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О базируемости классов функций трехзначной логики, порожденных периодическими симметрическими функциями
С. 209–212.
Closed classes of three-valued logic, generated by periodical functions taking values from the set {0,1} are considered. Criteria of basis exitstence and finite basis existence for classes generated by periodical functions with period of the form p^k (p is fixed prime number, k is arbitrary natural number) are obtained.
Keywords: функции многозначной логикизамкнутые классыбазисmulti-valued logic functionsgenerating systemsbasisclosed classesпорождающая система
Publication based on the results of:
In book
М.: Изд-во механико-математического факультета МГУ, 2016.
Mikhailovich A., Kochergin V., М.: Физматлит, 2024.
Added: March 10, 2025
Gabdullin M., A. O. Radomskii, Sbornik: Mathematics 2024 Vol. 215 No. 5 P. 612–633
For a positive integer $n$ we denote by $F(n)$ the distance of $n$ to the nearest prime number. Using the technique from the recent paper ``Long gaps in sieved sets'' by Ford, Konyagin, Maynard, Pomerance and Tao (J. Eur. Math. Soc., 23:2 (2021), 667--700) we prove that every sufficiently large positive integer $N$ can be ...
Added: September 22, 2024
Габдуллин М. Р., Radomskii A., Математический сборник 2024 Т. 215 № 5 С. 47–70
Для натурального $n$ обозначим через $F(n)$ расстояние от $n$ до ближайшего простого числа. Используя метод из недавней работы К. Форда, С. Конягина, Дж. Мейнарда, К. Померанса и Т. Тао ``Long gaps in sieved sets'' (J. Eur. Math. Soc., 23:2 (2021), 667--700), мы доказываем, что всякое достаточно большое натуральное $N$ может быть представлено в виде $N=n_1+n_2$, ...
Added: May 22, 2024
Н. Л. Поляков, В кн.: Algebra and Model Theory 14Vol. 14.: Novosibirsk: ., 2023. С. 102–112.
The Galois theory for closed classes of infinitary functions and some of its applications in the theory of ultrafilters are considered. ...
Added: November 23, 2023
Kochergin V., Mikhailovich A., Mathematical notes 2023 Vol. 113 No. 5 P. 794–803
The problem of determining the nonmonotone complexity of the implementation ofk-valued logic functions by logic circuits in bases consisting of all monotone (with respect to thestandard order) functions and finitely many nonmonotone functions is investigated. In calculatingthe complexity measure under examination only those elements of the circuit which are assignednonmonotone basis functions are taken into ...
Added: November 19, 2023
Kochergin V., Mikhailovich A., В кн.: Материалы XIV Международного семинара "Дискретная математика и ее приложения" имени академика О.Б.Лупанова (Москва, МГУ, 20-25 июня 2022 г.).: М.: Институт прикладной математики им. М.В. Келдыша РАН, 2022. С. 76–79.
Установлена нижняя оценка немонотонной сложности функций многозначной логики, отличающающаяся от известной верхней оценки не более чем на абсолютную константу ...
Added: October 29, 2022
Mikhailovich A., Kochergin V., В кн.: Материалы XIII Международного семинара "Дискретная математика и её приложения" имени академика О.Б. Лупанова.: Изд-во механико-математического факультета МГУ, 2019. С. 129–131.
Added: December 7, 2021
Kochergin V., Mikhailovich A., В кн.: Проблемы теоретической кибернетики. Материалы заочного семинара XIX международной конференции.: Издательство Казанского (Приволжского) федерального университета, 2021. С. 75–78.
В работе исследуется сложность реализации функций многозначной логики над базисами, содержащими все монотонные функции и конечное число немонотонных функций. Получены верхняя и нижняя оценка, отличающиеся на константу, не зависящую от базиса. ...
Added: December 6, 2021
Kochergin V., Mikhailovich A., Ученые записки Казанского университета. Серия: Физико-математические науки 2020 Т. 162 № 3 С. 311–321
The problem of the complexity of multi-valued logic functions realization by circuits
in a special basis is investigated. This kind of basis consists of elements of
two types. The first type of elements are monotone functions with zero weight.
The second type of elements are non-monotone elements with unit weight.
The non-empty set of elements of this type is ...
Added: December 6, 2021
Troitskaya A., Теоретическая и прикладная экономика 2021 № 3 С. 14–29
This article is dedicated to practical implementation of quantitative assessment of labor potential of the company. The author provides the results of implementation of the original methodology for calculating labor potential of the company on the example of “Foundry and Mechanical Plant” OJSC in the city of Semyonov of Nizhny Novgorod region. In the course ...
Added: October 29, 2021
Толкачев П. А., Давтян Ц. А., Философская мысль 2020 № 7 С. 59–71
Rehabilitation of Marxist thought present in Althusser’s compilation of the articles titled by catching appeal “For Marx” is carried out in two directions: general – when theoretical line of understanding of the society and history is derived out of Marxism as political ideology; specific – when revealing the “ rational kernel” of Marxist philosophy of ...
Added: January 11, 2021
V.V. Kochergin, A.V. Mikhailovich, Computational Mathematics and Modeling 2019 Vol. 30 No. 1 P. 13–25
We investigate the realization complexity of k-valued logic functions k ≥ 2 by combinational circuits in an infinite basis that includes the negation of the Lukasiewicz function, i.e., the function k−1−x, and all monotone functions. Complexity is understood as the total number of circuit elements. For an arbitrary function f, we establish lower and upper ...
Added: April 22, 2019
Polyakov N. L., Шамолин М. В., Вестник Самарского государственного университета. Естественнонаучная серия 2013 № 6(107) С. 61–73
We give an effective description of symmetric closed classes of discrete functions preserving any unary predicate. ...
Added: October 5, 2018
Kochergin Vadim V., Mikhailovich Anna V., Discrete Mathematics and Applications 2017 Vol. 27 No. 5 P. 295–302
The paper is concerned with the complexity of realization of 𝑘-valued logic functions by logic circuits over an infinite complete bases containing all monotone functions; the weight of monotone functions (the cost of use) is assumed to be 0. The complexity problem of realizations of Boolean functions over a basis having negation as the only ...
Added: March 14, 2018