Information about the Chair of Mathematical Theory of Intelligent Systems (MaTIS)
History
Intelligent systems are targeted at finding internal
laws, creating theory and models of cognitive processes,
storing and processing information, decisionmaking and
behavior in complex abstract environments, for both technical
and biological objects.
The principal progress in "thinking" system creation
(in both theoretical and practical aspects) was achieved
in late 1930s and early 1940s thanks to A. Turing,
C. Shannon, N. Vinner, J. von Neumann, F. Rosenblatt and some
other researchers. The progress was caused by the emerging
applied problems, such as message decoding and decryption,
moving target capturing, fast calculations, etc.
In Soviet Union these results were appreciated and developed
in 19501960, when the key aspects of this field were formed,
including formal languages, pattern recognition, memory organization,
decisionmaking, reasonable behavior, reproduction,
optimal structural organization, etc. The special role
in this process belonged to the seminar on cybernetics held
at the Department of Mechanics and Mathematics in early 1950s
by A.A. Liapunov and S.V. Yablonskiy. The seminar was attended
by such prominent scientists as A.I. Berg, L.V. Krushinskiy,
N.V. TimofeevResovskiy, P.S. Novikov, A.P. Yershov,
A.A. Markov, O.B. Lupanov, and Y.I Zhuravlev.
Later there emerged a number of other seminars devoted
to control system theory, complexity theory, automata theory,
pattern recognition, databases and knowledge bases,
decisionmaking, artificial intelligence, etc.
These seminars were first organized by the Chair of Computational
Mathematics, then – by the Chair of Mathematical Logic, then 
by the Chair of Discrete Mathematics.
Research in the area of intelligent systems at the
Department of Mechanics and Mathematics had been significantly
stimulated since 1986, when the Section for Applied Research
in Mechanics and Mathematics headed by V.A. Sadovnichiy was founded.
This section united researchers working together on problems on the edge of
mechanics and mathematics. A number of results in the
area of space research were implemented in aerospace industry,
received governmental awards and international recognition.
The Laboratory for Problems of Theoretical Cybernetics
(PTC Laboratory) was created as the part of this Section.
Its main areas of research were intelligent systems in
both theoretical and applied aspects.
Later, in 1991, the new Chair of Mathematical Theory of
Intelligent Systems (MaTIS) was founded on the basis
of the Chair of Discrete Mathematics and PTC Laboratory.
The pair MaTIS Chair – PTC Laboratory significantly
improved intelligent system research at the Department of Mechanics
and Mathematics and in Moscow State University as a whole.
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Officials
V.B. Kudryavtsev – Dr. of Sc., Academician, Professor, Head of MaTIS Chair, Head of PTC Laboratory.
E.E. Gasanov – Dr. of Sc., Professor, Deputy Head of MaTIS Chair, Curator of PostGraduate Students.
A.A. Irmatov – Ph.D., M.B.A., Associate professor, Deputy Head of the Chair.
A.S. Strogalov – Ph.D., Associate professor, Deputy Head of the Chair.
A.B. Kholodenko – Junior researcher, Scientific Secretary of MaTIS chair.
P.A. Aliseychick – Ph.D., Senior Researcher, scientific secretary of the PTC laboratory.
D.N. Babin – Dr. of Sc., Professor, Deputy Head of the PTC Laboratory.
V.N. Kozlov – Dr. of Sc., Professor, Deputy Head of the PTC Laboratory.
A.A. Zolotykh – Ph.D., Senior Researcher, scientific secretary of the PTC laboratory.
M.V. Nosov – Ph.D., Senior Researcher, chief scientific secretary of the PTC laboratory.
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Main areas of research and results
Let us describe a general outline of an intelligent system called
Turing system presented in the following figure.
The object O is placed into environment C. The object is linked
with C – O can accept information from C, and O can influence
C, as it is shown in the figure.
When information from C arrives into O, it is first placed into a
recognition block P, then moves to a memory block M for the purpose
of analysis. Analysis is performed with the help of
a block of databases and knowledge bases by a control
block Y. Y can take into account both internal parameters
describing object state and external parameters describing
environment state.
Databases and knowledge bases along with a control block
form "the brain" of the system. The expressive power of the system
primarily depends in information sufficientness and internal operator
efficiency of this brain.
The object behavior is considered to be stepwise; it is evaluated
by series of internal and external functional values.
These series are considered to describe the interconnection
of O and C. They are used to evaluate object "intelligence"
including the conclusion whether O can solve the given problem.
Various interpretations of the system constituents lead to various
intelligent system types.
Let us consider a solver of mathematical problems as an intelligent
system example. The environment is a collection of problems on
algebra, geometry and calculus. The system functioning is
looking for a solution, and the result is the solution or
rejection, if the solver can not find a solution.
Databases and knowledge bases contain the list of standard
techniques like identical transformations of algebraic
and trigonometric expressions, basic theorems, and logical
operations.
Y is the most sophisticated block in this example.
The main goal of Y is the optimal selection of database
elements (due to some heuristics) that could allow
to reduce branching to reduce time spent while looking for a
solution.
In our example Y utilizes a new idea that allows to
avoid ineffective attempts to use logical and axiomatic approach
(used e.g. in "General Problem Solver" and "Mathematika").
The described intelligent solver created by A.S. Podkolzin
exposed high efficiency. It takes under 1 second
to solve most of the problems from known textbooks.
Research and teaching process in the area of intelligent system
are carried on by staff of both MaTIS Chair and PTC Laboratory.
This team includes 10 Dr. of Sc., 12 Ph.D., and 10 young researchers
and consists of specialists not only in intelligent systems and
discrete mathematics and cybernetics, but also in algebra, geometry,
function theory and other areas of mathematics.
As the result, the team can perform complex research in the area
of intelligent systems, reflecting the nature of this direction.
The main areas of research include.
a) Creating methods for recognition of audio, visual and abstract
patterns.
b) Optimal information search and storage.
c) Intelligent solvers in various areas.
d) Teaching systems modeling real teaching process.
e) Discrete structures and processes.
f) Automata and algorithms.
g) Computer modeling in science, technology and humanities.
h) Information security.
The main results in these areas include:
 a new combinatorial and logical method of pattern recognition was
developed, its metrical properties and efficiency were studied;
with the help of this method a number of problems on mineral
search (e.g. oil and tin) was solved (V.B. Kudryavtsev, A.E. Andreev,
A.A. Kibkalo);

