Русский
2018 year, volume 22 issue 2 (PDF)
The paper considers the possibilities of applying the technology of assessment and monitoring of complex processes of ensuring information security in the task of sustainable development of the critical infrastructure of the Russian Federation. The structure of the critical infrastructure stability model, the possible scenarios for the system of information security assessment and monitoring, the analytical capabilities of the system are discussed.
Keywords: information security, critical infrastructure, technology for assessment and monitoring of complex processes, sustainable development.
In the framework of the Ilyushin’s theory of elastoplastic processes, in [3] for mathematical modeling of complex loading processes we use special type quasilinear equation with three state functionals. The functionals was calibrated using the experimental results [4] (R.A.Vasin, etc.) for 3D- helical trajectories of deformations. It turned out that the response on a helical trajectory of deformation takes a completely definite loading form, not exactly, but after the exhaustion of some trace of retard. On the helical trajectories of deformations the form of loading is the same: helical trajectory of deformations is becoming to helical trajectory of loading there and back. The used map preserves the geometry of space. This correspondence by Ilyushin is called as isomorphism theorem. All new theories use as the basis the directing vector of stresses and vectors constructed on the base of Frenet basis. For high-dimensional processes, the number of state functionals increases, so and the methods of their identification become more complicated. All models are completly verified. The results are given below.
Keywords: plasticity, plastic deformations, complex loading, state functional, identification of functionals, isomorphism theorem
The article is devoted to the drop and paste operations, which have been promoted by V.I. Levenshtein. The following two questions are asked and answered. What is the class of regular languages that are stable to the drop/paste operations? Are there any irregular languages that are stable to these operations?
Keywords: drop and paste operations, closed class, regular language.
The paper I.B. Kazakov, “Encoding in a covert channel of packet permutations” introduced a number of error models for codes over sets of permutations. Such error models induce graph structure on sets of permutations. Our research is focused on properties of these graphs. We show that the graphs consist of layers of independent sets; the layer that contains the given permutation is determined by the number of edges in the characteristic graph of the permutation. We estimate vertex degrees in the layers of the graph \((S_n)^2\) and use this estimate to bound the cardinality of an error-correcting kayer-based code. After that we develop a number of aids that allow to obtain upper bounds of code cardinality. We introduce the notions of symmetric layers and graph partitions and decompose \(S_n\) for some values of n into prisms and into graph products, i.e. generalised prisms. We also embed the graph \(S_n\) into \(E_{\frac{n(n−1)}{2}}\). Finally establish a connection between sizes of subgroups H ⊂ \(S_n\) and presence of n-step permutations in these subgroups.
Keywords: permutations, graph structure, error-correcting code.
This paper describes the lattice of all clones on the three-element set that contain all constant functions 0, 1, 2 and functions min, max. The clones are characterized as sets of predicates being preserved by them.
Keywords: clone theory, lattice of clones, three-valued logic.
A hyperautomatа is a finite automatа whose states are the sets of states of some finite automata. A hyperautomatа is called a group hyperautomatа if the semigroup of the automatа on which it is based is a finite group. In this paper, we study the question of the maximum number of regular languages that can be recognized by group hyperautomata.
Keywords: finite automata, hyperautomata, regular languages, finite groups.
The paper presents description the main problems of the development of systems evaluation and monitoring of processes in socio-technical systems. The tasks and technologies associated with them are considered, too. Solutions of the problems are discussed. The perspective directions of personalization of human interaction with the digital world and augmented intelligence are considered in the paper. The article is prepared based on the results of the author’s speech at the cathedral seminar of the Department of Mathematical Theory of Intelligence Systems of the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University «Theory of Automata» under the supervision of Professor V B. Kudryavtsev on March 21, 2018.
Keywords: Socio-technical systems, evaluation and monitoring of complex processes, fuzzy sets, personalization.
Flash memory in the last decade became dominant technology for storing data both for personal electronic devices and enterprise products: servers, network storages and data centers. Initially flash memory technology assumed storing only one data bit in flash cell (SLC-memory). Further development of production technology of flash memory and inegration of more powerfull error correction codes in flash memory modules made it possible to store 2 bits (MLC-memory) and even 3-bits (TLC-memory) of data. Increase of number of bits stored in each cell leads to significant increase of probability of error during read operation. Furthermore whith increase of programm-erase cycles electric charges stored in flash memory cells have tendency to decrease. This process also leads to increase of probability of error during read operation. Finally this process of charge decrease leads to flash memory failure when error correction code cannot fix all read errors. Rank method of storing data in flash cells is resilient to process of graduate decrease of cell charges. Moreover this method theoretiacally has higher area efficiency in comparison with conventional SLC/MLC/TLC memory. First in this paper brief description of conventional flash memory is given. Read operation is analyzed, basic model of read errors is described. Then rank method of storing data is presented. Estimated amount of memory stored by this method in comparison with conventional flash memory. Introduced Kendall-Tau distance between permutations. By means of this distance estimated area of rank memory taking in account technological limitations. Finally it’s analyzed area efficiency of rank flash memory in comparison with conventional flash memory. Explicitly described cases when rank memory has higher area efficiency than conventional SLC/MLC/TLC memory.
Keywords: rank flash memory, SLC/MLC/TLC flash memory, flash memory area efficiency.
Classes of linear automata over finite fields with composition operations (superposition and feedback) are considered. Previously an algorithm for checking the completeness of finite subsets was obtained for these classes. In the case of a simple field, all precomplete classes whose set is a countable reduced criterial system are found. Previously in the general case the set of closed classes was constructed, which is a criterial system, including the family of classes generated by maximal subfields in the transcendental extension of the finite field under consideration. For simple fields, all classes of this family were absorbed by other classes from the reduced criterial system. Therefore, in the present paper the family is being investigated in the case of finite fields that are not simple. It turned out that part of the elements of the family is also absorbed in this case, but also among its elements there are precomplete classes that are finitely generated and not contained among the precomplete classes of other families.
Keywords: linear automaton, adder, delay, feedback, composition operations, completeness check algorithm, precomplete class.