Abstract: Logical expression reduction is the important content for the analysis and design of digital circuits. The granular computing model based on tolerance relation is an effective tool for processing incomplete information. This paper defines the incomplete truth table and converts the logical expression reduction to the rules extraction of the incomplete truth table. Then from the view of multi-granularity point, calculating the tolerance matrix and logical relation matrix from coarse to fine granularity space, according to the information relations in the matrix, this paper proposes a new algorithm of logical expression reduction. Finally, this paper verifies the effectiveness of new algorithm by theorem proof, case analysis and the correctness analysis of the algorithm.

Key words: logical expression reduction, granular computing, digital circuits, tolerance matrix

摘要： 逻辑表达式化简是数字电路分析与设计的重要内容，基于相容关系的粒计算模型是处理不完备信息的有效工具。定义了不完备真值表，并将传统的逻辑表达式化简转化为不完备真值表的规则提取，从多粒度角度出发，在由粗到细的粒度空间下，计算每个属性集合的相容矩阵和逻辑关系矩阵，根据矩阵所包含信息之间的关系提出一种新的逻辑表达式化简算法。最后通过定理证明、实例分析和算法正确性分析验证了该算法的有效性。

关键词: 逻辑表达式化简, 粒计算, 数字电路, 相容矩阵