Granular Matrix Based Rapid Parallel Reduction Algorithm for MIMO Truth Table

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.