a new approach to visual pattern recognition based on presenting
images by finite sets of points and internal encoding of these
sets (the encoding is invariant to affine transformations)
was developed and implemented in a software complex (V.N. Kozlov);
 a new approach to dynamical recognition systems based on finite
automata was developed (S.V. Aleshin);

a new theory of information storage and search based on
a new information graph model was developed; optimal
information graphs for a large number of problems were
designed (E.E. Gasanov);

a new approach to logical process modeling was developed;
on the basis of this approach a computer solver of mathematical
problems (in algebra, geometry, calculus and differential
equations) was created; both the approach itself and the solver
are constantly improved (A.S. Podkolzin);

the behavior of automata collections in labyrinths was investigated
(V.B. Kudryavtsev, G. Kilibarda, A.S. Podkolzin);

a theory of finitegenerated finite functional systems
with Ð_{ê}support based on a general constructive model of
functional systems was developed; this theory embraces
a collection of the existing concrete functional systems
(V.B. Kudryavtsev);

algorithmic unsolvability of Acompleteness for finite automata
was proved; the problem of tcompleteness for finite automata was
solved (V.A. Buevich);

a classification of automata bases according to the solvability
of completeness problem for these bases was created; an explicit
boundary (in terms of Post lattice) of solvable and unsolvable cases
was found (B.N. Babin);

the first example of a Boolean function with almost exponential
complexity in the class of monotonous functional element schemes
was designed, thus solving Shannon problem that remained unsolved
for over fifty years (A.E. Andreev);

an "industrial" method of selfcorrecting schemes synthesis design
for Boolean functions correcting an almost exponential number
of errors without asymptotic complexity growth was developed
(A.E. Andreev);

