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37
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Introduction
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September 2000 - September 2001
September 2006 - October 2020
Education
September 1986 - December 1997
Publications
Publications (37)
Problem and goal. Language disorders of different kinds may cause personal issues and prevent the successful development of an individual. Early diagnostics and precise correctional recommendations enable such issues to be resolved efficiently in childhood. A modern speech therapist needs mobile facilities that can both make his/her work with presc...
The article presents the results of experiments on the conjunctive decomposition of various representations of Boolean functions (ZDD, BDD, OKFDD, AIG) by methods that are derived by specializing the general decomposition algorithm. Test sets are random Boolean functions with various parameters, as well as a set of well-known benchmarks used to tes...
Polynomial factorization is a classical algorithmic problem in algebra, which has a wide range of applications. Of special interest is factorization over finite fields, among which the field of order two is probably the most important one due to the relationship to Boolean functions. In particular, factorization of Boolean polynomials corresponds t...
We consider the complexity of decomposing a Boolean function into a conjunction of components, which may share a (possibly empty) given set of variables Δ. Boolean functions are given as expressions in CNF, DNF, full DNF, and ANF and it is assumed that decomposition components must be in the same normal form as the input expression. We show that de...
In this paper, we present several software tools to diagnose and correct child language disorders. These tools implement a playing strategy to decrease stress and improve effectiveness. In addition, we describe a tool for an alternative communication via pictograms.
In 2010, Shpilka and Volkovich established a prominent
result on the equivalence of polynomial factorization and identity testing. It follows from their result that a multilinear polynomial over the finite field of order 2 can be factored in time cubic in the size of the
polynomial given as a string. Later, we have rediscovered this result and prov...
We consider a Cartesian decomposition of datasets, i.e. finding datasets such that their unordered Cartesian product yields the source set, and some natural generalization of this decomposition. In terms of relational databases, this means reversing the SQL CROSS JOIN and INNER JOIN operators (the last is equipped with a test verifying the equality...
In 2010, A. Shpilka and I. Volkovich established a prominent result on the equivalence of polynomial factorization and identity testing. It follows from their result that a multilinear polynomial over the finite field of order 2 (a multilinear boolean polynomial) can be factored in time cubic in the size of the polynomial given as a string. We have...
In this article, we present an algorithm for conjunctive bi--decomposition of boolean polynomials where decomposition components share only prescribed variables. It is based on the polynomial--time algorithm of disjoint decomposition developed before. Some examples and evaluation of the algorithm are given.
AND-decomposition of a boolean formula means finding two (or several) formulas such that their conjunction is equivalent to the given one. Decomposition is called disjoint if the component formulas do not have variables in common. In the paper, we show that deciding AND-decomposability is intractable for boolean formulas given in CNF or DNF and pro...
We propose an algorithm for reconstructing a tree path from a root to a primitive Pythagorean triple. The algorithm has polynomial time complexity with respect to the input length relating to the “size” of the primitive Pythagorean triple.
Disjoint AND-decomposition of a boolean formula means its representation as a conjunction of two (or several) formulas having disjoint sets of variables. We show that deciding AND-decomposability is intractable in general for boolean formulas given in CNF or DNF and prove tractability of computing AND-decompositions of boolean formulas given in pos...
The article presents the concept of a virtual museum. The data model and the main data entities of such a museum as well as its content management system are described. Splitting entities into subtypes using the polymorphism of classes allows us to adjust the model to a specific museum/subject area. The model comprises several groups of classes imp...
Because of development of the society, information and educational technologies, the timetabling problem becomes more and more complicated not only in its algorithmics but in description of used data. The authors attempt to systemize their gathered experience in this domain and to propose a data modeling language for universities timetabling proble...
Program system reengineering is an important domain of informatics using wide specter of scientific methods and technologies and attracting strong attention of researchers, engineers, and the business society. In particular, a reengineering project of a program system handling the problem of interest can establish a new knowledge about its characte...
The task of business logic recovery by source code analysis is an actual problem. This process is too complex to do manually therefore automation is needed. In this article the authors consider some methods and tools for analysis of legacy software systems to recover its business logic which is used to document and to maintain applications.
Keywor...
In this article, we make use of some known method to investigate some properties of the numbers represented as sums of two equal odd powers, i.e., the equation $x^n+y^n=N$ for $n\ge3$. It was originated in developing algorithms to search new taxicab numbers (i.e., naturals that can be represented as a sum of positive cubes in many different ways) a...
In this article, we discuss a flow--sensitive analysis of equality relationships for imperative programs. We describe its semantic domains, general purpose operations over abstract computational states (term evaluation and identification, semantic completion, widening operator, etc.) and semantic transformers corresponding to program constructs. We...
We consider requirements for the visualization of semantic properties of programs appearing in engineering processes in which the use of an hierarchical ordering is an appropriate way to visualize the information of interest. We consider two algorithms of graph placement that implement a geometrical inclusion of the object hierarchy. They use (non-...
Analysis, maintenance, and modification of large program systems require adequate tools for information representation in easy-to-read form. This work describes a number of facilities for program visualization and the experience of using them for reengineering of outdated software.
A new upper bound is presented for the length of a snake in a hypercube of dimension n. This bound is better than all bounds derived thusfar for 37<=n<=19079.
properties for the analysis of equality relations are presented by means of context--free grammars of a special type. This presentation allows to perform all operations over semantic properties in an almost--linear average time with respect to a grammar size (number of rules). The abstract semantic domain does not satisfy the chain condition, and t...
By refining some details of the proof in the paper [1], a more precise bound is obtained for the length of an arbitrary snake in the n-dimensional unit cube.
In this article an abstract interpretation and formal language based analysis for imperative programs is presented. This analysis makes a lower approximation of the equality relations for the program terms, i.e. for a given program point our analysis produces a set of equalities t
1=t
2 where t
1 and t
2 represent program expressions such that thei...
By refining some details of the proof in the paper of Snevily a more precise bound is obtained for the length of an arbitrary snake in the n-dimensional unit cube.
