基于粒矩阵的多输入多输出真值表快速并行约简算法  

Granular Matrix Based Rapid Parallel Reduction Algorithm for MIMO Truth Table

作　　者：陈泽华[1] 马贺[1] 

机构地区：[1]太原理工大学信息工程学院,太原030024

出　　处：《电子与信息学报》2015年第5期1260-1265,共6页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61402319);山西省回国留学人员科研资助项目(2013-031)资助课题

摘　　要：真值表是表征逻辑输入与输出之间因果关系的重要工具,真值表约简在数字逻辑电路的分析与设计中具有重要意义。该文将真值表看作逻辑信息系统,将真值表约简转化为逻辑信息系统的最简规则获取。采用粒计算分层粒化的思想,在不同粒度下,利用粒矩阵的知识表示形式、粒矩阵中的启发式知识以及粒矩阵运算,设计了多输入多输出真值表快速并行约简算法。以发光二极管七段数字显示器为例进行了算法说明,通过数学证明和算法复杂性分析证明了算法的正确性和有效性。Truth table is an important tool to represent the logic causal relationships between inputs and outputs. The reduction of the truth table is of great significance in analysis and design of digital logic circuit. In this paper, the MIMO truth table is considered as a Logical Information System （LIS）, and the traditional truth table reduction issue is converted into the minimal rule discovery of LIS. Granular Computing （GrC） method is then introduced. Firstly, the logical information system is hierarchically granulated. Secondly, the Granular Matrix （GrM） is defined and operated to represent the knowledge in different granularity, together with heuristic information hidden in the matrix, the rapid parallel reduction algorithm for the MIMO truth table is proposed. Light-Emitting Diode （LED） digital display is applied to illustrate the computing process. The mathematical proof and the complexity analysis proves the efficiency and validity of the proposed algorithm.

关 键 词：数字逻辑电路 真值表 粒度 粒矩阵 并行约简 粒计算 

分 类 号：TN79[电子电信—电路与系统] TP181[自动化与计算机技术—控制理论与控制工程]