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Prikladnaya Diskretnaya Matematika最新文献

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Direct powers of algebraic structures and equations 代数结构与方程的直接幂
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.17223/20710410/58/4
Artyom N. Shevlyakov
{"title":"Direct powers of algebraic structures and equations","authors":"Artyom N. Shevlyakov","doi":"10.17223/20710410/58/4","DOIUrl":"https://doi.org/10.17223/20710410/58/4","url":null,"abstract":"We study systems of equations over graphs, posets and matroids. We give the criteria when a direct power of such algebraic structures is equationally Noetherian. Moreover, we prove that any direct power of any finite algebraic structure is weakly equationally Noetherian.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67583371","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
Михайлов Владимир Гаврилович (10.09.1945-13.04.2023)
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.4213/dm1788
{"title":"Михайлов Владимир Гаврилович (10.09.1945-13.04.2023)","authors":"","doi":"10.4213/dm1788","DOIUrl":"https://doi.org/10.4213/dm1788","url":null,"abstract":"","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"19 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75333609","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
The generic complexity of the graph triangulation problem 图三角形化问题的一般复杂性
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.17223/20710410/58/10
A. Rybalov
{"title":"The generic complexity of the graph triangulation problem","authors":"A. Rybalov","doi":"10.17223/20710410/58/10","DOIUrl":"https://doi.org/10.17223/20710410/58/10","url":null,"abstract":"Generic-case approach to algorithmic problems was suggested by A. Miasnikov, V. Kapovich, P. Schupp, and V. Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we study the generic complexity of the graph triangulation problem. This problem is as follows. Given a finite simple graph with 3n vertices, determine whether the vertices of the graph can be divided into n three-element sets, each of which contains vertices connected by edges of the original graph (that is, they are triangles). NP-completeness of this problem was proved by Shaffer in 1974 and is mentioned in the classic monograph by M. Garey and D. Johnson. We prove that under the conditions P ≠ NP and P = BPP there is no polynomial strongly generic algorithm for this problem. A strongly generic algorithm solves a problem not on the whole set of inputs, but on a subset whose frequency sequence converges exponentially to 1 with increasing size. To prove the theorem, we use the method of generic amplification, which allows one to construct generically hard problems from the problems that are hard in the classical sense. The main component of this method is the cloning technique, which combines the inputs of a problem together into sufficiently large sets of equivalent inputs. Equivalence is understood in the sense that the problem for them is solved in a similar way.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67582818","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
The method for constructing uniform planar approximations of the filter generator 构造滤波器发生器均匀平面近似的方法
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.17223/20710410/58/6
Ludmila A. Kuschinskaya
{"title":"The method for constructing uniform planar approximations of the filter generator","authors":"Ludmila A. Kuschinskaya","doi":"10.17223/20710410/58/6","DOIUrl":"https://doi.org/10.17223/20710410/58/6","url":null,"abstract":"Planar approximations of filter generators can be used to restore its initial state from a segment of the output sequence. The results of the study of one method for constructing plane approximations of a special form are presented.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67583514","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
Effective algorithm for finding shortest paths in dense Gaussian networks 稠密高斯网络中寻找最短路径的有效算法
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.17223/20710410/58/9
E. Monakhova, O. Monakhov
{"title":"Effective algorithm for finding shortest paths in dense Gaussian networks","authors":"E. Monakhova, O. Monakhov","doi":"10.17223/20710410/58/9","DOIUrl":"https://doi.org/10.17223/20710410/58/9","url":null,"abstract":"As a promising topology of networks on a chip, we consider a family of Dense Gaussian Networks, which are optimal circulant degree four graphs of the form C(D2 + (D + 1)2; D, D + 1). For this family, an algorithm for finding the shortest paths between graph vertices is proposed, which uses relative addressing of vertices and, unlike a number of the known algorithms, allows to calculate the shortest paths without using the coordinates of neighboring lattice zeros in a dense tessellation of graphs on the ℤ2 plane. This reduces the memory and execution time costs compared to other algorithms when the new algorithm is implemented on a network-on-chip with a Dense Gaussian Network topology.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67583593","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
Атака Винера и слабые ключи криптосистемы RSA 维纳攻击和RSA密码系统的薄弱钥匙。
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.4213/dm1773
Андрей Евгеньевич Тришин, Andrei Evgen'evich Trishin
