基于或-符合运算Reed-Muller展开系数的对称变量检测算法
The algorithm for identifying symmetric variable of logical function based on OR-Coincidence Reed-Muller coefficients
厉晓华 1杭国强 2陈偕雄3
作者信息
- 1. 浙江大学信息中心,浙江杭州310028
- 2. 浙江大学城市学院信息与电气工程学院,浙江杭州310015
- 3. 浙江大学信息与电子工程学系,浙江杭州310028
- 折叠
摘要
针对或-符合代数系统中缺失对称变量检测的有效方法等问题,提出了该代数系统基于或-符合运算Reed-Muller展开系数的十二类变量对称性检测算法.该算法通过分析逻辑函数关于变量χi、χj展开的子函数系数矩阵和或-符合运算Reed-Muller展开系数按变量Xi、χi组合分解系数矩阵的对应关系,揭示了任意两变量间各类对称性所满足的分解系数矩阵的约束条件,提出了各类逻辑变量的对称性检测步骤.应用结果表明,与传统方法相比,免去了从逻辑函数的CRM展开式变换为最小项展开式或RM展开式的变换域转换过程,也解决了在该域中图形方法检测的完备性问题,具有简单、直观、完备及适合计算机编程等优点.
Abstract
A new symmetry detection algorithm which is used for identifying twelve type symmetric variables based on OR-Coincidence Reed-Muller coefficients is proposed to resolve the lack of the effective methods for identifying symmetric variables of OR-Coincidence algebra system.The algorithm analyzes the correlation between the subfunction coefficients matrix which is expanded with regard to xi and xj and the ordered combination decomposed coefficients matrix based on OR-Coincidence Reed-Muller coefficients expansion of the variable xi and xj.It reveals the ordered combination decomposed coefficients matrix constraint conditions which is satisfied in every type of symmetry with arbitrary two variables,identifies the symmetric variables and then.The application results show that compared with the traditional method,the algorithm is simpleness,intuition,completeness and suited to programming on computers avoiding the transformation process from the CRM in OR-Coincidence algebra system to the minterms in AND/OR/NOT algebra system,or to the RM in AND-Exclusive OR algebra system,solving the completeness to identify the symmetric variables with the graphic method in OR-Coincidence algebra system also.
关键词
或-符合代数系统/Reed-Muller展开/对称检测/逻辑函数Key words
OR-Coincidence algebra system/Reed-Muller expansion/detection of symmetry/logical function引用本文复制引用
出版年
2013
NETL
NSTL
维普
万方数据