On Optimization of Multiple-Valued Logic Functions

M. Abd-El-Barr (Kuwait)

Keywords

Multivalued logic (MVL), Direct Cover algorithm, MVL synthesis, weighted direct cover (WDC), ordered direct cover (ODC), Fuzzybased DC (FDC) heuristic.

Abstract

A number of heuristic algorithms for optimization of none binary, multiple-valued logic (MVL) functions have been reported in the literature. The Direct Cover (DC) algorithm is one such heuristics. In this paper, we present and compare the performance of three possible improvements to the DC heuristics. The three improvements are: Weighted Direct Cover (WDC), Ordered Direct Cover (ODC), and Fuzzy-based Direct Cover (FDC). The WDC uses a weighted-sum scheme for combining a number of criteria for minterm and implicant selection. The ODC applies a set of ordered criteria for minterm and implicant selection. The FDC is a fuzzy based algorithm for minterm and implicant selection. A benchmark consisting of 50000 randomly generated 2 variable 4-valued functions and 50000 2-variable 5 valued randomly generated functions has been used to assess the performance of the three heuristics. The results obtained show that the three heuristics outperform existing approaches in terms of the average number of product terms required to realize a given MVL function. Among the three heuristics, the FDC outperforms the two other heuristics.

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