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Efficient calculation of the Reed-Muller form by means of the Walsh transform

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Porwik P.

International Journal of Applied Mathematics and Computer Science

2002

tom 12

nr 4

571-579

The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to build the Reed-Muller form based on the analysis of Walsh-Hadamard coefficients. The presented method has much less complexity than the procedures which have been applied until now. Both the transforms and the presented Walsh-Hadamard spectral characterization of the Reed-Muller expansion are compared. An analysis of the properties of the spectra obtained from these transforms is made.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Porwik P.

1 2002

Wyniki wyszukiwania

Efficient calculation of the Reed-Muller form by means of the Walsh transform