theorems on mainstream for optimal trajectories of dynamical
multiproduction economical models with constant, asymptotic
constant and variable technological set were formulated and proved
(Y.N. Cheremnykh).
The members of MaTIS Chair and PTC Laboratory have published
over 20 monographs and over 100 articles. The main monographs
include "Logical Algebra Functions and Post Classes" by
S.V. Yablonskiy, G.P. Gavrilov and V.B. Kudryavtsev, "Introduction
to Automata Theory" by V.B. Kudryavtsev, S.V. Aleshin and A.S. Podkolzin,
"Introduction to Cellular Automata" by V.B. Kudryavtsev, A.S. Podkolzin
and A.A. Bolotov, "Information Storage and Search Theory" by E.E. Gasanov
and V.B. Kudryavtsev published by "Nauka", and a number books published
in Moscow State University including "Functional Systems" by V.B. Kudryavtsev,
"Introduction to Abstract Automata Theory" by V.B. Kudryavtsev,
A.S. Podkolzin and S. Ushchumlich. A number
of scientists have won grants of RFDBR, INTAS,
Intel Corp., scientific contests, international and
Russian honorary ranks.
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Applications
The members of MaTIS Chair and PTC Laboratory also work
in the area of applications. The most significant results in this
are include:

"Iskra" project ordered by CNIIMash, that included
creating a mathematical model of selforganizing distributed
system situated partly on Earth, partly in space, capable
of functioning when controlled from Earth and in autonomous mode,
targeted at investigations of Earth and space;

a software complex for chip design automation protected
by over 100 US patents;

a computer intelligent system for mathematical problem solving;

a software complex for creating teaching systems; this complex was
used to create teaching systems in the area of computer science,
foreign languages, arts, etc.;

systems for recognition and analysis of visual, audio and abstract
information used in problems of geology, medicine, cartography, etc.;

information monitoring systems, one of which is related
to nuclear technologies and is currently used by IAEA;

a system for automata modeling of gene mechanism of plants
developed under NATO grant.
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Teaching process
Specialized courses and seminars of MaTIS Chair embrace all main areas
of intelligent system theory.
The basic 1year course "Discrete Mathematics"
is taught by V.B. Kudryavtsev and A.S. Strogalov. The course
explains core ideas and notions and main results of discrete mathematics.
The basic 1year course "Intelligent System Theory",
is taught
by V.B. Kudryavtsev, A.S. Podkolzin, E.E. Gasanov, A.A. Chasovskikh and
V.A. Nosov. The main areas covered by this course include
pattern recognition, databases, decisionmaking, expert systems
and solvers, logics, modeling and complexity theory.
The course
"Automata Theory"
is taught by V.B. Kudryavtsev,
V.A. Buevich, A.S. Podkolzin, S.V. Aleshin and D.N. Babin.
It contains main results in automata theory, the major part
of which belongs to the members of MaTIS Chair.
The course "Algorithm Theory" taught by V.A. Buevich,
I.A. Lavrov and V.A. Nosov is a traditional one.
It allows students to master algorithms – one of the main tools
in mathematics.
The course
"Pattern Recognition", taught by S.V. Aleshin and
M.V. Nosov describes the main approaches to pattern recognition.
The course
"Databases",
taught by E.E. Gasanov is a new one.
It describes an information graph approach to information
storage and search problems as well as the traditional approaches.
The course
"Intelligent solvers",
taught by A.S. Podkolzin
is also new. It describes the principles of intelligent
behavior and their formalization. The results presented in this course
are obtained by the researchers of MaTIS Chair.
The course "Mathematical Cybernetics" taught by E.E. Gasanov
is for postgraduate students. The course is based on VAK
program; it contains such areas as algorithms and schemes complexity,
discrete function algebras, identical transformations, optimization, etc.
The course
"Introduction to the Algebraic Theory of Codes",
taught by A.A. Irmatov gives the overview of the main problems and
results in errorcorrecting code theory.
The course "Information Security" taught by V.A. Nosov
contains the main theoretical and applied results in this area.
The course "Cellular Automata Theory" taught by A.S. Podkolzin
is devoted to cellular automata – infinite locally homogeneous
automata schemes.
The course "VLSI Synthesis Methods" taught by A.E. Andreev
and A.A. Chasovskikh is an applied one. It describes the
procedures used in VLSI synthesis, estimates the complexity,
and shows how to create a design on the basis of a macrodescription
of its functioning.
The course "Mathematical Economics" taught by Y.N. Cheremnykh
is devoted to modeling of economical processes by the means of
mathematics.
The course "Mathematical Models of Economical Calculations"
taught be A.A. Irmatov is new. It is devoted to mathematical
models and acceptable formalizations used in decisionmaking
in macroeconomics and microeconomics.
The course
"Mathematical Biology", taught by V.N. Kozlov
consists of several layers corresponding to modeling
of biological structures of cells, tissues, organisms and population.
The course
"Fuzzy Mathematics", taught by A.P. Ryjov is devoted
to a relatively new approach to studying events and processes
that can not be described precisely. This approach allows
to suggest a technology for processing fuzzy data and creating
corresponding computer models.
For every course there is a seminar for students of second year and
older.
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Scientists

