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

• Autorzy: Piotr Porwik
• 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

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

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: 12
• Numer: 4
• Strony: 571-579

Daty

wydano

2002

otrzymano

2001-12-06

poprawiono

2002-05-16

Twórcy

autor

Piotr Porwik

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

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