关键词: 逻辑表达式化简, 粒计算, 数字电路, 相容矩阵

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