Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures
In the work the basic aspects of mathematical modeling of AFP-structures as universal functional converters of spatial type on the basis of decomposition of multiple-valued structures are investigated, also there have been investigated an approach to the implementation of the linear logical tran...
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irk-123456789-599332014-04-11T03:02:32Z Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures Chetverikov, G.G. Vechirska, I.D. Leshchynskyi, V.A. Интеллектуальные системы планирования, управления, моделирования и принятия решений In the work the basic aspects of mathematical modeling of AFP-structures as universal functional converters of spatial type on the basis of decomposition of multiple-valued structures are investigated, also there have been investigated an approach to the implementation of the linear logical transformation finding method for solving the problem of finding hypothetically connected subscribers in the automated system of complex calculations of telecommunication enterprise. У роботі досліджено основні аспекти математичного моделювання АСП-структур як універсальних функціональних перетворювачів просторового типу на основі декомпозиції багатозначних структур, а також був розглянутий підхід впровадження лінійного логічного методу виявлення перетворення, щоб вирішити гіпотетично зв’язану проблему передплатників в автоматизованій системі складних обчислень телекомунікаційного підприємства. В работе исследованы основные аспекты математического моделирования АКП-структур как универсальных функциональных преобразователей пространственного типа на основе декомпозиции многозначных структур, а также был рассмотрен подход к выполнению линейного логического метода обнаружения преобразования для того, чтобы решить гипотетически связанную проблему подписчиков в автоматизированной системе сложных вычислений телекоммуникационного предприятия. 2011 Article Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures / G.G. Chetverikov, I.D. Vechirska, V.A. Leshchynskyi // Штучний інтелект. — 2011. — № 3. — С. 319-326. — Бібліогр.: 11 назв. — англ. 1561-5359 http://dspace.nbuv.gov.ua/handle/123456789/59933 007.519.714:519.766 en Штучний інтелект Інститут проблем штучного інтелекту МОН України та НАН України |
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Интеллектуальные системы планирования, управления, моделирования и принятия решений Интеллектуальные системы планирования, управления, моделирования и принятия решений |
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Интеллектуальные системы планирования, управления, моделирования и принятия решений Интеллектуальные системы планирования, управления, моделирования и принятия решений Chetverikov, G.G. Vechirska, I.D. Leshchynskyi, V.A. Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures Штучний інтелект |
| description |
In the work the basic aspects of mathematical modeling of AFP-structures as universal functional converters
of spatial type on the basis of decomposition of multiple-valued structures are investigated, also there have
been investigated an approach to the implementation of the linear logical transformation finding method for
solving the problem of finding hypothetically connected subscribers in the automated system of
complex calculations of telecommunication enterprise. |
| format |
Article |
| author |
Chetverikov, G.G. Vechirska, I.D. Leshchynskyi, V.A. |
| author_facet |
Chetverikov, G.G. Vechirska, I.D. Leshchynskyi, V.A. |
| author_sort |
Chetverikov, G.G. |
| title |
Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures |
| title_short |
Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures |
| title_full |
Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures |
| title_fullStr |
Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures |
| title_full_unstemmed |
Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures |
| title_sort |
solving the problem of finding hypothetically connected objects by means of spatial multi-valued structures |
| publisher |
Інститут проблем штучного інтелекту МОН України та НАН України |
| publishDate |
2011 |
| topic_facet |
Интеллектуальные системы планирования, управления, моделирования и принятия решений |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/59933 |
| citation_txt |
Solving the Problem of Finding Hypothetically Connected Objects by Means of Spatial Multi-Valued Structures / G.G. Chetverikov, I.D. Vechirska, V.A. Leshchynskyi // Штучний інтелект. — 2011. — № 3. — С. 319-326. — Бібліогр.: 11 назв. — англ. |
| series |
Штучний інтелект |
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AT chetverikovgg solvingtheproblemoffindinghypotheticallyconnectedobjectsbymeansofspatialmultivaluedstructures AT vechirskaid solvingtheproblemoffindinghypotheticallyconnectedobjectsbymeansofspatialmultivaluedstructures AT leshchynskyiva solvingtheproblemoffindinghypotheticallyconnectedobjectsbymeansofspatialmultivaluedstructures |
| first_indexed |
2025-07-05T11:05:06Z |
| last_indexed |
2025-07-05T11:05:06Z |
| _version_ |
1836804741686886400 |
| fulltext |
«Штучний інтелект» 3’2011 319
5Ch
UDK 007.519.714:519.766
G.G. Chetverikov, I.D. Vechirska, V.A. Leshchynskyi
Kharkiv National University of Radioelectronics (KHNURE), Kharkiv, Ukraine
chetvegg@kture.kharkov.ua, ira_se@list.ru, Vladimir.Leshchinsky@gmail.com
Solving the Problem of Finding Hypothetically
Connected Objects by Means of Spatial
Multi-Valued Structures
In the work the basic aspects of mathematical modeling of AFP-structures as universal functional converters
of spatial type on the basis of decomposition of multiple-valued structures are investigated, also there have
been investigated an approach to the implementation of the linear logical transformation finding method for
solving the problem of finding hypothetically connected subscribers in the automated system of
complex calculations of telecommunication enterprise.
