# Computer Sciences

## The Application of a Genetic Algorithm to Global Optimization Problem Solving on Parallel and Distributed Computing Systems

This article presents the results of the adaptation of method of searching the global minimum of multiextremal criterion function of multiple variables with constraints based on genetic algorithm for parallel and distributed computing systems. Two variants of genetic algorithm parallelization are proposed. The reliability and performance of parallel versions of an algorithm, depending on its parameters and the number of nodes in parallel computer system is investigated.

## On Varieties of Groupoids of Binary Relations

In the paper, the bases of identities of varieties generated by classes of groupoids of the binary relations are found.

## Abstract Characterization of Semigroups of Input Signals of Universal Planar Automata

Universal planar automata are universally attracted objects in the category of automata, for which sets of states and output signals are endowed with structures of planes. The main results of the paper give us necessary and sufficient conditions under which an arbitrary automaton is isomorphic to a universal planar automaton and an arbitrary semigroup is isomorphic to the semigroup of input signals of a universal planar automata.

## Models of Information K-Channels with Memory

Analysis of non-binary (K-ary, K > 3) information channels (IC) with memory as complex stochastic structures is rather complicated mathematically. Of significant interest is the synthesis of simplified mathematical models for such channels that allow clarifying relatively simply the most important regularities occurring in real processes. Modeling of IC (K-channels) with memory is a vital problem that has both theoretical and practical importance.

## Increasing of Information Reliability of Digital Systems with QAM/COFDM-Modulation

Ensuring of a high level of information reliability is one of the most important tasks of the synthesis of digital communication systems for various applications.

## Optimization of Calculus Mesh for Cryobiology Problem Based on Multidimensional Hashing Using NumPy

In this paper, by the example of solving the problem of constructing the temperature field in cryotherapy shows efficiency of geometric hashing performed on the basis of the NumPy package for constructing appropriate computational grid. Such an arrangement implies for each node to determine its position relative to the polygonal area of irregular shape. Such forms often modeled surfaces of internal organs. Solution build computational grid will allow for 3D visualization of the temperature field in the vicinity of cryotherapy, which will facilitate the timely temperature control.

## Minimal vertex 1-extensions of palm trees

Minimal vertex 1-extension of graphs can be regarded as a model of optimal 1-node fault tolerant implementation of a system. This paper is about of the 1-vertex extensions of a graphs from a special class named palm trees.This article presents a solution to the problem of finding the minimal vertex 1-extension of palm trees with two leafs.

## Recognition of a linear automaton outputs by the fuzzy outputs

A method is proposed to solve the recognition problem for unknown input sequences of a linear automaton when observed the fuzzy outputs.

## The parallel variant of conditional optimization algorithm with Box complex method

This article presents the results of the adaptation algorithm for global extremum searching with presence explicit and implicit constraints complex method created by Box for systems of the distributed and parallel computing. The optimal count of nodes of computing system from the point of view of reliability a global extremum finding and time of its search is defined.

## Affine transformations of geometrical images of finite automata

A subclass of affine transformations on the set of geometrical images of finite automata is investigated. The results about the characteristics and the form of these transformations are described.