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Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements 单调布尔函数的传播准则，其最小向量支持集为 1 或 2 个元素
IF 0.5
Discrete Mathematics and Applications Pub Date : 2024-04-01 DOI: 10.1515/dma-2024-0006
Gleb A. Isaev
{"title":"Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements","authors":"Gleb A. Isaev","doi":"10.1515/dma-2024-0006","DOIUrl":"https://doi.org/10.1515/dma-2024-0006","url":null,"abstract":"\u0000 The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140771040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse homomorphisms of finite groups 有限群的逆同态
IF 0.5
Discrete Mathematics and Applications Pub Date : 2024-04-01 DOI: 10.1515/dma-2024-0010
Igor G. Shaposhnikov
{"title":"Inverse homomorphisms of finite groups","authors":"Igor G. Shaposhnikov","doi":"10.1515/dma-2024-0010","DOIUrl":"https://doi.org/10.1515/dma-2024-0010","url":null,"abstract":"\u0000 Replacing the equality in the condition of the homomorphism of a multi-based universal algebra with inequality leads to the definition of an inverse homomorphism of a multi-based universal algebra. In this paper methods for constructing nontrivial inverse homomorphisms of finite groups are studied.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140782340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model 蜂窝电路模型中多路复用器面积的渐近尖锐估计值
IF 0.5
Discrete Mathematics and Applications Pub Date : 2024-04-01 DOI: 10.1515/dma-2024-0009
S. A. Lozhkin, V. S. Zizov
{"title":"Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model","authors":"S. A. Lozhkin, V. S. Zizov","doi":"10.1515/dma-2024-0009","DOIUrl":"https://doi.org/10.1515/dma-2024-0009","url":null,"abstract":"\u0000 A general cellular circuit of functional and switching elements (CCFSE) is a mathematical model of integral circuits (ICs), which takes into account peculiarities of their physical synthesis. A principal feature of this model distinguishing it from the well-known classes of circuits of gates (CGs) is the presence of additional requirements on the geometry of the circuit which ensure the accounting of the necessary routing resources for IC creation. The complexity of implementation of a multiplexer function of Boolean algebra (FBA) in different classes of circuits has been extensively studied. In the present paper, we give asymptotically sharp upper and lower estimates for the area of a CCFSE implementing a multiplexer FBA of order n. We construct a family of circuit multiplexers of order n of area equal to the halved upper estimate, and provide a method of delivering the corresponding lower estimate.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140769112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the approximation of high-order binary Markov chains by parsimonious models 关于用解析模型逼近高阶二元马尔可夫链
IF 0.5
Discrete Mathematics and Applications Pub Date : 2024-04-01 DOI: 10.1515/dma-2024-0007
Yuriy S. Kharin, V. Voloshko
{"title":"On the approximation of high-order binary Markov chains by parsimonious models","authors":"Yuriy S. Kharin, V. Voloshko","doi":"10.1515/dma-2024-0007","DOIUrl":"https://doi.org/10.1515/dma-2024-0007","url":null,"abstract":"\u0000 We consider two parsimonious models of binary high-order Markov chains and discover their ability to approximate arbitrary high-order Markov chains. Two types of global measures for approximation accuracy are introduced, theoretical and experimental results are obtained for these measures and for the considered parsimonious models. New consistent statistical parameter estimator is constructed for parsimonious model based on two-layer artificial neural network.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140796468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the complexity of implementation of a system of three monomials of two variables by composition circuits 论用组合电路实现二变量三单项式系统的复杂性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2024-04-01 DOI: 10.1515/dma-2024-0008
Sergey A. Korneev
{"title":"On the complexity of implementation of a system of three monomials of two variables by composition circuits","authors":"Sergey A. Korneev","doi":"10.1515/dma-2024-0008","DOIUrl":"https://doi.org/10.1515/dma-2024-0008","url":null,"abstract":"\u0000 We study the complexity of implementation of systems of monomials by composition circuits. Here, by the complexity we mean the smallest possible number of operations required for computation of the system of monomials from the variables;\u0000under this approach, results of intermediate computations can be used several times. The main result of this paper establishes, for an arbitrary system of three monomials of two variables without zeroth powers, a formula for the complexity of their joint implementation by composition circuits with an additive error which is either 1 or 0.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140775246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limit theorem for stationary distribution of a critical controlled branching process with immigration 有移民的临界受控分支过程静态分布的极限定理
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0030