Introduction
Developing and improving computer facilities underline the process of automatizing
mental activity, which was the starting point of emergence of concept of artificial
intelligence. However, the successes in the field of intellectualizing computer machines are
insignificant especially if one compares the achieved results with anticipated ones and
forecast. The orientation to the attain of qualitatively new technologies of information
processing manifests itself in attempts to realize systems of artificial intelligence (AI) on
Neumann computers. Therefore, new requirement of the technology of information
processing are caused by need for solving problems, which are badly formalized and the
availability of user who is not a professional programmer. Thus, we came to realizing one
of the variants of developing AI systems are the way of analyzing modeling and
synthesizing a natural language intelligent interface by means of multiple-valued logical
systems, in particular by algebra finite predicates as well as the theory of multiple-valued
structures and coding. Since the advent of computers facilities research has been carried
out and realization at the level of engineering solutions multi-valued structures and coding
in view of high information saturation of their signals has been conducted. Structures of
data processing means, which are conducted on the basis of multiple-valued logical
elements and modules with appropriate links, are called multiple-valued structures. All the
objects, which are described by finite structural alphabet: elements, modules, structures,
system of computer, measuring and control facilities and natural language information
tools are classified among such structures.
At present there exist a great number of uncoordinated approaches and methods of
building and applying multiple-valued structures, however, their systematization and
classification are not available (i.e. any kind of an ordered system of realization means). At
the same time the optimum design and technical realization of computer machines on the
base of multi-valued structures are impossible without simultaneous development of
entirely new (nontraditional) kinds of mathematical models and their research for various
G.G. Chetverikov, I.D. Vechirska, V.A. Leshchynskyi
«Искусственный интеллект» 3’2011 320
5Ch
models of operation and interpretation of the modeling results. All this has resulted in a
critical situation, which is caused by absence of the integral theory of constructed highly
effective multi-valued structures of spatial type. The analysis done shows that the problem
of developing the generalized theory of building highly effective multiple-valued computer
structures and coding for language systems can be solved only within the class of intuitive
and constructivist theories [1-4].
Today, data processing in intellectual systems is based on the particular knowledge
about subject domain. However, knowledge representation systems itself that simulate
human activity, are insufficiently formalized. There have been developed a lot of methods
of knowledge representation. Herewith, usually, every knowledge representation system
has its own advantages and disadvantages, endowed with the specific structure and
efficient only in specific subject domains. It is natural that the more general the language
character of data representation, the bigger the area of subject domains, where it can be
implemented. Such universal language of knowledge representation can be considered the
finite predicates logic, owing to through algebraic logic apparatus it became possible to
formalize arbitrary ratio. The finite predicate logic and predicate operations are effective
and convenient for the description of various information, formation of queries in
databases and simulation of human activities.
The purpose of the given work is dedicated to development of adequate algebra and
logic systems engineering tools of language phenomena objectification on the basis of their
formalization and corresponding approbation.
Choosing the Body of Mathematics
The availability of algebra of finite predicates (AFP) provides an interesting
opportunity of realizing a transition from algebraic description of information processes to
their description in the form of equation in the language of given algebra and the equations
specify relations between its variables [5], [6]. All the variables in the equation possess
equal rights and any of them can be both independent and dependent ones. The presence of
equations and their advantage over algorithms consist in the fact that there appears an
opportunity to calculate the reaction of the system even in case of the incomplete
definiteness of initial information, whereas an incompletely developed algorithm is unable
to operate. One should note that by means of AFP-structures which realize appropriate finite
predicates. The given approach is similar to the process of constructing combinational
circuits by the formula of algebra of logic. Depending on the level of functional and
structural realization we have AFP-structures of the first, second and third level [6].
The algebra of finite predicates is used as the body of mathematics of the research.
We treat AFP as the one which is represented by the set M of all the predicates mU . Let T
be a set of all relations on mU , Q be a set of all predicates on mU . The relation T and
predicate Q are called corresponding to each other, if for any mxxx ,,, 21 we have:
.,,,,1
;,,,,0
),,,(
21
21
21 Txxxif
Txxxif
xxxQ
m
m
m
(1)
In accord with (1) there can be a transition from the arbitrary relation T to predicate
Q corresponding to the said relation T . The predicate Q which is found by the expression
is called the characteristic function of relation T .
