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A Multiple-Valued Reed-Muller Transform for Incompletely Specified Functions
August 1995 (vol. 44 no. 8)
pp. 1012-1020

Abstract—This paper considers the Reed-Muller transform for incompletely specified multiple-valued logic functions, which is obtained as the finite field polynomial representation. A new algorithm for dealing with single-variable functions is presented. It is applicable to finite fields of small sizes (two to four), which is of interest because only these fields are readily implementable with today’s MVL technology. It is shown how such or any similar single-variable algorithm can be used to obtain a fast n-variable Reed-Muller transform. Based on this transform, a heuristic scheme is derived for dealing with incompletely specified functions. It has better computational properties than other methods and achieves the best results when applied to functions with a large number of unspecified points.

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Index Terms:
Multiple-valued logic, Reed-Muller transform, incompletely specified functions, synthesis of logic functions, finite fields.
Citation:
Zvonko G. Vranesic, Zeljko Zilic, "A Multiple-Valued Reed-Muller Transform for Incompletely Specified Functions," IEEE Transactions on Computers, vol. 44, no. 8, pp. 1012-1020, Aug. 1995, doi:10.1109/12.403717
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