Computer Sciences

Solving Some Problems of Automata Behaviour Analysis

Authors: Tyapaev L. B.

In the context of the geometrical approach and by means of geometrical methods automaton behaviour is studied as curves on the plane. The attention is called to a new way of setting the finite-state machines as a functional curve on the plane. Also within the limits of the geometrical approach problems of automaton analysis, synthesis, diagnosis and transformation have been also investigated. 

Construction of Diagnostic Expert Systems on the Basis of Neural Networks

Authors: Solovyev V. M.

In work questions of construction of diagnostic expert systems (DES) on the basis of neural networks (NN) with lateral braking are considered. Methods of training of such networks are offered. Questions of reception of the diagnostic information in the heterogeneous computer network and uses of the aprioristic information on the importance of diagnostic attributes are analyses. Results of work can be used at construction NN diagnostic systems (clustering).

On Recognition of Languages of Arbitrary words by Finite Semigroups

Authors: Molchanov V. A.

Based on methods of nonstandard analysis we elaborate in this paper a new approach to the theory of infinite products in finite semigroups. The main theorems of the paper show that infinite products of elements of standard sequences in finite semigroups can be viewed as a two-sided algebraic counterpart of finite products of a special kind. Using these results we construct a universal functor of the category of finite semigroups to the category of finite four-sorted algebras of a special kind and introduce a notion of a language of arbitrary words recognized by finite semigroups.

On Minimal Strongly Connected Congruences of a Directed Path

Authors: Mirzayanov M. R.

Let G = (V, α) be a directed graph. An equivalence relation θ ⊆ V × V is called a strongly connected congruence of G if the quotient graph  G/θ is strongly connected. Minimal (under inclusion) strongly connected congruences of a directed  path are described and the total amount of them is found.

Some Questions on Minimal Extensions of Graphs

Authors: Abrosimov M. B.

Some statements concerning minimal extensions of graphs are presented that seem to be quite evident at first sight but are not so simple under closer inspection.