Kudryavtsev Valery Borisovich
Dr. of Sc., Academician, Professor, Head of MaTIS Chair, Head of PTC Laboratory
Area of Scientific Interests: image recognition, automata, intellectual systems, discrete functions
Email: v dît b dît kudryavtsev àt intsys dît msu dît ru 


Andreev Alexander Egorovich
Dr. of Sc., Professor
Area of Scientific Interests: complexity of schemas and algorithms
Email: 


Buevich Vyacheslav Alexandrovich
Dr. of Sc., Professor
Area of Scientific Interests: finite automata, discrete functions
Email: buevich àt intsys dît msu dît ru 


Kozlov Vadim Nikitovich
Dr. of Sc., Professor
Area of Scientific Interests: pattern recognition, mathematical biology
Email: v dît n dît kozlov àt intsys dît msu dît ru 


Chechkin Alexander Vitalyevich
Dr. of Sc., Corresponding member of RATS, Professor
Area of Scientific Interests: mathematical foundation of computer science
Email: a dît v dît chechkin àt intsys dît msu dît ru 


Irmatov Anvar Adhamovich
Ph.D., M.B.A., Associate professor, Deputy Head of the Chair
Area of Scientific Interests: combinatorics, cryptography, mathematical economics, functional analysis, algebraic topology
Email: irmatov àt intsys dît msu dît ru 


Strogalov Alexander Sergeevich
Ph.D., Associate professor, Deputy Head of the Chair
Area of Scientific Interests: finite automata, computer learning, teaching systems
Email: strogalov àt intsys dît msu dît ru 


Nosov Valentin Alexandrovich
Ph.D., Senior Researcher
Area of Scientific Interests: cryptography, combinatorics
Email: v dît a dît nosov àt intsys dît msu dît ru 


Zolotykh Andrej Alexeevich
Ph.D., Senior researcher, scientific secretary of the PTC laboratory
Area of Scientific Interests: computer algebra, automata theory, theory of identities of algebraic systems
Email: a dît zolotykh àt intsys dît msu dît ru 


Belenky Alexander Grigoryevich
Ph.D., Researcher
Area of Scientific Interests: integrated information and analytical systems, applied semiotics, system analysis
Email: belenki àt intsys dît msu dît ru 


Pankratiev Anton Evgenyevich
Ph.D., Researcher
Area of Scientific Interests: cryptography, algebra
Email: pankratiev àt intsys dît msu dît ru 


Alexeev Dmitry Vladimirovich
Researcher, Curator of the 4thYear Students
Area of Scientific Interests: theory of functions, pattern recognition
Email: d dît alexeev àt intsys dît msu dît ru 


Galatenko Alexey Vladimirovich
Junior researcher
Area of Scientific Interests: automata theory, information security
Email: agalat àt intsys dît msu dît ru 


Rodin Sergei Borosovich
Junior researcher
Area of Scientific Interests: automata theory, computer science
Email: s dît rodin àt intsys dît msu dît ru 


Aleshin Stanislav Vladimirovich
Dr.Sc., Professor
Area of Scientific Interests: pattern recognition, finite automata
Email: s dît v dît aleshin àt intsys dît msu dît ru 


