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2002 | 12 | 4 | 571-579
Tytuł artykułu

Efficient calculation of the Reed-Muller form by means of the Walsh transform

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to build the Reed-Muller form based on the analysis of Walsh-Hadamard coefficients. The presented method has much less complexity than the procedures which have been applied until now. Both the transforms and the presented Walsh-Hadamard spectral characterization of the Reed-Muller expansion are compared. An analysis of the properties of the spectra obtained from these transforms is made.
Rocznik
Tom
12
Numer
4
Strony
571-579
Opis fizyczny
Daty
wydano
2002
otrzymano
2001-12-06
poprawiono
2002-05-16
Twórcy
autor
  • Institute of Computer Science, Silesian University, ul. Będzińska 39, 41-200 Sosnowiec, Poland
Bibliografia
  • Breuer M.A. and Friedman A.D. (1976): Diagnosis and Reliable Design of Digital Systems. - Potomac, Maryland: Computer Science Press.
  • Damarla T.R. and Karpovsky M. (1989): Fault detection in combinational networks by Reed-Muller transforms. - IEEE Trans. Comp., Vol. 38, No. 6, pp. 788-797.
  • Falkowski B.J. and Chang C.H. (2000): Minimisation of k-variable mixed-polarity Reed-Muller expansions. - VLSI Design, Vol. 11, No. 4, pp. 311-320.
  • Falkowski B.J. and Chang C.H. (1995): An exact minimizer of fixed polarity Reed-Muller expansion. - Int. J. Electron., Vol. 79, No. 3, pp. 389-409.
  • Falkowski B.J. and Chang C.H. (1999): Hadamard-Walsh spectral characterization of Reed-Muller expansions. - Comp. Electr.Eng., No. 25, pp. 111-134.
  • 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.
  • Giani A., Sheng S., Hsiao M.S. and Agraval V.D. (2001): Efficient spectral techniques for sequential ATPG. - Proc. Int. Conf. IEEEs Design Automation Test in Europe, Munich, Germany, pp. 204-208.
  • Hurst S.L., Miller D.M. and Muzio J.C. (1985): Spectral Techniques in Digital Logic. - London: Academic Press.
  • Karpovsky M.G. (1976): Finite Orthogonal Series in the Design of Digital Devices. - New York: Wiley.
  • Karpovsky M.G. (1985): Spectral Techniques and Fault Detection. - London: Academic Press.
  • Micheli De G. (1994): Synthesis and Optimization of Digital Circuits. - Boston: McGraw-Hill.
  • Perkowski M. (1996): A unified approach to exor-based representation of Boolean functions. - Proc. XIX Nat. Conf. Circuit Theory and Electronics Circuits, Krynica, Poland, Vol. 1, pp. 27-41.
  • Porwik P. (1996): Fault path detection using a spectral method. - Proc. Int. Baltic Electronic Conference, BEC'96, Tallin, Estonia, pp. 315-318.
  • Porwik P. and Falkowski B.J. (1999): Informatics properties of the Walsh transform. - Proc. 2-nd Int. Conf. Information Communications and Signal Processing, ICISC'99, Singapore, paper 2B2.4, pp. 1-5.
  • Sasao T. (1993): Logic Synthesis and Optimalization. - Dordrecht: Kluwer.
  • Sasao T. (1995): Representation of logic functions using EXOR operators. - Proc. Workshop Applications of the Read-Muller Expansion in Circuit Design, Makuhari, Japan, pp. 308-313.
  • Yanushkevich S. (1998): Logic Differential Calculus in Multi-Valued Logic Design. - Szczecin, Poland: Technical University Press.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv12i4p571bwm
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