Solving the Problem of Finding Hypothetically Connected Objects by Means
«Штучний інтелект» 3’2011 321
5Ch
The condition of the form:
.,1
;,0
)(
i
ia
ii xaif
xaif
xxa (2)
is called predicate of recognizing an object Ua of variable ),(, mlixi .
The predicate )( ixa should be considered as the predicate ),,,,,( 21 mi xxxxa from
QP , whose all arguments, except ix , are negligible. We will replace the expression in the
form )( ixa , where mli , , Ua by a
ix (here a is called an exponent of the variable ix . Thus,
the set T and basic elements a
ix ( mli , , Ua ) and basic operations: disjunction,
conjunction and negation is called the algebra of finite predicates over M . Eliminating the
operation of negation out of the basis of the given algebra enables to obtain so called
disjunction and conjunction algebra of predicates (DCAP). Its completeness is proven [7].
Thus, the given algebra is considered as an instrument of research but not as its subject.
The linear logical transformation (LLT) degree finding method. LLT degree finding
method has been presented and proved
)()(
1
)( yQKyQ i
n
i
n
, where ),(),( xyKyxKKKi
)()(
1
)( xPKxP i
n
i
n
, where ),(),( yxKxyKKKi .
The developed LLT degree finding method )()( yQ n can be divided into the following
stages. You must first find the matrix K , superposition of kernels of linear LLT from xP
into yQ and, respectively, form yQ into xP : ),(),( xyKyxKK .
The next step is to find the conjunction of all n kernel LLT superpositions and the
input vector.
Thus, we can conclude that n is a linear logical transformations ( 1n ) depends on the
type of matrix K . It is important that the matrix K depends only on the definition domain of
variable x. As the step, in which the degree of LLT in the further actions does not change,
and directly depends on the dimensionality of the definition domain of variable x.
The assertion that if for finding of LLT degree in two successive steps of conversion
value is repeated, this value will be repeated also in the following steps [7]. That is, if the
finding of n-th LLT degree obtained similar results were obtained for n-th and n-1 steps,
this result also will be received on the following n +1-th, n +2-th, etc. d. steps. Then this
linear transformation is desired.
We will continue to use this assertion in solving the problem of finding hypothe-
tically connected subscribers.
Formalizing the Concept of Unification of Spatial
Multiple-Valued Structures
A concept of unifying (reducing to uniformity and indissoluble interaction) two-digit
and multi-valued means of processing appropriate (symbolic) data semi digital in a natural
language. The present approach is based upon a single methodological and special purpose
principle by applying the proposed methods of the theory of intelligence [8] for mathematical
description and appropriate formalization of the concept of unifying input/output data [9]
and their intermediate transformation [10] an appropriate AFP-structure of the third sort [5].
G.G. Chetverikov, I.D. Vechirska, V.A. Leshchynskyi
«Искусственный интеллект» 3’2011 322
5Ch
AFP-structure of the third sort is proposed on the basis of the SDF architectural
studies presented in the works [5], [6], [9], as well as proceeding from the need for
structurizing problems in developing the intuitive and constructivistical theory of
constructing multiple-valued structures of spatial type for language systems.
AFP-structure of the third sort based upon a two-input universal multivalued
functional converter [5] includes the following components: a recognition element n-
valued variable which is formed by a parallel analog-to-digital converter together with a
spatial decoder, a matrix selector and a matrix switch, a control unit, a parallel digital-to-
analogue converter (key switch). After describing the logic of operation of these components by
the appropriate equations of the algebra of finite predicates, we will obtain their mathema-
tical models. The use of the concept of unification and the given algebra will ensure
boundary parallelism and uniformity of the structure as a whole. Obtaining analytical relations of
input /output variables of component will make it possible to formalize and synthesis procedure
of multiple-valued structures of spatial type [5], [6].
The research has shown that the application of traditional methods of combinational
synthesis in functionally complete bases as disjunction (conjunction) normal forms to
multiple-valued structures of spatial type is ineffective from the point of view of retaining
the properties of uniformity and parallelism of structural formations [3], [5]. There is a need
for seeking objects of research which are the most natural and closest to the inner logic of
functioning for a natural language particulary of corresponding structures a variety of
algebraic and logical means of modeling and new methods of synthesis of corresponding
structures [5], [10].
Solving the Problem of Finding
Hypothetically Connected Objects
Currently, the structure, conditions of application, interconnections with other
systems and complex problems with each other, modes of operation and automated system
of complex calculations functioning principles (CCFP) of integrated informational and
computational enterprise system of telecommunication are being developed.
One of the problems that CCFP solves is a hypothetically connected subscribers
finding problem (HCSFP) [11]. Input data is presented as a set of all subscribers of the
city of Kharkiv, the set of subscribers, with whom the hypothetical connection is required
to be set up, as well as phone numbers that were used to call during certain period of time.
