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VLSI Design
Volume 14 (2002), Issue 3, Pages 307-313

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

1School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Block S1, Singapore 639798, Singapore
2Temasek Polytechnic, School of Engineering/Electronics, 21 Tampines Avenue 1, Singapore 529757, Singapore

Received 1 May 2000; Revised 10 August 2000

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.