多值函数的最坏和最佳积和表达式的比较

Tsutomu Sasao, J. T. Butler
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引用次数: 13

摘要

由于大多数实际的逻辑设计算法产生无冗余积和(ISOP)表达式,因此对ISOP的理解至关重要。我们展示了一类函数,Morreale-Minato的ISOP生成算法产生最坏的ISOPs (WSOP), ISOPs具有最多的乘积项。我们证明了该类具有这样的性质:当变量数量无界时,WSOP中的产品数量与最小ISOP (MSOP)中的产品数量之比是任意大的。这种情况的后果是显著的;在设计产生ISOPs的算法时必须非常小心。我们还证明了2/sup n-1/是n个变量上切换函数的任意ISOP中乘积项数目的确定上界,回答了一个已经开放了30年的问题。我们展示了实验数据,并将我们的结果推广到多值变量函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparison of the worst and best sum-of-products expressions for multiple-valued functions
Because most practical logic design algorithms produce irredundant sum-of-products (ISOP) expressions, the understanding of ISOPs is crucial. We show a class of functions for which Morreale-Minato's ISOP generation algorithm produces worst ISOPs (WSOP), ISOPs with the most product terms. We show this class has the property that the ratio of the number of products in the WSOP to the number in the minimum ISOP (MSOP) is arbitrarily large when the number of variables is unbounded. The ramifications of this are significant; care must be exercised in designing algorithms that produce ISOPs. We also show that 2/sup n-1/ is a firm upper bound on the number of product terms in any ISOP for switching functions on n variables, answering a question that has been open for 30 years. We show experimental data and extend our results to functions of multiple-valued variables.
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