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## Behavior of the Shannon Function for Some Families of Classes of Three-Valued Logic Functions

Moscow University Mathematics Bulletin. 2012. Vol. 67. No. 4. P. 182-184.

Turkensteen M., Malyshev D., Goldengorin B. I. et al., Journal of Global Optimization 2017 Vol. 68 No. 3 P. 601-622

The tolerance of an element of a combinatorial optimization problem with respect to its optimal solution is the maximum change of the cost of the element while preserving the optimality of the given optimal solution and keeping all other input data unchanged. Tolerances play an important role in the design of exact and approximation algorithms, ...

Added: December 10, 2016

Дали Ф. А., Mironkin V., Проблемы информационной безопасности. Компьютерные системы 2018 № 1 С. 113-121

Two models of the tree modes of hash functions are introduced. For each model algorithms of computing of the hash code are formulated and their numerical characteristics are obtained. In terms of the constructed models we classify some existing algorithms for parallel hashing and identify some weaknesses of corresponding primitives. ...

Added: May 28, 2018

St. Petersburg : The Euler International Mathematical Institute, 2014

The conference Philosophy, Mathematics, Linguistics: Aspects of Interaction 2014 (PhML-2014) is a sequel in the series of conferences intended to provide a forum for philosophers, mathematicians, linguists, logicians, and computer scientists who share an interest in cross-disciplinary research. The conference PhML-2014 is endorsed by the American National Committee of the Division of Logic, Methodology and Philosophy ...

Added: June 23, 2014

Kochergin V. V., Kochergin D. V., Moscow University Mathematics Bulletin 2016 Vol. 71 No. 2 P. 55-60

The problem of the complexity of word assembly is studied. The complexity of the word refers to the minimum number of concatenation operations sufficient to obtain this word on the basis of one-letter words over a finite alphabet $A$ (repeated use of the received words is permitted). Let $L_A^c(n)$ be maximum complexity of words of ...

Added: October 8, 2018

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

MDPI Open Access Publishing, 2018

Added: October 4, 2018

Dagaev D., Вестник Московского университета. Серия 1: Математика. Механика 2011 Т. 66 № 3 С. 60-63

The problem of the realization complexity for functions of the three-valued logic taking values from the set {0, 1} by formulas over incomplete generating systems is considered. Upper and lower asymptotic estimates for the corresponding Shannon functions are obtained. ...

Added: October 4, 2012

Ilya Makarov, Olga Gerasimova, Logica Universalis 2017

We describe a method of finding the canonical types of formulas based on three-valued projection logic functions. The method focuses on a separation of all tuples of values for variables into disjoint sets and write indicators of these sets using only functions from the closed class under consideration. We obtain the required canonical type combining ...

Added: September 25, 2015

Kanovich M., Ban Kirigin T., Nigam V. et al., Computer Languages, Systems & Structures 2014 No. 40 P. 137-154

It is well-known that the Dolev–Yao adversary is a powerful adversary. Besides acting as the network, intercepting, decomposing, composing and sending messages, he can remember as much information as he needs. That is, his memory is unbounded. We recently proposed a weaker Dolev–Yao like adversary, which also acts as the network, but whose memory is ...

Added: March 23, 2015

Dagaev D., Вестник Московского университета. Серия 1: Математика. Механика 2012 Т. 67 № 4 С. 58-61

A certain countable set of families of classes of three-valued logic functions taking values from the set {0,1} is considered. For each class from these families and for each its finite generating system, the order of growth of the corresponding Shannon depth function is obtained. ...

Added: October 4, 2012

Makarov D., Yashunsky A., Journal of Applied and Industrial Mathematics 2019 Vol. 13 No. 2 P. 280-289

We consider the two-dimensional generalizations of de Bruijn sequences; i.e., the integer-valued arrays whose all fragments of a fixed size (windows) are different. For these arrays, dubbed sub-de Bruijn, we consider the complexity of decoding; i.e., the determination of a position of a window with given content in an array. We propose a construction of ...

