173-180.
[7] KANNURAO S, FALKOWSKI B. Identification of complement single variable symmetry in Boolean functions through Walsh transform[C]//IEEE International Symposium on Circuits and Systems. Phoenix, AE:IEEE,2002:745-748.
[8] 练益群,厉晓华,陈偕雄.基于表格法的部分对称函数检测[J].科技通报,2005,21(2):214-217. LIAN Y Q, LI X H, CHEN X X. Detection of partial symmetric functions based on tabular method[J]. Bulletin of Science and Technology,2005,21(2):214-217.
[9] 厉晓华,杭国强,陈偕雄.逻辑函数对称变量检测算法[J].电路与系统学报,2013,18(2):31-35. LI X H, HANG G Q, CHEN X X. The algorithm for identifying symmetric variable of logical function[J]. Journal of Circuits and Systems,2013,18(2):31-35. |
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