Русский
06.2014 - Volume 18 Issue 2 (PDF)
The article describes the MaTIS department, its main areas of activity, tasks and achievements.
Keywords: mathematical theory of intelligent systems.
Methods for modeling incomplete and unreliable knowledge of the model \(M(x)\) of an object, depending on an unknown x ∈ X, expressed in the form of subjective judgments of the researcher are considered. The mathematical model of subjective judgments is defined as an uncertain element xe, canonical for the space \((X,\rho(X),Pl^\widetilde{x})\) with measures of likelihood and confidence, which characterizes the subjective judgments of the researcher about the truth of each value x ∈ X by the values of likelihood \(Pl^\widetilde{x}\) of the equality \(\widetilde{x} = x\) and confidence \(Bel^\widetilde{x} = x\) of the inequality \(\widetilde{x} \neq x\). Examples of studying uncertain models of a measuring and computing converter, ionospheric radio sounding, and Maxwell's pendulum are given.
Keywords: subjective judgments, likelihood, confidence, integral, measure, random uncertain element, intelligent dialogue, measuring and computing systems.
This paper sets the task of analyzing the security of an information network. An automata-theoretic approach is used to model the behavior of an intruder, a partial order relation is introduced on a set of states - vectors, the value of the coordinates of which reflects the level of access rights to the corresponding services on the analyzed nodes. The concept of an attack path is considered and the corresponding quantitative characteristics are studied. The problem of detecting network vulnerabilities is reformulated in terms of finding states reachable from a certain initial state and describing possible paths to them. Based on the constructed mathematical model, algorithms are proposed that solve the problems and their possible modifications. Approaches to reducing the constructed automaton are also considered.
Keywords: computer security, security assessment, finite state machines, attack paths.
The paper shows how a flat environment "generates" images, and how pattern recognition is represented in this case. Some statements about the properties of image codes are proved.
Keywords: pattern recognition, visual images, mathematical modeling in biology, robotic vision.
A system of relations for knowledge formalisms, which constitute a fragment of the family of recognized approaches to knowledge description formats in intelligent systems, is proved.
Keywords: knowledge representation formalism, semantic structure, algebraic structure, semantic embedding.
The paper considers the problem of automatic recognition of texts of laws related to filling out reporting forms. This task is as follows: to create a computer program that would accept texts of laws as input and would output another program that would fill out a form in accordance with these laws. A method for solving this problem is proposed, based on the technology of computer modeling of logical processes.
Keywords: semantic analysis of texts, normative legal acts, computer modeling of logical processes.
A number of papers study the relationship between such important, from the point of view of theoretical cryptography, properties of Boolean functions as nonlinearities of various orders (the distance of a function to polynomials of degree no higher than a fixed one) and algebraic immunity. One of the main areas of research is the issue of obtaining lower bounds for nonlinearity of a fixed order via the value of algebraic immunity of a function. In particular, exact bounds for nonlinearities of the first and second orders were obtained. In this paper, we prove a new bound for nonlinearity of an arbitrary order via the value of algebraic immunity, which is stronger than previous similar results by different authors.
Keywords: Boolean function, algebraic immunity, Boolean function degree, nonlinearity, high-order nonlinearity, Reede-Muller code.
This paper considers the problem of approximating time series by shortest-length broken lines with a given accuracy. A time series is interpreted as a sequence of plane points, and the problem of approximating this sequence by a broken line leads to finding the shortest path between two segments. An algorithm is obtained that solves the problem using the construction of a visibility graph and Dijkstra's algorithm.
Keywords: plane point approximation, visibility graph, plane with polygonal obstacles, shortest path, Dijkstra's algorithm.
The article discusses the implementation of a CRM system for the Android platform. The system allows you to manage clients, contacts, and contacts. The article describes the interface of this system and its implementation, as well as the implementation of data synchronization with the server part.
Keywords: Android, CRM, synchronization.
The problem of synchronizing data and code between servers physically located in different places is considered. A database replication system is implemented, a version control system is configured, as well as a directory content replication system.
Keywords: version control system, database replication, git, unison.
The work is devoted to the presentation of the results of computer modeling of logical processes in the logical system "Iskra". The issues related to the training of computer problem solvers and automatic synthesis of techniques were studied.
Keywords: intelligent system, self-learning, logical system, computer problem solver, automatic synthesis of techniques.
Given a natural number N, a scheme for checking the affine equivalence of two flat N-point images is constructed using a basis of linear functions, a logarithm, an exponential, a signum function, and a frame root extraction function. The nonlinear depth of the schemes does not depend on N. Thus, the processing time of images by the obtained schemes does not depend on the size of the problem.
Keywords: keypoints of images, keypoint dynamics, video sequence, affine transformation of a plane, checking the affine equivalence of images, nonlinear depth scheme.
The article considers the power of flat circuits simulating VLSI. A flat circuit is a laying out of a circuit of functional elements on a two-dimensional integer grid. All power estimates for flat circuits are also true for more complex VLSI models. The considered power measure models the electrical power allocated both to logical elements and to circuit wires. It is assumed that the electrical power consumed by a wire of unit length is commensurate with the power consumed by one logical element. A lower bound \((m\sqrt{|D|})/(\sqrt{min(m,log|D|)}\) for the average cardinality of almost all partial Boolean operators with domain D and m outputs is obtained. Lower bounds for the cardinality under some constraints on the arrangement of the circuit outputs are also obtained.
Keywords: circuits from functional elements, VLSI model, flat circuits, circuit cardinality, Shannon function, lower bounds, partial Boolean operators.
This paper generalizes the construction of a parametric family of Latin squares over a direct product of Abelian groups, previously proposed in work [2], to the multidimensional case in order to increase the number of parameters. A criterion for the feasibility of this design is given. The issue of the relationship between correctness and cycles in the essential dependence graph for functions over residue rings is also considered.
Keywords: correct family of functions, Latin squares, parametric family of Latin squares, criterion for a multidimensional Latin square, essential dependence graph of a family of functions, relationship between correctness and cycles in the essential dependence graph.
In the author's dissertation "On the Optimization of Structural Implementation of Neural Networks", neural circuits were considered over the field of real numbers. Most of the results related to McCulloch-Pitts circuits are literally transferred to neural circuits over the field of rational numbers, but the concept of a transcendental number was significantly used to prove one of the theorems. Nevertheless, the result of the theorem for neural circuits over the field of rational numbers is preserved. A new proof is given in this paper.
Keywords: neural circuits, Shannon function.
This paper studies quasi-cyclic low-density codes. An upper bound for the minimum distance is given, which depends on the minimum and maximum number of ones in the columns of the parity-check matrix of the code.
Keywords: minimum distance, quasi-cyclic low-density code.