Babin Dmitry Nickolayevich
Dr. of Sc., Professor, Deputy Head of the PTC Laboratory
Area of Scientific Interests: automata, pattern recognition
Email: babin àt intsys dît msu dît ru 


Gasanov Elyar Eldarovich
Dr. of Sc., Professor, Deputy Head of MaTIS Chair, Curator of PostGraduate Students
Area of Scientific Interests: databases and knowledge bases, computer science
Email: e dît gasanov àt intsys dît msu dît ru 


Podkolzin Alexander Sergeevich
Dr. of Sc., Professor
Area of Scientific Interests: artificial intelligence, finite automata
Email: 


Cheremnykh Yury Nickolayevich
Dr. of Economical Sciences, Ph.D., Professor, Academician of the International Management Academy
Area of Scientific Interests: mathematical economics
Email: 


Ryjov Alexander Pavlovich
PhD, MBA, Associate professor
Area of Scientific Interests: fuzzy mathematics, information retrieval in fuzzy infomedia, intelligent information systems for monitoring and evaluation of business, economical and sociopolitical problems and processes
Email: ryjov àt intsys dît msu dît ru 


Chasovskikh Anatoly Alexandrovich
Ph.D., Associate professor, Director of Physics and Math School of MSU
Area of Scientific Interests: pattern recognition, finite automata, cryptography
Email: chasovskikh àt intsys dît msu dît ru 


Aliseychik Pavel Aleksandrovitch
Ph.D, Senior Researcher, Deputy Head of the PTC Laboratory
Area of Scientific Interests: finite automata, computer science, teaching systems
Email: aliseychick àt intsys dît msu dît ru 


Nosov Mikhail Vasilyevich
Ph.D., senior researcher, scientific secretary of the PTC laboratory
Area of Scientific Interests: pattern recognition, computer science
Email: 


Mazurenko Ivan Leonidovich
Ph.D., Researcher
Area of Scientific Interests: speech recognition, computer science
Email: mazurenko àt intsys dît msu dît ru 


Kudrin Alexander Alexandrovich
Ph.D., Junior researcher
Area of Scientific Interests: finite automata, complexity theory
Email: a dît kudrin àt intsys dît msu dît ru 


Panteleev Pavel Anatolievich
Junior researcher
Area of Scientific Interests: automata theory
Email: panteleev àt intsys dît msu dît ru 


Safiullin Alexander Naifovich
Junior researcher
Area of Scientific Interests: mathematical ecomomics, automata theory
Email: a dît safiullin àt intsys dît msu dît ru 


Kholodenko Alexander Borisovich
Junior researcher, Scientific Secretary of MaTIS chair
Area of Scientific Interests: mathematical linguistics, formal languages theory, computer science
Email: kholodenko àt intsys dît msu dît ru 



The Chair is teaching over 30 postgraduate students and
over 100 undergraduate students.
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Scientific and Cultural Connections
The Chair is closely cooperating with the RussianGerman
"Moscow Scientific Center on Culture and Information
Technologies" (MSC CIT) and related MSU departments.
The chair keeps in touch with
scientific centers of Moscow,
Novosibirsk, Saratov, Volgograd, Tver, Donetsk,
etc. There are joint research projects with scientific centers
of Germany, USA, Japan, Belgium, Yugoslavia, Slovenia and other
countries.
MaTIS Chair is one of cofounders of
RussianGerman Institute of Science and Culture (with Bochum
University)
and of RussianAmerican Center for VLSI synthesis
automation (with LSI Logic).
MaTIS Chair stages the Open Seminar "Science and Culture", íà êîòîðîì
visited by such honored speakers as S. Govorukhin,
M. Botvinnik, A. Logunov, N. Gubenko, U. Vlasov,
I. Glazunov, V. Belov, V. Rasputin, A. Chuchalin, N. Leonov, etc.
MaTIS Chair is the organizer of the
International conference "Intelligent Systems and
Computer Sciences". It publishes
"Intelligent systems" magazine.
The activities of the Chair are supported by RBRF, LSI Logic
(USA), and Mirantis Corp. (USA). The supporters offer
grants and scholarships, provide publishing of scientific
papers and monographs, assist in conference organization.
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