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

Porwik, Piotr

International Journal of Applied Mathematics and Computer Science, Tome 12 (2002), p. 571-579 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2002-01-01

Zbl 1026.94556

EUDML-ID : urn:eudml:doc:207613

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