Use of Gray Decoding for Implementation of Symmetric Functions

  • Osnat Keren
  • Ilya Levin
  • Radomir S. Stankovic
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 291)

We study a problem of reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity Reed-Muller (FPRM) expansions. We propose a method, based on the Gray decoding, for reduction of the number of product terms, and, consequently, the implementation cost of the symmetric functions. The method is founded on the principles of linear transformations of the input variables of an initial function. It provides significant simplification both of the SOPs and the FPRMs representations of the functions. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method.


Autocorrelation Function Linear Transformation Boolean Function Symmetric Function Product Term 
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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Bar-Ilan UniversityIsrael
  2. 2.Tel-Aviv UniversityIsrael
  3. 3.Nis UniversitySerbia

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