Computer Sciences

About closed queuing networks with variable number of queues

Authors: Tananko I. E.

Consider a closed queueing network with the possibility of breakdowns at each server. When a breakdown occurs at one server, all customers there are transferred in queue with operational server immediately, and the server is then sent for repair. Steady- state probability of the queue sizes is obtained, and is shown to have a product form solution.

Some interval problems of the theory of discrete linear systems

Authors: Kupriyanova Y. V., Speranskii D. V.

Artificial neural networks can be used effectively for a quite general class of problems. Still there exists no formal foundation of some important constructions used in the theory. In this paper an
attempt is undertaken to formalize some concepts of neuroinformatics and consider their properties from the point of view of applied universal algebra. It is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems on homomorphisms and congruences.

Geometrical images of finite state machines

Authors: Tverdokhlebov V. A.

In this work a new way of defining finite state machines (FSM) is being suggested. The discrete word geometry is built for that purpose, in which machine image is expressed as a set of lines. The methods of synthesis and analysis of geometrical images of FSMs and their features are researched. The new way of defining the FSMs allows analyzing the machine's behavior, excluding the exhausting recursive procedure of defining the initial fragments of machine functioning.

Algebraic properties of recurrent neural networks of discrete time

Authors: Slepovichev I. I.

Artificial neural networks can be used effectively for a quite general class of problems. Still there exists no formal foundation of some important constructions used in the theory. In this paper an attempt is undertaken to formalize some concepts of neuroinformatics and consider their properties from the point of view of applied universal algebra. It is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems on homomorphisms and congruences.

T-irreducible extension for unions of complete graphs

Authors: Kurnosova S. G.

T-irreducible extension is one of kinds of optimal extensions of graphs. Constructions of optimal extensions are used in diagnosis of discrete systems and in cryptography. A graph H with n+1 vertices is called an extension of a graph G with n vertices if G can be embedded in every maximal subgraph of H. Any graph Ghas the trivial extension that is the join ng+of G with some outer vertex v. T-irreducible extensions are obtained from the trivial extension by removal of maximal number of edges in such a way that the extension property is preserved.