检测含无关项特殊布尔函数的表格算法
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摘要
从冗余函数、线性函数、自反函数、自双反函数四类特殊布尔函数的定义出发,讨论了检测含无关项特殊布尔函数的表格算法。该算法应用表格列出布尔函数1值最小项及无关项的二进制编码,取反1值最小项及无关项二进制编码中的相应位产生新项。通过比较新项与原最小项之间的异同实现特殊布尔函数的检测。应用实例表明,表格算法具有快速便捷、适用于多变量函数及易于计算机编程操作等优点。
Starting from the definition of linear function,redundant function,self-dual function,and selfnegative function,the tabular algorithm is discussed for identifying the special Boolean function with don't-care-terms. The binary code of the 1-value minterms and the don't-care-terms are listed,the new terms are produced based on negating operation of the binary code of the 1-value minterm and the don't-careterms. The special Boolean function is identified by comparing the differences between the minterms and the new terms. The application results show that the tabular algorithm is simple and convenient for operation,suitable for solving multi-variable Boolean function and programming on computers.
Starting from the definition of linear function,redundant function,self-dual function,and selfnegative function,the tabular algorithm is discussed for identifying the special Boolean function with don't-care-terms. The binary code of the 1-value minterms and the don't-care-terms are listed,the new terms are produced based on negating operation of the binary code of the 1-value minterm and the don't-careterms. The special Boolean function is identified by comparing the differences between the minterms and the new terms. The application results show that the tabular algorithm is simple and convenient for operation,suitable for solving multi-variable Boolean function and programming on computers.
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.
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[3]王卓,张志杰,丁要军.一个特殊的线性函数与H布尔函数的关系[J].西北民族大学学报:自然科学版,2007,28(1):3-10.
[4]陆慧娟,陈偕雄.线性函数的性质及其应用[J].浙江大学学报:理学版,2006,33(2):165-168.
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[6]唐金花,陈偕雄.检测逻辑函数中线性变量的代数方法[J].浙江大学学报:理学版,2006,43(5):411-415.
[7]任兵,陈偕雄.基于图形方法的冗余函数与自反函数检测[J].浙江大学学报:理学版,2007,34(3):318-320.
[8]赵美玲,陈偕雄.基于分解图检测特殊函数的新方法[J].浙江大学学报:理学版,2008,35(4):412-415.
[9]练益群,刘观生,陈偕雄.检测线性函数与线性变量的表格方法[J].浙江大学学报:理学版,2006,33(3):295-299.
[10]郦可,陈偕雄.基于表格方法的冗余函数、自反函数及自双反函数的检测[J].浙江大学学报:理学版,2007,34(5):520-523.
[11]王勇超,俞天秀.含任意项特殊逻辑函数的图形化检测[J].浙江大学学报:理学版,2007,36(5):539-541.
[12]厉晓华.基于分解图检测含任意项特殊逻辑函数的方法[J].浙江大学学报:理学版,2009,36(5):545-548.
[13]Hurst S.L.Detection of symmetries in combinatorial functions by spectral means[J].Electronic Circuits and System,1977,1(5):173-180.
[2]曹浩,魏仕民.具有高代数免疫布尔函数的构造[J].华东理工大学学报:自然科学版,2007,33:74-76.
[3]王卓,张志杰,丁要军.一个特殊的线性函数与H布尔函数的关系[J].西北民族大学学报:自然科学版,2007,28(1):3-10.
[4]陆慧娟,陈偕雄.线性函数的性质及其应用[J].浙江大学学报:理学版,2006,33(2):165-168.
[5]练益群,陈偕雄.关于冗余函数和自反函数性质之研究[J].浙江大学学报:理学版,2006,33(5):532-534.
[6]唐金花,陈偕雄.检测逻辑函数中线性变量的代数方法[J].浙江大学学报:理学版,2006,43(5):411-415.
[7]任兵,陈偕雄.基于图形方法的冗余函数与自反函数检测[J].浙江大学学报:理学版,2007,34(3):318-320.
[8]赵美玲,陈偕雄.基于分解图检测特殊函数的新方法[J].浙江大学学报:理学版,2008,35(4):412-415.
[9]练益群,刘观生,陈偕雄.检测线性函数与线性变量的表格方法[J].浙江大学学报:理学版,2006,33(3):295-299.
[10]郦可,陈偕雄.基于表格方法的冗余函数、自反函数及自双反函数的检测[J].浙江大学学报:理学版,2007,34(5):520-523.
[11]王勇超,俞天秀.含任意项特殊逻辑函数的图形化检测[J].浙江大学学报:理学版,2007,36(5):539-541.
[12]厉晓华.基于分解图检测含任意项特殊逻辑函数的方法[J].浙江大学学报:理学版,2009,36(5):545-548.
[13]Hurst S.L.Detection of symmetries in combinatorial functions by spectral means[J].Electronic Circuits and System,1977,1(5):173-180.