Skip to main content
SpringerLink
Log in

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

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Pospelov, D.A., Logicheskie metody analiza i sinteza skhem (Logical Methods of Analysis and Synthesis of Circuits), Moscow: Energiya, 1974.

    Google Scholar 

  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. Suprun, V.P., Complexity of Boolean functions in the class of canonical polarized polynomials, Diskretn. Mat., 1993, vol. 5, no. 2, pp. 111–115.

    MathSciNet  MATH  Google Scholar 

  4. Peryazev, N.A., Complexity of Boolean functions in the class of polynomial polarized forms, Algebra Logika, 1995, no. 3, pp. 323–326.

    MathSciNet  MATH  Google Scholar 

  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. Suprun, V.P., Table method of polynomial expansion of Boolean functions, Kibernetika, 1987, no. 1, pp. 116–117.

    MathSciNet  MATH  Google Scholar 

  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. 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 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Belarusian State University, Minsk, 220030, Belarus

    V. P. Suprun

Authors
  1. V. P. Suprun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Suprun.

Additional information

Original Russian Text © V.P. Suprun, 2017, published in Avtomatika i Vychislitel’naya Tekhnika, 2017, No. 5, pp. 46–58.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suprun, V.P. The complexity of Boolean functions in the Reed–Muller polynomials class. Aut. Control Comp. Sci. 51, 285–293 (2017). https://doi.org/10.3103/S0146411617050078

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411617050078

Keywords

Search

Navigation