On the equality problem of finitely generated classes of exponentially-polynomial functions
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Sergey S. Marchenkov
Abstract
We consider the class EPℕ of exponentially-polynomial functions which can be obtained by arbitrary superpositions of the constants 0, 1 and arithmetic operations of addition, multiplication, and powering. For this class, we solve the algorithmic equality problem of two functions that assume a finite number of values. Next, this class is restricted to the class PEPℕ, in which the function xy is replaced by a sequence of functions {
Originally published in Diskretnaya Matematika (2022) 34, №1, 64–75 (in Russian).
Acknowledgment
The author is grateful to the referee for valuable suggestions.
[1] Darsaliya V. Sh., “Completeness conditions for polynomials with natural, integer and rational coefficients”, Fundam. prikl. mat., 2:2 (1996), 365–374 (in Russian).Suche in Google Scholar
[2] Mamontov A. I., Meshchaninov D. G., “The completeness problem in the function algebra of linear integer-coefficient polynomials”, Discrete Math. Appl., 20:5-6 (2010), 621–641.Suche in Google Scholar
[3] Mamontov A. I., Meshchaninov D. G., “The algorithm for completeness recognizing in function algebra L(ℤ)”, Discrete Math. Appl., 24:1 (2014), 21–28.Suche in Google Scholar
[4] Marchenkov S. S., Functional Systems with Superposition Operation, Fizmatlit, Moscow, 2004 (in Russian), 104 pp.Suche in Google Scholar
[5] Marchenkov S. S., Representation of functions by superpositions, M.: KomKniga, 2010 (in Russian), 192 pp.Suche in Google Scholar
[6] Marchenkov S. S., Selected Chapters of Discrete Mathematics, M.: MAKS Press, 2016 (in Russian), 133 pp.Suche in Google Scholar
[7] Marchenkov S. S., “Completeness criterion in class of exponential-polynomial functions”, Moscow Univ. Comput. Math. and Cybern., 44:2 (2020), 87–94.Suche in Google Scholar
[8] Yablonskii S. V., “Functional constructions in a k-valued logic”, Collection of articles on mathematical logic and its applications to some questions of cybernetics, Trudy Mat. Inst. Steklov., 51, 1958, 5–142 (in Russian).Suche in Google Scholar
[9] Rosenberg I. G., “Über die funktionale Vollständigkeit in den mehrwertigen Logiken”, Rozpravy Československé Akad. Věd Řada Mat. Přírod. Věd, 80 (1970), 3–93.Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space
- On a number of particles in a marked set of cells in a general allocation scheme
- On the equality problem of finitely generated classes of exponentially-polynomial functions
- Fault-tolerant resolvability of some graphs of convex polytopes
- On bases of all closed classes of Boolean vector functions
- 10.1515/dma-2023-0018
Artikel in diesem Heft
- Frontmatter
- On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space
- On a number of particles in a marked set of cells in a general allocation scheme
- On the equality problem of finitely generated classes of exponentially-polynomial functions
- Fault-tolerant resolvability of some graphs of convex polytopes
- On bases of all closed classes of Boolean vector functions
- 10.1515/dma-2023-0018