{"title":"Атака Винера и слабые ключи криптосистемы RSA","authors":"Андрей Евгеньевич Тришин, Andrei Evgen'evich Trishin","doi":"10.4213/dm1773","DOIUrl":"https://doi.org/10.4213/dm1773","url":null,"abstract":"Доказано, что обобщенная атака Винера на криптосистему RSA позволяет находить не только малые, но и некоторые большие показатели расшифрования $d$, а доля слабых относительно данной атаки показателей $d$ эвристически оценивается величиной $O(N^{-1/2})$.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"41 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73763768","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
Linear-time minimization of Aho-Corasick automaton Aho-Corasick自动机的线性时间最小化
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.4213/dm1730
Е.И. Фурлетова, Evgeniya Igorevna Furletova
{"title":"Linear-time minimization of Aho-Corasick automaton","authors":"Е.И. Фурлетова, Evgeniya Igorevna Furletova","doi":"10.4213/dm1730","DOIUrl":"https://doi.org/10.4213/dm1730","url":null,"abstract":"Автомат Ахо - Корасик используется при поиске вхождений слов в текст. В работе предложено отношение эквивалентности $stackrel{R}{sim}$ на состояниях автомата Ахо - Корасик и доказана неотличимость $stackrel{R}{sim}$-эквивалентных состояний. Также разработан алгоритм построения $stackrel{R}{sim}$-минимального автомата, состояния которого - классы $stackrel{R}{sim}$-эквивалентности. Емкостная и временная сложности алгоритма линейны по числу состояний изначального автомата Ахо - Корасик. Рассмотрены случаи, при которых отношения $stackrel{R}{sim}$-эквивалентности и неотличимости состояний тождественны и, соответственно, предложенный автомат является приведенным.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"35 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80089838","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
Hadamard square of linear codes pasted side-by-side 线性代码并排粘贴的阿达玛正方形
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.4213/dm1763
Иван Владимирович Чижов, I. Chizhov
{"title":"Hadamard square of linear codes pasted side-by-side","authors":"Иван Владимирович Чижов, I. Chizhov","doi":"10.4213/dm1763","DOIUrl":"https://doi.org/10.4213/dm1763","url":null,"abstract":"Последовательно соединенные коды порождаются матрицами, которые получаются последовательным соединением порождающих матриц других линейных кодов. В работе получена оценка вероятности того, что квадрат Адамара последовательно соединенных случайных линейных кодов равен декартову произведению квадратов Адамара линейных кодов, участвующих в соединении.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89293892","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
Предельное совместное распределение статистик критериев приближенной $phi$-энтропии 接近美元/ phi -熵标准的极限综合统计分布
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.4213/dm1775
Максим Павлович Савелов, M. P. Savelov
{"title":"Предельное совместное распределение статистик критериев приближенной $phi$-энтропии","authors":"Максим Павлович Савелов, M. P. Savelov","doi":"10.4213/dm1775","DOIUrl":"https://doi.org/10.4213/dm1775","url":null,"abstract":"Рассмотрим последовательность независимых полиномиальных испытаний с $s$ исходами. Одним из критериев, используемых для проверки гипотезы о равновероятности исходов, является критерий приближенной энтропии. В 2000 г. А. Л. Рухиным была предложена статистика $T^{phi}$ более общего критерия приближенной $phi$-энтропии и найдено ее предельное распределение. В настоящей работе обобщение этого результата получено более простым способом. Кроме того, установлено предельное совместное распределение $(T^{phi_1}, …, T^{phi_r}$) в ситуации, когда исходы равновероятны. Как следствие, в случае $s=2$ найдено предельное совместное распределение статистик двух критериев пакета NIST: критерия приближенной энтропии и критерия «Serial Test» в предположении о том, что тестируемая последовательность является последовательностью испытаний Бернулли с параметром $frac12$.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"10 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78759111","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
О соотношениях между активностью схем из функциональных элементов и положительной чувствительностью функций алгебры логики
IF 0.2
Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI: 10.4213/dm1750
Михаил А Местецкий, Mikhail A Mestetskiy, М.С. Шуплецов, Mikhail Sergeevich Shupletsov
{"title":"О соотношениях между активностью схем из функциональных элементов и положительной чувствительностью функций алгебры логики","authors":"Михаил А Местецкий, Mikhail A Mestetskiy, М.С. Шуплецов, Mikhail Sergeevich Shupletsov","doi":"10.4213/dm1750","DOIUrl":"https://doi.org/10.4213/dm1750","url":null,"abstract":"Рассматривается связь между нижними оценками статической активности $E(Sigma)$ и динамической активности $S(Sigma)$ приведенной схемы из функциональных элементов $Sigma$ и положительной чувствительностью $operatorname{ps}(f)$ функции алгебры логики $f$, реализуемой данной схемой. Для достаточно широкого класса базисов, состоящих из монотонных функций алгебры логики от не более чем $m$ переменных, элемента отрицания и булевских констант $0$ и $1$, доказана нижняя оценка $E(Sigma)geqslant lfloorfrac{operatorname{ps}(f)-1}{m}rfloor$. Для динамической активности схем построен контрпример, показывающий, что для стандартного базиса из элементов дизъюнкции, конъюнкции и отрицания не существует линейной по $operatorname{ps}(f)$ нижней оценки динамической активности.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"33 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82353742","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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