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逻辑函数对称变量检测算法 被引量：3

The algorithm for identifying symmetric variable of logical function
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摘要 针对图形方法、谱系数方法和传统表格方法在检测逻辑函数变量对称性过程中步骤繁琐、适用对象局限及完备性不足等问题,提出了与-或-非代数系统中基于1值最小项的E(xi|xj)、N(xi|xj)、S(xi|xj)、S(xi|xj)、S(xj|xi)、S(xj|xi)六类对称性检测算法。该算法从逻辑函数1值最小项中提取变量xi、xj为各类特征编码时的余子变量编码,通过比较余子变量编码是否满足两两相等来检测变量xi、xj的各类对称性。该算法通过表格模拟了检测过程,应用结果表明,与图形方法、谱系数方法和传统的表格法相比,在考虑的项数、检测的完备性和算法实现方面是最优的。该算法已用C语言实现,实验结果验证了快速有效。 A new symmetry detection algorithm which is used for identifying symmetric variables over E（xi｜xj）、N（xi｜xj）、S（xi｜xj）、S（xi｜xj）、S（xj｜xi）、S（xj｜xi） of AND/OR/NOT type function based on 1-value minterms is proposed to resolve the complicated process,the limited application and lack of completeness for identifying symmetric variables of logical function by the traditional tabular method,the graphic method and the coefficients method.The algorithm is applied to find out the complement minor variable coding when the variables xi and xj accord with every type of feature coding of logical function based on 1-value minterms,the symmetric variables are able to identify by judging whether the complement minor variable coding is equal to another or not.The application results show that compared with the graphic method,the traditional tabular method and the coefficients,is the most excellent in the terms considered,the completeness of detection and the realized algorithm.The proposed algorithm has been implemented in C language,the experimental results show that the proposed algorithm is quick and efficient.
作者 厉晓华 杭国强 陈偕雄
机构地区 浙江大学信息中心 浙江大学城市学院信息与电气工程学院 浙江大学信息与电子工程学系
出处 《电路与系统学报》 北大核心 2013年第2期31-35,共5页 Journal of Circuits and Systems
基金 国家自然科学基金资助项目(60971061)
关键词 逻辑函数 与-或-非代数系统 对称检测 logical function AND/OR/NOT algebra system detection of symmetry
分类号 TN431 [电子电信—微电子学与固体电子学] TN402 [电子电信—微电子学与固体电子学]
  • 相关文献

参考文献12

  • 1Heinrich-Litan L, Molitor P. Least Upper bounds for the size of OBDDs using symmetry properties [J]. IEEE Transations On Computers, 2000, 49(4): 360-368.
  • 2Rahaman H, Das D, Bhattacharya B. Mapping symmetric functions to hierarchical modules for delay fault testability [A]. Proceeding of the 12th Asian Test Symposium [C]. Xian, China, 2003-12. 284-289.
  • 3Peng Jie, Wu Quan-shui, Kan Hai-bin. On symmetric boolean functions with high algebraic immunity on even number of variables [J]. IEEETransations on Information Theory, 2011, 57(10): 7205-7220.
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二级参考文献8

  • 1程捷,陈偕雄.归一化Haar变换谱技术在逻辑函数对称性检测中的应用[J].浙江大学学报（理学版）,2001,28(6):635-639. 被引量：8
  • 2MUKHOPADHYAY 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.
  • 3DAS S R,SHENG C L. On detecting total or partial symmetry of switching functions [J]. EEE Transactions on Computers, 1971, C-20: 352-355.
  • 4BUTLE J,SASAO T. On the properties of multiplevalued functions that are symmetric in both variable values and labels[A]. IEEE Proc Iht Symp on MVL[C]. Piscataway NJ: IEEE Service Center, 1998.83-88.
  • 5HURST S L. Detection of symmetries in combinatorial functions by spectral means[J]. IEE J. Electronic Circuits and Systems, 1977, 1:173-180.
  • 6MUZIO J C, MILLER D M. Multi-variable symmetries and their detection [J]. IEE Proc. pt.E, 1983, 130: 141-148.
  • 7BUTLE J, SASAO T. On the properties of multiple-valued functions that are symmetric in both variable values and labels [A]. IEEE Proc. ISMVL, [C] IEEE Press,1998, 83-88.
  • 8刘观生,郑茂生,陈偕雄.部分变量取反的RM型对称函数检测的新方法[J].浙江大学学报（理学版）,2002,29(2):154-159. 被引量：7

共引文献11

同被引文献11

  • 1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. 被引量：8
  • 2HEINRICH-LITAN L, MOLITOR P. Least upper bounds for the size of OBDDs using symmetry proper- ties[J]. IEEE Transations On Computers, 2000,49 (4) : 360-368.
  • 3RAHAMAN H, DAS D, BHATTACHARYA B. Mapping symmetric functions to hierarchical modules for path-delay fault testability[C]//Proceeding of the 12th Asian Test Symposium. Xian: IEEE, 2003: 284- 289.
  • 4PENG Jie, WU Quanshui, KAN Haibin. On symmet ric boolean functions with high algebraic immunity on even number of variables[J]. IEEE Transations on In- formation Theory, 2011,57 (10) : 7205-7220.
  • 5SHPILKA A, TAL A. On the minimal fourier degree of symmetric boolean functions[C]//The 26th Annual IEEE Conference on Computational Complexity. San Jo- se:IEEE,2011:200-209.
  • 6CHOWDURY M, HASAN G, TALUKDER K. A composition technique of multiple switching functions based on BDD[C]//Computer and Information Tech- nology 13th International Conference. Dhaka: IEEE, 2010:337-342.
  • 7ACHARYA J, JAFARPOUR A, ORLITSKY A. Ex- pected query complexity of symmetric boolean func- tions [ C]//Communication, Control and Computing 49th Annual Allerton Conference. Urbana: IEEE, 2011:26-29.
  • 8MUKHOPADHYAY A. Detection of total or partial symmetry of a switching function with the use of de- composition charts[J]. IEEE Transations on Electronic Computers, 1963,12(5) :553-557.
  • 9HURST S L. Detection of symmetries in combinatorial functions by spectral means[J]. Electronic Circuits and Systems, 1977,1 (5) : 173-180.
  • 10BOGDAN J, S KANNURAO. Skew symmetry de-tection using the walsh spectral coefficients [C]// IEEE International Symposium on Circuits and Sys- tems. Geneva: IEEE,2000 : 321-324.

引证文献3

二级引证文献2

电路与系统学报
2013年 第2期

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