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2006 | 16 | 2 | 271-278

Tytuł artykułu

Dedicated spectral method of Boolean function decomposition

Treść / Zawartość

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

Tom

16

Numer

2

Strony

271-278

Opis fizyczny

Daty

wydano
2006
otrzymano
2005-06-28
poprawiono
2005-11-10

Twórcy

autor
  • Institute of Informatics, University of Silesia, ul. Będzińska 39, 41-200 Sosnowiec, Poland
  • Department of Computer Science, Faculty of Electronics, University of Nis, Beogradska 14, 18 000 Nis, Serbia

Bibliografia

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  • 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.
  • Curtis H.A. (1962): A New Approach to the Design of Switching Circuits. - Princeton: Van Nostrand.
  • Bertacco V. and Damiani M. (1997): The disjunctive decompositionof logic functions. - Proc. Computer-Aided Design, ICCAD'97, San Jose, CA, pp. 78-82.
  • 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.
  • 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.
  • Hurst S.L., Miller D.M. and Muzio J.C. (1985): Spectral Techniquesin Digital Logic. - London: Academic Press.
  • Karpovsky M.G. (1976): Finite Orthogonal Series in the Designof Design of Digital Devices. - New York: Wiley.
  • 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.
  • 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.
  • MacWilliams F.J. and Sloane N.J. (1977): The Theory of Error-Correctiong Codes. - Amsterdam: Nord-Holland Publishing Company.
  • 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.
  • 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.
  • Porwik P. (2003): The spectral test of the Boolean function linearity. - Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 4, pp. 567-575.
  • Porwik P. (2004a): Efficient spectral method of identification of linear Boolean function. - Int. J. Contr. Cybern., Vol. 33, No. 4, pp. 663-678.
  • Porwik P. (2004b): Walsh coefficients distribution for some types of Boolean function. - Arch. Theoret. Appl. Informat., Vol. 16, No. 2, pp. 109-120.
  • 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.
  • 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.
  • Stanković R.S. and Astola J.T., (2003): Spectral Interpretation of Decision Diagram. - New York: Springer.
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  • 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.
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  • Yaroslavsky L. (2003): Digital Image Processing. - Boston, MA: Kluwer Academic Publisher.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-amcv16i2p271bwm
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