Iterative Synthesis Techniques for Multiple-Valued Logic Functions
Keywords:
MVL functional synthesis, Direct-Cover algorithms (DCA), Weighted DC (WDC), Ordered DC (ODC), Fuzzified DC (FDC), non-binary digital signal processing (DSP).Abstract
A major challenge facing Multiple-Valued Logic
(MVL) synthesis techniques is the enormous size of the
functional search space. Accordingly, deterministic synthesis
techniques of MVL functions are prohibitively expensive and
complex in terms of algorithmic running time. Therefore, a
number of heuristics for near optimal functional synthesis of
MVL have been reported in the literature. Among the
well-known heuristics is the Direct Cover algorithm (DCA). We
have introduced a number of improved versions of the DCA.
These include the Weighted Direct Cover (WDC), the Ordered
Direct Cover (ODC), and the Fuzzy Direct Cover (FDC). In this
paper, we review and compare the performance of those
heuristic iterative techniques using two set of benchmarks. The
first consists of 50000 randomly generated 2-varaible 4-valued
functions and the second consists of 50000 2-variable 5-valued
functions. The average number of product terms required to
synthesize a given MVL function is used as the criterion for
comparison. The results obtained show that the modified
iterative synthesis heuristics outperformed the DCA and that
among the modified techniques the FDC produces the best
results.
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