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Dedicated spectral method of Boolean function decomposition

100%
Porwik P., Stankovic R. S.
International Journal of Applied Mathematics and Computer Science
|
2006
|
tom 16
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nr 2
271-278
EN
Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using the Walsh transform and autocorrelation characteristics.
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Function classes and relational constraints stable under compositions with clones

88%
Couceiro M., Foldes S.
Discussiones Mathematicae - General Algebra and Applications
|
2009
|
tom 29
|
nr 2
109-121
EN
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.
3
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Efficient calculation of the Reed-Muller form by means of the Walsh transform

88%
Porwik P.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 4
571-579
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.
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