• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Quasiuniversal Boolean Automaton with Four Constant States
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
July 16, 2026
Team Success: Aligning Means with Objectives
In corporations, sports, and academia, people often face challenges they cannot handle alone. In such cases, selecting the right team is crucial. Tatiana Mayskaya, Associate Professor at the HSE Faculty of Economic Sciences and the International College of Economics and Finance, together with colleagues from foreign universities, examined team characteristics and found that less diverse teams are better suited to objectives where a high average performance is important, whereas more diverse teams are preferable when avoiding failure is critical. The paper has been published in Economic Theory.
July 15, 2026
Economists Propose More Effective Approach to Reducing Smoking
Economists at HSE University have examined how smokers respond to changes in cigarette prices. When tobacco prices increase, cigarette consumption does not always decline. In fact, spending on tobacco may even rise: according to the researchers, a 1% decrease in cigarette affordability leads to a 0.28% increase in per capita tobacco expenditure. The findings suggest that to reduce smoking rates, tobacco prices must rise faster than household incomes. The study has been published in Voprosy Statistiki.
July 15, 2026
HSE MIEM Students to Develop Two Satellites from Scratch for Orbital Experiments
The devices, created by student teams, will conduct space research on the properties of promising solar cells, on-board energy storage systems, and serial electronics for student satellites.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Quasiuniversal Boolean Automaton with Four Constant States

Moscow University Mathematics Bulletin. 2019. Vol. 74. No. 6. P. 241–245.
Sysoeva L.
Translator: В. Д. Валединский

The problem of realization of Boolean functions by initial Boolean automata with constant states and n inputs is considered. Initial Boolean automaton with constant states and n inputs is an initial automaton with output such that in all states the output functions are n-ary constant Boolean functions 0 or 1. An example of an initial Boolean automaton with the minimum number of constant states and n inputs realizing the maximum possible number of n-ary Boolean fonctions, where n ≥ 3, is constructed.

Priority areas: mathematics
Language: English
DOI
Text on another site
Keywords: булева функцияBoolean functioninitial automatonrealization of Boolean functionинициальный автоматреализация булевых функций
Similar publications
On functional equations for Chow polylogarithms
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity. To prove this, we study ...
Added: July 16, 2026
On Goncharov’s conjecture in next to Milnor degree
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Strong Approximations for Markov Chains Weakly Converging to Diffusions
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Bifurcations and Structural Stability of Generic PC-HC Families
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
On the minimum number of maximal distance-k independent sets in trees
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
On Arithmetic Mirror Symmetry for smooth Fano fourfolds
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$,  on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
On the dimension of the space of static potentials on three-manifolds
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Using predefined vector systems to speed up neural network multimillion class classification
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Homogeneous maximizers of the Blaschke-Santalo-type functionals
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2  sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of  N>2 sets. We also discuss links to the ...
Added: February 13, 2026
Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
On finding formal power-logarithmic expansions of solutions to q-difference equations
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Ideal of the variety of flexes of plane cubics
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves of degree 3 in the projective plane is an ideal theoretic complete intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Random walks on rank one symmetric spaces of noncompact type
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Cascades of Lorenz attractors in the Shimizu-Morioka model
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Асимптотический вариант метода параметрикс для цепей Маркова, сходящихся к диффузиям
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Disjunctive Complexity
Ivanov N., Rubtsov A. A., Vyalyi M., , in: Descriptional Complexity of Formal Systems. 26th IFIP WG 1.02 International Conference, DCFS 2025 Loughborough, UK, July 22–24, 2025. Proceedings.: Springer, 2025. P. 137–150.
Added: August 24, 2025
ЗАДАЧНИК ПО ДИСКРЕТНОЙ МАТЕМАТИКЕ
Дехтярь М. И., Dudakov S., Карлов Б. Н., Тверь: Тверской государственный университет, 2021.
Учебное пособие адресовано изучающим курс дискретной математики, прежде всего, студентам младших курсов, обучающимся по направлениям укрупненных групп 01.03.00 "Математика и механика", 02.03.00 "Компьютерные и информационные науки", 09.03.00 "Информатика и вычислительная техника". Настоящий сборник задач является пособием для практических занятий по некоторым разделам дискретной математики и может быть использован преподавателями и студентами для подготовки к семинарским  занятиям и ...
Added: November 12, 2023
Лекции по дискретной математике
Дехтярь М. И., Dudakov S., Карлов Б. Н., Тверь: Тверской государственный университет, 2021.
Учебник содержит лекционный материал по дисциплине "Дискретная математика", а также примеры задач с решениями и задачи для самостоятельной работы. Основные разделы учебника: множества, математическая индукция, комбинаторика, булевы функции, логика высказываний и предикатов, графы, автоматы и формальные языки, алгоритмы. Учебник адресован, прежде всего, студентам младших курсов, обучающихся по направлениям укрупненных групп 01.03.00 "Математика и механика", 02.03.00 "Компьютерные ...
Added: November 12, 2023
Об эвристическом подходе к построению биективных векторных булевых функций с заданными криптографическими характеристиками
Коврижных М. А., Fomin D., Прикладная дискретная математика. Приложение 2021 № 14 С. 181–184
Bijective vector Boolean functions (permuta- tions) are used as nonlinear primitives of many symmetric ciphers. In this paper, we study a generalized construction of (2m, 2m)-functions using monomial and arbitrary m-bit per- mutations as constituent elements. A heuristic algorithm for obtaining bijective Boolean functions with given nonlinearity and differential uniformity, based on this construction, is proposed. For ...
Added: September 22, 2021
О некоторых инвариантах действия расширения GA(n,2) на множестве булевых функций
Fedorov S., Логачёв О. А., Ященко В. В., Дискретная математика 2021 Т. 33 № 2 С. 66–85
Рассматривается действие на множестве булевых функций расширения G полной аффинной группы преобразований с помощью группы аффинных функций: действие заключается в преобразовании булевых функций невырожденными аффинными заменами переменных и сложением с аффинными булевыми функциями. Введены и исследованы параметры булевых функций, инвариантные относительно действия группы G: амплитуда (тесно связанная с нелинейностью), размерность функции и некоторые другие. Эти ...
Added: June 16, 2021
On the Δ-equivalence of Boolean functions
Fedorov S., Логачёв О. А., Ященко В. В., Discrete Mathematics and Applications 2020 Vol. 30 No. 2 P. 93–101
Added: June 16, 2021
Об одном методе решения систем квадратичных булевых уравнений, использующем локальные аффинности
Fedorov S., Логачёв О. А., Сукаев А. А., Информатика и ее применения 2019 Т. 13 № 2 С. 37–46
Как известно, вычислительная задача решения систем нелинейных уравнений над полем из двух элементов является NP-трудной. Этим обстоятельством обуславливается стремление исследователей разрабатывать алгоритмы ее решения, минимизирующие необходимые вычислительные ресурсы для тех или иных классов систем уравнений. В статье предлагается метод решения систем квадратичных булевых уравнений, использующий представление функций их аффинными нормальными формами, то есть, в некотором смысле, аппроксимацию ...
Added: June 16, 2021
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit