基于粒矩陣的多輸入多輸出真值表快速并行約簡算法
doi: 10.11999/JEIT141129
基金項目:
國家自然科學(xué)基金(61402319)和山西省回國留學(xué)人員科研資助項目(2013-031)資助課題
Granular Matrix Based Rapid Parallel Reduction Algorithm for MIMO Truth Table
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摘要: 真值表是表征邏輯輸入與輸出之間因果關(guān)系的重要工具，真值表約簡在數(shù)字邏輯電路的分析與設(shè)計中具有重要意義。該文將真值表看作邏輯信息系統(tǒng)，將真值表約簡轉(zhuǎn)化為邏輯信息系統(tǒng)的最簡規(guī)則獲取。采用粒計算分層?；乃枷?，在不同粒度下，利用粒矩陣的知識表示形式、粒矩陣中的啟發(fā)式知識以及粒矩陣運算，設(shè)計了多輸入多輸出真值表快速并行約簡算法。以發(fā)光二極管七段數(shù)字顯示器為例進行了算法說明，通過數(shù)學(xué)證明和算法復(fù)雜性分析證明了算法的正確性和有效性。Abstract: 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.
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