Efficient Calculation of the Reed-Muller Form by Means of the Walsh Transform

• Autorzy: Porwik P.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Reed-Muller coefficients; Walsh coefficients; coefficient distribution; Boolean function; synthesis of Boolean functions

PL

współczynnik Walsha; rozkład współczynników; funkcja boolowska

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 4
• Strony: 571--579
• Opis fizyczny: Bibliogr. 17 poz., tab.

Twórcy

autor

Porwik P.

• Institute of Computer Science, Silesian University ul. Bedzinska 39, 41-200 Sosnowiec, Poland,

Bibliografia

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