?
О нижних оценках сложности схем в базисе антицепных функций
Вестник Московского университета. Серия 1: Математика. Механика. 2013. Т. 2. С. 17–23.
Podolskaya O.
The antichain function is a characteristic function of antichain on the Boolean cube. The set of antichain functions is an infinite complete basis. We study computational complexity of Boolean functions over antichain functional basis. In this paper we prove $\sqrt{n}$ asymptotic lower bound on the computational complexity of the linear function, the majority function and almost all Boolean function of $n$ variables.
Priority areas:
mathematics
Language:
Russian
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
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
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
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
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
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
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
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
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
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
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
V. V. Kochergin, A. V. Mikhailovich, Mathematical notes 2025 Vol. 117 No. 4 P. 579–594
The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function. ...
Added: February 28, 2026
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
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
Kochergin V., Mikhailovich A., Математические заметки 2025 Т. 117 № 4 С. 523–542
The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function. ...
Added: April 8, 2025
Alexander Kozachinskiy, Vladimir Podolskii, Theory of Computing 2022 Vol. 18 No. 15 P. 1–33
We propose a generalization of the Karchmer--Wigderson communication games to the multiparty setting. Our generalization turns out to be tightly connected to circuits consisting of threshold gates. This allows us to obtain new explicit constructions of such circuits for several functions. In particular, we provide an explicit (polynomial-time computable) log-depth monotone formula for the Majority ...
Added: December 10, 2022
Высоцкий Л. И., Жуков В. В., Шуплецов М. С., В кн.: Проблемы разработки перспективных микро- и наноэлектронных систем (МЭС-2018)Вып. 1.: М.: ИППМ РАН, 2018. С. 30–37.
При обнаружении ошибок или изменении
спецификации
проектируемой
сверхбольшой
интегральной схемы (СБИС) на поздних этапах
маршрута проектирования откат на более ранние этапы
проектирования и их повторное выполнение очень часто
становится непрактичным в силу существенных
временных затрат. Для целей сокращения времени
проектирования
в
современные
маршруты
проектирования интегрируют специальные этапы
функциональной коррекции схемы (англ. Engineering
Change Order, ECO). В основе указанного подхода лежит
анализ уже спроектированной схемы и построение
небольшой подсхемы-заплатки, внедрение которой в уже
синтезированную ...
Added: November 10, 2020
Danilov B. R., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2014 Т. 3 № 31 С. 78–100
Background
The problem of synthesis of discrete control systems is one of the main problems of mathematical cybernetics. In general form it consists in construction of an optimal (in a varying sense) structural implementation of a given discrete function in a given class of control systems. Theoretical results obtained during the solution of the mentioned problem ...
Added: December 2, 2019
Danilov B. R., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2015 Т. 4 № 36 С. 58–77
Background
The problem of synthesis of discrete control systems is one of the main problems of mathematical cybernetics. In general form it consists in construction of an optimal (in a varying sense) structural implementation of a given discrete function in a given class of control systems. Theoretical results obtained during the solution of the mentioned problem ...
Added: December 2, 2019
Danilov B. R., Ложкин С. А., Прикладная математика и информатика 2018 № 59 С. 40–49
В работе предлагается метод синтеза усилительных схем из функциональных элементов (УСФЭ), позволяющий установить асимптотику функции Шеннона для обобщённой глубины УСФЭ – то есть глубины самой «плохой» функции алгебры логики, зависящей от заданных переменных – в специальном базисе (модели глубины), где глубина элемента определяется как его типом, так и степенью ветвления выхода в схеме. Асимптотическое поведение ...
Added: December 2, 2019
Lozhkin S. A., Shupletsov M. S., Danilov B.R., Математические вопросы криптографии 2017 Vol. 8 No. 2 P. 87–96
We propose several asymptotically size-optimal Boolean circuits synthesis methods that implement arbitrary Boolean functions of a given number of Boolean variables with a given protection level from functionality inference when concealing some number of local interconnections. These methods rely on the structure of Boolean circuits over arbitrary finite complete basis. Constructed by methods of generalized ...
Added: December 1, 2019