# Computer Sciences

## 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.

## The Geometric Form of Automaton Mappings, Recurrent and Z-recurrent Deﬁnition of Sequences

For automaton mappings we present a method to construct geometric images, a method for complexity estimate by geometric forms, a method of Z-recurrent deﬁnition of sequences. A method for complexity estimate for ﬁnite sequences by recurrent and Z-recurrent numerical indicators is proposed. Numerical indicators of recurrent and Z-recurrent deﬁnitions of sequences are systematized into the spectrum of recurrent deﬁnitions with 5 levels of numerical indicators.

## The Sperner Property for Polygonal Graphs Considered as Partially Ordered Sets

A ﬁnite poset is said to have the Sperner property if at least one of its maximum antichains is formed from elements of the same height. A polygonal graph is a directed acyclic graph derived from a circuit by some orientation of its edges. The reachability relation of a polygonal graph is a partial order. A criterion is presented for posets associated with polygonal graphs to have the Sperner property.

## On Applications of Wavelets in Digital Signal Processing

Discrete Wavelet transform associated with the Walsh functions was deﬁned by Lang in 1998. The article describes an application of Lang’s transform and some its modiﬁcations in analysis of ﬁnancial time series and for the compression of fractal data. It is shown that for the processing of certain signals the studied discrete wavelet transform has advantages over the discrete transforms Haar, Daubechies and the method of zone coding.