2021 year, volume 25, issue 1 (PDF)

In memory of Oktay Muradovich Kasim-Zade

Vtorushin Yu.I. Evidence algorithm for first-order logic with equality

The article is a continuation of the article [1]. An algorithm for verifying formalized mathematical proofs for first-order predicate logic with equality is considered. Theorems about its correctness and completeness are proved.

Keywords: automated theorem proving, system for automated deduction, first order language, predicate calculus, production system, artificial intelligence.

Chechkin A.V. The thesis about the presence of artificial intelligence

The thesis about the necessary and sufficient requirement for the presence of artificial intelligence in smart systems for various purposes is formulated and substantiated. Necessity is the presence of redundant readings of the first signaling system or the primary sensorium of smart systems. Sufficiency is the presence of a second signaling system or language of communication of smart systems as a linguistic superstructure, a linguistic sensorium of the conscious part of the primary sensorium. The problems of creation and safe operation of smart systems are discussed. The article was written for the purpose of active participation in the current discussion of highly respected specialists of the M.V. Lomonosov on the topic “Artificial Intelligence: Problems and Prospects” [1].

Keywords: artificial intelligence, smart system, radical, language, internet of things, interface, natural intelligence, information and system security of intelligence.

Aleshin S.V. Triangles and Lagrange Equations

The paper considers the problem of the equilibrium mutual arrangement of two triangles and proposes a solution to this problem based on the method of Lagrange multipliers. Two-time iteration of this method gives analytical solution.

Keywords: Lagrange method, transformation on a plane, similarity, rotation, shift, triangle.

Zhuravlev A. D. Possible approach to the problem of predicting sports results using data analysis methods

This article is devoted to the construction of an algorithm for reducing the problem of predicting sports results to the problem of binary classification. At the same time, the optimality of this algorithm has been substantiated from the point of view of the application of forecasting results in the game against bookmakers.

Keywords: machine learning, predicting sports results, binary classification.

Sokolov A.P., Aliseychik P.A., Moiseev S.V. Distributed companion trajectory search algorithm

The work is focused on development of the distributed algorithm for search of companion-trajectories. We call two trajectories as companion-trajectories if they both contain section of required duration on which at any time moment distance between two objects is no larger than specified threshold. It’s assumed that search is performed on database that is so big that it cannot be stored and processed on a single work station. Such tasks are usually called big-data tasks. We define trajectory quantization procedure, introduce cell index data structure, define similar trajectories. Then we build effective algorithm for search of similar trajectories. Based on this algorithm we develop effective local and distributed algorithms for search of companion trajectories. Asymptotic complexity of these algorithms is estimated.

Keywords: big-data, geo-spatial data analysis, trajectory analysis, companion-trajectory search, similar trajectory search, traffic analysis.

Valinurov D.Y. Locally recoverable codes on graphs

The locally recoverable codes (LRC codes) are linear codes with an important for applications property that every symbol of a codeword can be recovered from a small set of other symbols. Codeword symbols can be interpreted as servers with information. It is natural to define a topology of these servers as a graph so that every server can be recovered using neighborhood servers in this graph. The paper provides LRC code constructions for some topologies and bounds on the rate of such codes.

Keywords: erasure coding, locally recoverable codes, codes on graphs.

Konovalov A.Yu. \( \Lambda \)-expressions for primitive recursive functions in the Grzegorczyk hierarchy

In this paper we consider \( \Lambda \)-expressions constructed from universal functions for functional classes of the Grzegorczyk hierarchy. We will find a sufficient condition such that a given \( \Lambda \)-expression determines a primitive recursive function from some level of the Grzegorczyk hierarchy.

Keywords: Grzegorczyk hierarchy, primitive recursive functions, strictly primitive recursive realizability.

Kuznetsova E.V. The number of states of a universal automaton of an infinite screen that implements bidirectional motion on a ray

The paper considers the implementation of one class of laws of motion by a cellular automaton on an infinite screen. It is shown that the minimum number of states of a cellular automaton simulating the bidirectional movement of a point on a ray at which the point does not make 2 movements to the right in a row is 5.

Keywords: cellular automaton, number of states, infinite screen, bidirectional motion, image construction.

Ronzhin D.V. A-completeness recognition for finite systems with additives of linear automata over the ring of dyadic rationals

This work concerns questions of A-completeness of finite systems of linear automata over the ring of dyadic rationals. Condition of completeness of linear automata system, which includes automaton that models addition in the first step is described. For the formulated set of maximum subclasses in the class of linear automata over the ring of dyadic rationals decidability of a problem of finite set inclusion into these classes is proven.

Keywords: finite state automata, linear automata, dyadic rationals, A-completeness, maximum subclasses, decidability.

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