Automatic Control and Computer Sciences

, Volume 51, Issue 5, pp 285–293 | Cite as

The complexity of Boolean functions in the Reed–Muller polynomials class

Article
  • 18 Downloads

Abstract

This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of n variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.

Keywords

Boolean function symmetric Boolean function Reed–Muller polynomial Zhegalkin polynomial polynomial complexity Shannon functions Boolean derivative triangle method logical scheme 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pospelov, D.A., Logicheskie metody analiza i sinteza skhem (Logical Methods of Analysis and Synthesis of Circuits), Moscow: Energiya, 1974.Google Scholar
  2. 2.
    Suprun, V.P. and Gorodetskii, D.A., The matrix method for polynomial expansion of symmetric boolean functions, Avtom. Vychisl. Tekh., 2013, no. 1, pp. 5–12.Google Scholar
  3. 3.
    Suprun, V.P., Complexity of Boolean functions in the class of canonical polarized polynomials, Diskretn. Mat., 1993, vol. 5, no. 2, pp. 111–115.MathSciNetMATHGoogle Scholar
  4. 4.
    Peryazev, N.A., Complexity of Boolean functions in the class of polynomial polarized forms, Algebra Logika, 1995, no. 3, pp. 323–326.MathSciNetMATHGoogle Scholar
  5. 5.
    Suprun, V.P., Estimations of Shennon’s function for polarity Reed–Muller expressions, Proc. of the IFIP WG 10.5 Workshop on Applications of the Reed–Muller Expansion in Circuit Design (Hamburg, Germany, September 16–17, 1993), Tubingen, 1993, pp. 107–114.Google Scholar
  6. 6.
    Suprun, V.P., Table method of polynomial expansion of Boolean functions, Kibernetika, 1987, no. 1, pp. 116–117.MathSciNetMATHGoogle Scholar
  7. 7.
    Suprun, V.P. and Korobko, F.S., Synthesis of logical devices for calculating self-dual symmetric Boolean functions, Avtom. Vychisl. Tekh., 2014, no. 1, pp. 26–35.Google Scholar
  8. 8.
    Avgul’, L.B. and Suprun, V.P., Synthesis of high-speed logic circuits by the cascade method, Izv. Vuzov. Priborostr., 1993, no. 3, pp. 31–36.Google Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsBelarusian State UniversityMinskBelarus

Personalised recommendations