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Determination of Sparse Representations of Multiple-Valued Logic Functions by Using Covering Codes

机译:使用覆盖码确定多值逻辑函数的稀疏表示

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The paper points out the relationships and similarities between some problems in the theory of covering codes and the determination of sparse functional expressions for logic functions. Based on these connections we propose a method to derive functional expressions that have an a priory specified number of product terms. The method can be applied to either binary or multiple-valued functions with different sets for values of variables or function values by selecting appropriately the underlying covering code. The number of product terms in the related functional expression is determined by the covering radius of the code. We present algorithms to determine the coefficients in these expressions, discuss their complexities, and provide a direct construction to extend the application of this approach to binary and multiple-valued functions for a large number of variables.
机译:指出了覆盖码理论中某些问题与逻辑函数稀疏函数表达式的确定之间的联系和相似性。基于这些联系,我们提出了一种导出具有事先指定数量的乘积项的函数表达式的方法。通过适当地选择基础覆盖代码,该方法可以应用于具有不同的变量或函数值集合的二进制或多值函数。相关功能表达式中乘积项的数量由代码的覆盖半径决定。我们提出了确定这些表达式中系数的算法,讨论了它们的复杂性,并提供了一种直接的结构,可以将该方法的应用扩展到具有大量变量的二进制和多值函数。

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