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.
@article{bwmeta1.element.bwnjournal-article-amcv16i2p271bwm, author = {Porwik, Piotr and Stankovic, Radomir}, title = {Dedicated spectral method of Boolean function decomposition}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {16}, year = {2006}, pages = {271-278}, zbl = {1134.94408}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv16i2p271bwm} }
Porwik, Piotr; Stankovic, Radomir. Dedicated spectral method of Boolean function decomposition. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) pp. 271-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv16i2p271bwm/
[000] Ahmed N. and Rao K.R. (1975): Orthogonal Transforms for Digital Signal Processing. - Berlin: Springer. | Zbl 0335.94001
[001] Ashenhurst R. (1957): The decomposition of switching functions. - Proc. Int. Symp.Theory of Switching, Annual Computation Laboratory, Harvard University, Vol. 29, pp. 74-116.
[002] Dubrova E. (1999): AOXMIN-MV: A heuristic algorithm for AND-OR-XOR minimization. - Proc. Int. Workshop Applications of Reed-Muller Expansion in Circuit Design, RM'99, Victoria, Canada, pp. 37-53.
[003] Curtis H.A. (1962): A New Approach to the Design of Switching Circuits. - Princeton: Van Nostrand.
[004] Bertacco V. and Damiani M. (1997): The disjunctive decompositionof logic functions. - Proc. Computer-Aided Design, ICCAD'97, San Jose, CA, pp. 78-82.
[005] Falkowski B.J. and Kannurao S. (2001): Analysis of disjunctive decomposition of balanced Boolean functions through Walsh spectrum. - IEE Proc. Comput. Digit. Techn., Vol. 148, No. 2, pp. 71-78.
[006] Falkowski B.J. and Porwik P. (1999): Evaluation of nonlinearity in Boolean functions by extended Walsh-Hadamard transform. - Proc. 2nd Int. Conf. Information Communications and Signal Processing, ICISC'99, Singapore, paper 2B2.2, pp. 1-4.
[007] Hurst S.L., Miller D.M. and Muzio J.C. (1985): Spectral Techniquesin Digital Logic. - London: Academic Press.
[008] Karpovsky M.G. (1976): Finite Orthogonal Series in the Designof Design of Digital Devices. - New York: Wiley. | Zbl 0336.94017
[009] Karpovsky M.G., Stankovic R.S. and Astola J.T. (2003): Reduction of size decision diagrams by autocorrelation functions. - IEEE Trans. Comput., Vol. 52, No. 5, pp. 592-606.
[010] Lai Y., Pedram M. and Vrudhula S. (1993): BDD based decompositionof logic function with application to FPGA synthesis. - Proc. 30-th Conf.Design Automation, DAC'93, Dallas, Texas, pp. 642-647.
[011] MacWilliams F.J. and Sloane N.J. (1977): The Theory of Error-Correctiong Codes. - Amsterdam: Nord-Holland Publishing Company. | Zbl 0369.94008
[012] Mishchenko A., Steinbach B. and Perkowski M. (2001): Analgorithm for bi-decomposition of logic functions. - Proc. 38-th Conf. Design Automation, DAC'01, Las Vegas, NV, pp. 103-108.
[013] Nowicka M., Rawski M. and Łuba T. (1999): DEMAIN - An interactive tool for FPGA-based logic decomposition. - Proc. 6-thInt. Conf. Mixed Design of Integrated Circuits and Systems, Cracow, Poland, pp. 115-120.
[014] Porwik P. (2003): The spectral test of the Boolean function linearity. - Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 4, pp. 567-575. | Zbl 1039.94017
[015] Porwik P. (2004a): Efficient spectral method of identification of linear Boolean function. - Int. J. Contr. Cybern., Vol. 33, No. 4, pp. 663-678. | Zbl 1167.94344
[016] Porwik P. (2004b): Walsh coefficients distribution for some types of Boolean function. - Arch. Theoret. Appl. Informat., Vol. 16, No. 2, pp. 109-120.
[017] Rawski M., Jozwiak L. and L uba T. (2001): Functional decomposition with an efficient input support selection for sub-functions based on information relationship measures. - J. Syst. Archit., Vol. 47, Elsevier Science, pp. 137-155.
[018] Rice J. and Muzio J.C. (2003): On the use of autocorrelation coefficients in the identification of three-level decompositions. - Proc. Int. Workshop Logic Synthesis, IWLS'03, Laguna Beach, CA, pp. 187-191.
[019] Stanković R.S. and Astola J.T., (2003): Spectral Interpretation of Decision Diagram. - New York: Springer. | Zbl 1038.94002
[020] Stankovic R.S. and Falkowski B. (2002): Spectral transforms calculation trough decision diagrams. - VLSI Design.,Vol. 14, No. 1, pp. 5-12.
[021] Sasao T. and Butler J.T. (1997): On bi-decomposition of logic functions. - Proc. Int. Workshop Logic Synthesis, Lake Tahoe, CA, Vol. 2, pp. 1-6. | Zbl 0883.11006
[022] Sasao T. and Matsuura M. (2004): A method to decompose multiple-output logic functions. - Proc. 41-th Conf. Design Automation, DAC'04, San Diego, CA, pp. 428-433.
[023] Tokmen V.H. (1980): Disjoint decomposability of multi-valued functions by spectral means. - Proc. IEEE 10-th Int. Symp. Multiple-Valued Logic, New York, USA, pp. 88-93.
[024] Tomczuk R. (1996): Autocorrelation and decomposition methods in combinational logic design. - Ph.D. thesis, University of Victoria, Victoria, Cadada.
[025] Yanushkevich S. (1998): Logic Differential Calculus in Multi-Valued Logic Design. - Szczecin: Techn. University of Szczecin Academic Publishers, Poland.
[026] Yaroslavsky L. (2003): Digital Image Processing. - Boston, MA: Kluwer Academic Publisher.