On the universality of product for classes of linear functions of two variables
-
Andrey A. Voronenko
Abstract
Earlier, the author introduced the concept of a universal function and proved the existence of universal functions for classes of linear k-valued functions of two variables for k ≥ 5. In this paper, we show that the product modulo k is a universal function for the class of linear k-valued functions of two variables if and only if k = 6l ± 1.
Note
Originally published in Diskretnaya Matematika (2022) 34, №1, 20-22 (in Russian).
References
[1] Karatsuba A. A., Ofman Yu. P., “Multiplication of multidigit numbers on automata”, Soviet physics. Doklady, 7 (1963), 595–596.Search in Google Scholar
[2] Fürer M., “Faster integer multiplication”, SIAM J. Computing 39:3 (2009), 979–1005.10.1137/070711761Search in Google Scholar
[3] Ol’shanskii A. Yu., “On the problem of a finite basis of identities in groups”, Mathematics of the USSR-Izvestiya, 4:2 (1970), 381–389.10.1070/IM1970v004n02ABEH000911Search in Google Scholar
[4] Kleiman Yu. G., “On a basis of the product of varieties of groups”, Math. USSR-Izv., 7:1 (1973), 91–94.10.1070/IM1973v007n01ABEH001927Search in Google Scholar
[5] Marchenkov S. S., “Superpositions of elementary arithmetic functions”, Diskretnyy analiz i issledovanie operatsiy, 13:4 (2006), 33-48 (in Russian).Search in Google Scholar
[6] Voronenko A. A., “On universal functions for the set of linear functions”, Discrete Math. Appl., 22:4 (2012), 421–425.10.1515/dma-2012-028Search in Google Scholar
[7] Voronenko A. A., Voronova N. K., Ilyutko V. P., “On the existence of universal functions for a class of linear k-valued functions for small k”, Prikladnaya matematika i informatika, 51 (2016), 100–108 (in Russian).Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph
- Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
- Short complete diagnostic tests for circuits with two additional inputs in some basis
- Nonlinearity of functions over finite fields
- The limit joint distributions of statistics of three tests of the NIST package
- On properties of multiaffine predicates on a finite set
- On the universality of product for classes of linear functions of two variables
Articles in the same Issue
- Frontmatter
- On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph
- Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
- Short complete diagnostic tests for circuits with two additional inputs in some basis
- Nonlinearity of functions over finite fields
- The limit joint distributions of statistics of three tests of the NIST package
- On properties of multiaffine predicates on a finite set
- On the universality of product for classes of linear functions of two variables