Vladimir I. Vinokurov
{"title":"Limit theorem for stationary distribution of a critical controlled branching process with immigration","authors":"Vladimir I. Vinokurov","doi":"10.1515/dma-2023-0030","DOIUrl":"https://doi.org/10.1515/dma-2023-0030","url":null,"abstract":"Abstract We consider the sequence {ξn,t}t≥1 of controlled critical branching processes with immigration, where n = 1, 2, … is an integer parameter limiting the population size. It is shown that for n → ∞ the stationary distributions of considered branching processes normalized by n $begin{array}{} sqrt{n} end{array} $ converge to the distribution of a random variable whose square has a gamma distribution.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139328386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence 用于检验二进制序列等概率的平滑版频谱检验的极限定理
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0029
M. P. Savelov
{"title":"Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence","authors":"M. P. Savelov","doi":"10.1515/dma-2023-0029","DOIUrl":"https://doi.org/10.1515/dma-2023-0029","url":null,"abstract":"Abstract We consider the problem of testing the hypothesis that the tested sequence is a sequence of independent random variables that take values 1 and –1 with equal probability. To solve this problem, the Discrete Fourier Transform (spectral) test of the NIST package uses the statistic TFourier, the exact limiting distribution of which is unknown. In this paper a new statistic is proposed and its limiting distribution is established. This new statistic is a slight modification of TFourier. A hypothesis about the limit distribution of TFourier is formulated, which is confirmed by numerical experiments presented by Pareschi F., Rovatti R. and Setti G.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions 广义四元组 2 上的片断-四元变换类
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0028
B. Pogorelov, M. Pudovkina
{"title":"Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions","authors":"B. Pogorelov, M. Pudovkina","doi":"10.1515/dma-2023-0028","DOIUrl":"https://doi.org/10.1515/dma-2023-0028","url":null,"abstract":"Abstract The class of nonabelian 2-groups H with cyclic subgroup of index 2 includes the dihedral group, the generalized quaternion group, the semidihedral group, and the modular maximal cyclic group, which have many various applications in discrete mathematics and cryptography. We introduce piecewise-quasiaffine transformations on a group H, and put forward criteria of their bijectivity. For the generalized group of quaternions of order 2m, we obtain a complete classification of orthomorphisms, complete transformations, and their left analogues in the class of piecewise-quasiaffine transformations under consideration. We also evaluate their cardinalities.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On polynomial-modular recursive sequences 关于多项式模块递归序列
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0027
S. Marchenkov
{"title":"On polynomial-modular recursive sequences","authors":"S. Marchenkov","doi":"10.1515/dma-2023-0027","DOIUrl":"https://doi.org/10.1515/dma-2023-0027","url":null,"abstract":"Abstract We consider recursive sequences over the set of integers, where as rules of generation we take arbitrary superpositions of polynomial functions and the function |x|; such sequences are referred to as polynomial-modular recursive sequences. We show how evaluations on three-tape Minsky machines can be simulated via polynomial-modular recursive sequences. Based on this result, we formulate algorithmically unsolvable problems related to polynomial-modular recursive sequences. We also consider recursive sequences in which the rules of generation are functions formed by some superpositions of polynomial functions and the function [x]. $begin{array}{} displaystyle [sqrt{x}]. end{array}$ For the set of such recursive sequences, an algorithmically unsolvable problem is indicated.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139328931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On algebraicity of lattices of ω-fibred formations of finite groups 论有限群的ω纤维阵的网格代数性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0026
Serafim P. Maksakov, M. Sorokina
{"title":"On algebraicity of lattices of ω-fibred formations of finite groups","authors":"Serafim P. Maksakov, M. Sorokina","doi":"10.1515/dma-2023-0026","DOIUrl":"https://doi.org/10.1515/dma-2023-0026","url":null,"abstract":"Abstract For a nonempty set ω of primes, V. A. Vedernikov had constructed ω-fibred formations of groups via function methods. We study lattice properties of ω-fibred formations of finite groups with direction δ satisfying the condition δ0 ≤ δ. The lattice ωδFθ of all ω-fibred formations with direction δ and θ-valued ω-satellite is shown to be algebraic under the condition that the lattice of formations θ is algebraic. As a corollary, the lattices ωδF, ωδFτ, τωδF, ωδnF of ω-fibred formations of groups are shown to be algebraic.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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