# Computer Sciences

## Representation of universal planar automata by autonomous input signals

Universal planar automata are universally attracted objects in the category of automata, whose sets of states and output signals are endowed with structures of planes. The main result of the paper shows that any universal planar automaton is isomorphic to a many-sorted algebraic system canonically constructed from autonomous input signals of the automaton.

## Queueing networks with batch movements of customers, blocking and clusters

Two types queueing networks with batch movements of customers – networks with blocking and networks with clusters are investigated. Product form stationary distribution for networks with blocking of transitions in states, in which the number of customers in queueing systems exceeds given values, is derived. For queueing networks with disjoint clusters of systems the problem of analyzing is solved and the product form stationary distribution is found. Examples of analysis of the network with blocking and the network with clusters are presented.

## Identification of a state machine structure with finites fragment of behavior

Identification of a state machine structure with finite fragments of behavior is discussed. The state machine behavior is a set of various finite-sequential (f.-s.) functions realized in a state machine, and under a finite fragment of behavior we mean traces of f.-s. functions and state machines. The concept of an identifying trace for a state machine irredundant over its realization is introduced.

## On stability theory of autonomous angular stabilization system for combined dynamical systems

Studied the effect on the stability of the longitudinal acceleration discretely-continuum model of single-channel angular stabilization system with of delayed argument. Methods of construction asymptotic stability areas and analysis of impulse transition functions are developed. The critical values of the longitudinal acceleration are defined.

## Characterization of graphs with a small number of additional arcs in a minimal 1-vertex extension

A graph G∗ is a k-vertex extension of a graph G if every graph obtained from G∗ by removing any k vertices contains G. k-vertex extension of a graph G with n+k vertices is called minimal if among all k-vertex extensions of G withn+k vertices it has the minimal possible number of arcs. We study directed graphs, whose minimal vertex 1-extensions have a specific number of additional arcs. A solution is given when the number of additional arcs equals one or two.

## Analysis of closed unreliable queueing networks with batch movements of customers

Closed unreliable queueing network with batch movements is considered. The main result of the paper is the steady state distribution for given type queueing networks.

## On upper bound of vertex distinguishing word length on vertex labeled graph

The problem of vertex distinguishing on vertex labeled graphs is considered. Two vertices are called distinguishable if associated languages over the alphabet of labels are different. A linear upper bound of vertex distinguishing word length equal to half the number of vertices is obtained.

## T-irreducible extension for union of paths and cycles

A graphH with nodes is an extension of a graph G with nnodes if each maximal subgraph of H contains G. Trivial extension of a graph G is the connection of graph G and the singleton graph (i.e. we add one node to the graph G and this node join with each node of G). T-irreducible extension of graph G is an extension of the graph G which is obtained by removing maximal set of edges from the trivial extension of G. One of T-irreducible extensions is constructed for an arbitrary union of cycles and paths.

## Ordered automata and tolerant images of FDA

Finite deterministic automaton (FDA) with partially ordered (an ordered automaton) sets of states, input and output symbols is described in the article. The mapping of FDA on an ordered automaton, which is named "p-morphism" is defined. It is shown that so called tolerant images, which are constructed with the help of compatible tolerances on the set of states of FDA, are particular case of ordered automata, which are connected with the original automaton by a p-morphism.

## Using parallel computing technologies for modeling of metallic photonic crystals

This article presents opportunities of using parallel computing technologies Message Passing Interface and Open Computing Language for modeling of metallic photonic crystals with the method of Green's functions and integral equations. The efficiency of these technologies is analized and the results are presented.