# Computer Sciences

## On the Directional Movement of a Collective of Automata without a Compass on a One-dimensional Integer Lattice

A collective of finite automata has to preserve unidirectional movement on one-dimensional integer lattice whose elements (vertices) are unlabelled. The automata does not distinguish between equally labelled vertices by their coordinates of direction (that means each automaton has no compass). We considered collectives consisting of an automaton and some pebbles, i.e. automata of the simplest form, whose positions are completely determined by automaton.

## Morphismes Based on Compatible Tolerances of Finite Automata

It is suggested a method of a construction with the help of some triple of tolerances deﬁned on the sets of states, input and output symbols of an ﬁnite deﬁnite automaton an another automaton which is connected with the original automaton by a certain morphism.

Considered construction generalizes the known method of ﬁnding of the homomorphic images of an automaton with the help of a triple of equivalences, which satisﬁes to the certain conditions.

## Hash Functions for Diagnostic Information Reduction

In this paper we present a new approach for the solution of problem of the diagnostic information reduction. This approach is based on use of hash functions delivering a compact signature for records in a fault dictionary. The experimental results show a considerable decrease in the storage requirement of diagnostic information reduced with the help of such functions.

## One Model for Representation of Production Knowledge Base

We offer a new approach to structure of production knowledge bases. In our approach the knowledge base is modeled by multigraph. We offer a deduction algorithm for such a model. The experimental results show the effectiveness of proposed methods.

## The Tasks of Interactive Processing of Search Queries in the Set Theory Formalization

In the paper description in the set theory of main mechanisms of query processing is fullﬁled. Focusing and widening of fullnes are described as query processing. The methods are used in the project of Intelligent Search Engine. Newness of the approach consists that there is the ﬁrst systematization of interactive methods of word sense disambiguation in man-machine complex «user-search engine». Engineer realization of the methods was done in SQL.

## Solving Some Problems of Automata Behaviour Analysis

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

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

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

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

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.