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

International Journal of Applied Mathematics and Computer Science (2002)

- Volume: 12, Issue: 4, page 571-579
- ISSN: 1641-876X

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topPorwik, Piotr. "Efficient calculation of the Reed-Muller form by means of the Walsh transform." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 571-579. <http://eudml.org/doc/207613>.

@article{Porwik2002,

abstract = {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.},

author = {Porwik, Piotr},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Boolean function; coefficient distribution; Walsh coefficients; synthesis of Boolean functions; Reed-Muller coefficients; logic synthesis; Walsh transform; Boolean functions},

language = {eng},

number = {4},

pages = {571-579},

title = {Efficient calculation of the Reed-Muller form by means of the Walsh transform},

url = {http://eudml.org/doc/207613},

volume = {12},

year = {2002},

}

TY - JOUR

AU - Porwik, Piotr

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2002

VL - 12

IS - 4

SP - 571

EP - 579

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/207613

ER -

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