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Dedicated spectral method of Boolean function decomposition

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Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Rocznik
Strony
271--278
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
  • Institute of Informatics, University of Silesia, ul. Będzińska 39, 41–200 Sosnowiec, Poland
  • Department of Computer Science, Faculty of Electronics, University of Niš, Beogradska 14, 18 000 Niš, Serbia
Bibliografia
  • [1] Ahmed N. and Rao K.R. (1975): Orthogonal Transforms for Digital Signal Processing. - Berlin: Springer.
  • [2] Ashenhurst R. (1957): The decomposition of switching functions. - Proc. Int. Symp. Theory of Switching, Annual Computation Laboratory, Harvard University, Vol. 29, pp. 74-116.
  • [3] 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.
  • [4] Curtis H.A. (1962): A New Approach to the Design of Switching Circuits. -Princeton: Van Nostrand.
  • [5] Bertacco V. and Damiani M. (1997): The disjunctive decomposition of logic functions.-Proc. Computer-Aided Design, ICCAD'97, San Jose, CA, pp. 78-82.
  • [6] 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.
  • [7] 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.
  • [8] Hurst S.L., Miller D.M. and Muzio J.C. (1985): Spectral Techniques in Digital Logic. -London: Academic Press.
  • [9] Karpovsky M.G. (1976): Finite Orthogonal Series in the Design of Design of Digital Devices. - New York: Wiley.
  • [10] Karpovsky M.G., Stankovi´c 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.
  • [11] Lai Y., Pedram M. and Vrudhula S. (1993): BDD based decomposition of logic function with application to FPGA synthesis. - Proc. 30-th Conf. Design Automation, DAC'93, Dallas, Texas, pp. 642-647.
  • [12] MacWilliams F.J. and Sloane N.J. (1977): The Theory of Error- Correctiong Codes. - Amsterdam: Nord-Holland Publishing Company.
  • [13] Mishchenko A., Steinbach B. and Perkowski M. (2001): An algorithm for bi-decomposition of logic functions. - Proc. 38-th Conf. Design Automation, DAC'01, Las Vegas, NV, pp. 103-108.
  • [14] Nowicka M., Rawski M. and Łuba T. (1999): DEMAIN - An interactive tool for FPGA-based logic decomposition. - Proc. 6-th Int. Conf. Mixed Design of Integrated Circuits and Systems, Cracow, Poland, pp. 115-120.
  • [15] Porwik P. (2003): The spectral test of the Boolean function linearity. - Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 4, pp. 567-575.
  • [16] Porwik P. (2004a): Efficient spectral method of identification of linear Boolean function. - Int. J. Contr. Cybern., Vol. 33, No. 4, pp. 663-678.
  • [17] Porwik P. (2004b): Walsh coefficients distribution for some types of Boolean function. - Arch. Theoret. Appl. Informat., Vol. 16, No. 2, pp. 109-120.
  • [18] Rawski M., Jóźwiak L. and Łuba T. (2001): Functional decomposition with an efficient input support selection for subfunctions based on information relationship measures. - J. Syst. Archit., Vol. 47, Elsevier Science, pp. 137-155.
  • [19] 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.
  • [20] Stanković R.S. and Astola J.T., (2003): Spectral Interpretation of Decision Diagram. -New York: Springer.
  • [21] Stanković R.S. and Falkowski B. (2002): Spectral transforms calculation trough decision diagrams. - VLSI Design., Vol. 14, No. 1, pp. 5-12.
  • [22] 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.
  • [23] 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.
  • [24] 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.
  • [25] Tomczuk R. (1996): Autocorrelation and decomposition methods in combinational logic design. - Ph.D. thesis, University of Victoria, Victoria, Cadada.
  • [26] Yanushkevich S. (1998): Logic Differential Calculus in Multi- Valued Logic Design. - Szczecin: Techn. University of Szczecin Academic Publishers, Poland.
  • [27] Yaroslavsky L. (2003): Digital Image Processing. - Boston, MA: Kluwer Academic Publisher.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0028-0024
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