Goal-oriented decomposition of switching functions

Diaz-Olavarrieta, L.; Illanko, K.; Zaky, S.G.

doi:10.1109/43.277610

Cited by 3 publications

(2 citation statements)

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“…By using a filtering procedure, the algorithm can eliminate the lack of existence of the bi-decomposition without the necessity of calculating and operating on the whole Walsh spectrum. This work extended the Walsh spectral theory of standard types of decomposition known earlier [6,8,9,15] to the bi-decomposition. Consideration of various types of bi-decomposition is important not only from theoretical but also from practical point of view as there are many recent programmable logic devices that can be efficiently used for direct implementation of types of bi-decompositions discussed in this article.…”

Section: Discussionmentioning

confidence: 83%

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Identification of Disjoint Bi‐decompositions in Boolean Functions through Walsh Spectrum

Falkowski

Kannurao

2000

VLSI Design

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A new algorithm for the identification of disjoint bi-decomposition in Boolean functions from its Walsh spectrum is proposed. The type of bi-decomposition and its existence is derived from the knowledge of a subset of Walsh spectrum for a Boolean function. All three types of bi-decomposition are considered including OR, AND and EXOR type. A filtering procedure that uses just few Walsh spectral coefficients (SC) is applied to quickly eliminate the functions that are not bi-decomposable and hence the algorithm is very efficient. The type of bi-decomposition and affirmation/negation of variables in its logic sub-functions are directly identified by manipulation on the reduced cubical representation of Boolean functions and their corresponding Walsh spectra. The presented algorithm has been implemented in C and tested on the standard benchmark functions. The number of Boolean functions having various disjoint bi-decompositions has also been enumerated.

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Section: Discussionmentioning

confidence: 83%

“…2,3,4,5,6,7,8,9,10,11,13,14,15).The DC coefficient is 2 12 and further calculating the first order coefficients, s 1 ¼ s 2 ¼ 4; s 3 ¼ s 4 ¼ 0; The second order coefficients are: s 12 ¼ s 34 ¼ 4 and all the other SCs are zero. Similarly, the other coefficients that are non zero of third and fourth order are s 134 , s 234 and s 1234 .…”

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confidence: 99%