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 -
References
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