Added: September 9, 2020

Granata D., Behdani B., Pardalos P. M., Journal of Combinatorial Optimization 2012 Vol. 24 No. 4 P. 459-467

We address the complexity class of several problems related to finding a path in a properly colored directed graph. A properly colored graph is defined as a graph G whose vertex set is partitioned into X(G) stable subsets, where X(G) denotes the chromatic number of G. We show that to find a simple path that ...

Added: January 24, 2013

Katchanov Y. L., Shmatko N., Applied Mathematical Sciences 2013 Vol. 7 No. 73 P. 3591-3599

http://dx.doi.org/10.12988/ams.2013.35256 This article puts forth an axiomatic description of the complexity of an object of sociological investigation. The proposed axioms allow us to determine complexity within the framework of mathematical sociology such as the variational principle, which is formed relative to the state of the object of sociological investigation. On the basis of this principle ...

Added: September 22, 2013

Lozhkin S. A., Danilov B.R., Computational Mathematics and Modeling 2012 Vol. 23 No. 4 P. 487-506

The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements may have different input delays. Asymptotic bounds of the form τ B n±O(1), where τ B is a constant that depends only on the basis B, are obtained for ...

Added: December 2, 2019

Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188

The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...

Added: December 2, 2019

Dagaev D., Вестник Московского университета. Серия 1: Математика. Механика 2010 Т. 65 № 2 С. 53-56

Upper and lower estimates for the complexity of functions of the 3-valued logic taking values from the set {0, 1} with linear Boolean restrictions are derived. ...

Added: October 4, 2012

Skripchenko A., Troubetzkoy S., Entropy and Complexity of Polygonal Billiards with Spy mirrors / Cornell University. Series math "arxiv.org". 2015. No. 1501.04584.

We prove that a polygonal billiard with one-sided mirrors has zero
topological entropy. In certain cases we show sub exponential and for other
polynomial estimates on the complexity. ...

Added: January 26, 2015

Springer, 2020

Springer Proceedings in Complexity publishes proceedings from scholarly meetings on all topics relating to the interdisciplinary studies of complex systems science. Springer welcomes book ideas from authors. The series is indexed in Scopus.
Proposals must include the following: - name, place and date of the scientific meeting - a link to the committees (local organization, international advisors etc.) - ...

Added: February 23, 2020

Kontchakov R., Pratt-Hartmann I., Zakharyaschev M., Artificial Intelligence 2014 Vol. 217 P. 43-75

The language RCC8RCC8is a widely-studied formalism for describing topological arrangements of spatial regions. The variables of this language range over the collection of non-empty, regular closed sets of n -dimensional Euclidean space, here denoted RC+(Rn)RC+(Rn), and its non-logical primitives allow us to specify how the interiors, exteriors and boundaries of these sets intersect. The key ...

Added: March 24, 2015

Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions

Makarov I., Logica Universalis 2015 Vol. 9 No. 1 P. 1-26

The article deals with finding finite total equivalence systems for formulas based on an arbitrary closed class of functions of several variables defined on the set \{0, 1, 2\} and taking values in the set \{0,1\} with the property that the restrictions of its functions to the set \{0, 1\} constitutes a closed class of ...

Added: February 28, 2015

Blank M., Problems of Information Transmission 2014 Vol. 50 No. 4 P. 350-363

We study functional consequences of the interlacing property consisting in
that a new configuration of “particles” occurs in gaps between elements of
a previous configuration. This property was introduced by I.M. Gelfand in
terms of spectra of sequences of matrices of increasing dimensions and turned
out to be highly needed in many areas of modern mathematics. We examine
conditions under ...

Added: March 20, 2015

Ложкин С. А., Danilov B. R., Прикладная математика и информатика 2011 № 39 С. 107-129

The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements may have different input delays. Asymptotic bounds of the form τ_B n ± O(1), where τ_B is a constant that depends only on the basis B, are obtained for ...

Added: December 2, 2019

L. Beklemishev, Flaminio T., Studia Logica 2016 Vol. 104 No. 1 P. 1-46

Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic. ...

Added: March 13, 2016

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016