Advertisement

Siberian Mathematical Journal

, Volume 60, Issue 1, pp 1–9 | Cite as

Lower Bounds of Complexity for Polarized Polynomials over Finite Fields

  • A. S. BaliukEmail author
  • A. S. ZinchenkoEmail author
Article
  • 5 Downloads

Abstract

We obtain an efficient lower bound of complexity for n-ary functions over a finite field of arbitrary order in the class of polarized polynomials. The complexity of a function is defined as the minimal possible number of nonzero terms in a polarized polynomial realizing the function.

Keywords

lower bound of complexity polarized polynomial finite field 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gegalkine J. J., “L’arithmétisation de la logique symbolique,” Mat. Sb., vol. 35, No. 3–4, 311–377 (1928).Google Scholar
  2. 2.
    Muller D. E., “Application of Boolean algebra to switching circuit design and to error detection,” IRE Trans. Electron. Comput., vol. EC–3, no. 3, 6–12 (1954).Google Scholar
  3. 3.
    Mukhopadhyay A. and Schmitz G., “Minimization of exclusive or and logical equivalence switching circuits,” IEEE Trans. Comput., vol. C–19, no. 2, 132–140 (1970).CrossRefzbMATHGoogle Scholar
  4. 4.
    Pradhan D. K. and Patel A. M., “Reed–Muller like canonic forms for multivalued functions,” IEEE Trans. Comput., vol. C–24, no. 2, 206–210 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Peryazev N. A., “Complexity of Boolean functions in the class of polarized polynomial forms,” Algebra and Logic, vol. 34, No. 3, 177–179 (1995).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Selezneva S. N., “On the complexity of the representation of functions of many–valued logics by polarized polynomials,” Discrete Math. Appl., vol. 12, No. 3, 229–234 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Baliuk A. S. and Yanushkovsky G. V., “Upper bounds of the complexity of functions over finite fields in some classes of Kronecker forms,” IIGU Ser. Matematika, vol. 14, 3–17 (2015).Google Scholar
  8. 8.
    Kazimirov A. S. and Reymerov S. Yu., “On upper bounds of the complexity of functions over non–prime finite fields in some classes of polarized polynomials,” IIGU Ser. Matematika, vol. 17, 37–45 (2016).Google Scholar
  9. 9.
    Markelov N. K., “A lower estimate of the complexity of three–valued logic functions in the class of polarized polynomials,” Moscow Univ. Comput. Math. and Cyber., vol. 36, No. 3, 150–154 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Baliuk A. S. and Zinchenko A. S., “Lower bound for the complexity of five–valued polarized polynomials,” Discrete Math. Appl., vol. 27, No. 5, 287–293 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lidl R. and Niederreiter H., Finite Fields, Addison–Wesley, Reading (1983).zbMATHGoogle Scholar
  12. 12.
    Bassa A. and Beelen P., “A proof of a conjecture by Schweizer on the Drinfeld modular polynomial ΦT (X, Y),” J. Number Theory, vol. 131, 1276–1285 (2011).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.LLC Informatics of MedicineIrkutskRussia
  2. 2.Irkutsk State UniversityIrkutskRussia

Personalised recommendations