关于布尔函数的布尔导数、e导数和c导数相互关系的研究
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摘要
基于对布尔函数内部结构和相关性质的进一步揭示,及其应用领域的拓展,深入研究了布尔函数的布尔导数、e导数和c导数的相互关系,讨论了布尔函数的布尔偏导数、e偏导数和c偏导数之间的关系,得到了相关性质并给出了证明。以进一步完善布尔函数的布尔导数、e导数和c导数这3类特殊导数的运算理论。
According to the further revelation of the internal structure and related properties of Boolean functions and the development of their application fields, the relationship between Boolean derivatives, e derivatives, and c derivatives of Boolean functions is studied in depth, and the relevant properties are investigated and proved. Our results further promote the study on the theory of Boolean derivatives, e derivatives, and c derivatives of Boolean functions.
According to the further revelation of the internal structure and related properties of Boolean functions and the development of their application fields, the relationship between Boolean derivatives, e derivatives, and c derivatives of Boolean functions is studied in depth, and the relevant properties are investigated and proved. Our results further promote the study on the theory of Boolean derivatives, e derivatives, and c derivatives of Boolean functions.
引文
[1]陈偕雄,沈继忠.近代数字理论[M].杭州:浙江大学出版社, 2001.CHEN X X, SHENG J Z.Modern Digital Theory[M]. Hangzhou:Zhejiang University Press, 2001.
[2] LI W W, WANG Z, HUANG J L. The e-derivative of Boolean functions and its application in the fault detection and cryptographic system[J].Kybernetes,2011, 40(5/6):905-911.
[3]何亮,王卓,李卫卫.减少平衡H-布尔函数相关度的算法和相关问题研究[J].通信学报, 2010,31(2):93-99.HE L, WANG Z, LI W W. Algorithm of reducing the balanced H-Boolean function correlation measure and research on correlative issue[J].Journal on Communications, 2010, 31(2):93-99.
[4]厉晓华,杭国强.简化分解图在计算布尔e导数中的应用[J].浙江大学学报(理学版), 2013, 40(6):646-649.LI X H, HANG G Q. The application of simplify decomposition maps in calculating Boolean e-derivative[J].Journal of Zhejiang University(Science Edition),2013, 40(6):646-649.
[5] WANG F. Research on properties of e-partial derivative of logic functions[J].Journal of Theoretical and Applied Information Technology,2013, 47(1):201-205.
[6]王芳,应时彦,肖林荣.布尔函数的c导数及其在组合电路故障检测中的应用[J].浙江大学学报(理学版), 2014,41(2):153-155.WANG F, YING S Y, XIAO L R. The c-derivative of Boolean functions and its application in fault detection of combinational circuits[J].Journal of Zhejiang University(Science Edition), 2014, 41(2):153-155.
[7]马汝星,陈偕雄.布尔特殊运算c-导数及其在Bent函数研究中的应用[J].浙江大学学报(理学版),2015,42(2):157-161.MA R X, CHEN X X. Boolean special operation cderivative and its application in studying Bent function[J].Journal of Zhejiang University(Science Edition), 2015, 42(2):157-161.
[8]王芳.计算布尔函数c-导数、c-偏导数的代数方法及其在检测特殊布尔函数中的应用[J].浙江大学学报(理学版), 2016,43(3):303-306.WANG F. Algebraic method for calculating cderivative, c-partial derivative and its application in detecting special Boolean function[J].Journal of Zhejiang University(Science Edition), 2016, 43(3):303-306.
[2] LI W W, WANG Z, HUANG J L. The e-derivative of Boolean functions and its application in the fault detection and cryptographic system[J].Kybernetes,2011, 40(5/6):905-911.
[3]何亮,王卓,李卫卫.减少平衡H-布尔函数相关度的算法和相关问题研究[J].通信学报, 2010,31(2):93-99.HE L, WANG Z, LI W W. Algorithm of reducing the balanced H-Boolean function correlation measure and research on correlative issue[J].Journal on Communications, 2010, 31(2):93-99.
[4]厉晓华,杭国强.简化分解图在计算布尔e导数中的应用[J].浙江大学学报(理学版), 2013, 40(6):646-649.LI X H, HANG G Q. The application of simplify decomposition maps in calculating Boolean e-derivative[J].Journal of Zhejiang University(Science Edition),2013, 40(6):646-649.
[5] WANG F. Research on properties of e-partial derivative of logic functions[J].Journal of Theoretical and Applied Information Technology,2013, 47(1):201-205.
[6]王芳,应时彦,肖林荣.布尔函数的c导数及其在组合电路故障检测中的应用[J].浙江大学学报(理学版), 2014,41(2):153-155.WANG F, YING S Y, XIAO L R. The c-derivative of Boolean functions and its application in fault detection of combinational circuits[J].Journal of Zhejiang University(Science Edition), 2014, 41(2):153-155.
[7]马汝星,陈偕雄.布尔特殊运算c-导数及其在Bent函数研究中的应用[J].浙江大学学报(理学版),2015,42(2):157-161.MA R X, CHEN X X. Boolean special operation cderivative and its application in studying Bent function[J].Journal of Zhejiang University(Science Edition), 2015, 42(2):157-161.
[8]王芳.计算布尔函数c-导数、c-偏导数的代数方法及其在检测特殊布尔函数中的应用[J].浙江大学学报(理学版), 2016,43(3):303-306.WANG F. Algebraic method for calculating cderivative, c-partial derivative and its application in detecting special Boolean function[J].Journal of Zhejiang University(Science Edition), 2016, 43(3):303-306.