All subscribers of Kharkiv, that can be hypothetically interconnected must to be found.
Hereinafter, “hypothetically connected” should be read as denoting a whole chain of
telephone calls, through which the information could be transmitted, rather than not direct
connection between objects (subscribers).
In the CCFP system, the HCSFP has not been solved completely. Only few searching
cycles were carried out, since there was no known search algorithm termination criterion.
In turn, the set of subscribers is big enough to implement a full search. The number of
cycles wasn’t big, from 2 to 5. That is why in most cases all solutions could be not found.
It can be assumed that this criterion developed, based on the LLT degree finding method,
allows the task to be solve.
For example, when receiving a request from certain services on the need acceptance
of data on the phone (i.e. phone numbers on which the calls were made from the given
telephone number during some period of time). Then again, the obtained results would
come in the form of inquiry: who was calling on this telephone numbers and so on few
times (cycles). Herewith, all actions were performed by the operator, rather than auto-
matically.
Solving the Problem of Finding Hypothetically Connected Objects by Means
«Штучний інтелект» 3’2011 323
5Ch
Let us give an example of solving the HCSFP. Data for the problem solving will be
taken from the database of the following structure (Fig. 1). Due to some requests there used
lookup tables of one-time services and lookup tables of trunking groups.
Automatic international telephone connection
State Duration of
conversation
Date Beginning
of
conversation
(time)
Outcome
telephone
number
Income
telephone
number code
Income
telephone
number
Subscribers
Telephone First/Last
name
Properties
Directions
Code Region City Country
Figure 1 – Database Scheme
Let the variables ix , ,...12,...,2,1i be the numbers of Kharkiv and Kharkiv region. The
problem is to find all the subscribers’ phone numbers, which subscribers with numbers 1x ,
2x , 4x , 7x , 9x can be connected to. The set of subscribers’ numbers to which the income
calls are recorded mark jy . Fig. 2 suggests that subscribers 1x , 2x , 4x , 7x , 9x are
hypothetically connected to subscribers 241 yy , the solution is found in 3 steps. Usage of
the developed LLT degree finding method allowed to minimize the solutions search time.
x2
y8 y9 y17y15y14y12y11y5 y6 y3
y24
y23
y23
y23
y22
y22
y21
y21
y21
y20
y20
y20
y20
y19
y19
y19
y18
y18
y18
y17
y17
y17
y16
y16
y16
y16
y15
y14
y14
y14
y13
y13
y13
y11
y11
y10
y10
y9
y9
y9
y8
y8
y8
y7
y7
y7
y7
y6
y6
y6
y5
y5
y5
y4
y4
y4
y3
y3
y3
y2
y2
y2
y2 y1
x10
x9
x9
x9
x8
x8
x1
x1
x1
x1
x2
x2
x2
x3
x3
x3
x3
x4
x4
x4
x4
x5
x5
x5
x5
x6
x6
x6
x6
x7
x7
x7
x7
x8
x8
x9
x10
x10
x10
x11
x11
x11
x11
x12
x12
x12
x12
y1
y1
y1
y4 y10
y10y11 y12
y12
y12
y13 y15
y15
y18 y19 y21 y22
y22
y23 y24
y24
y24
Figure 2 – Finding the HCS
G.G. Chetverikov, I.D. Vechirska, V.A. Leshchynskyi
«Искусственный интеллект» 3’2011 324
5Ch
Variables хі, ,...12,...,2,1i are Kharkiv and Kharkiv region phone numbers. We must
find subscribers’ phone numbers which subscribers with numbers 05722305081 x ,
05729453762 x , 05771243874 x , 05777740047 x , 05777116919 x can be connected to.
Thus, there were found the following Kharkiv and Kharkiv region subscribers’ phone
numbers: 05771532563 x , 05773565785 x , 05729956336 x , 05773323768 x , 057227874510 x ,
057712653411 x , 057293769412 x .
Analysis of Used Method
Let us perform further comparison of the method by which previously the HCSFP
and the method of n-th linear logical transformation was solved. Previously, while
searching at the solution for the given states space the search depth was defined. Thus,
before beginning the search the MAXSTEP parameter had to be installed, which presets
the number of iterations. It was usually limited by 5 steps.
The MAXSTEP parameter also considers solutions search time by finding n-th LLT,
and it also limits the number of iterations. But the difference is that if the solution satisfies
a criterion of method work end before the MAXSTEP step, the program finishes the
search.
Let us break the test in a few cases, if a solution is on the 1st, 2nd and n-th step.
1. Suppose that there is a set of numbers, which were called not often and not to
different phone numbers from. Then the solution is found already on the 2nd step, but
because it is not known in advance in how many steps it is found, it could take longer to
solve.
According to statistics there are about 35% of such subscribers.
Using the method of n-th LLT in any case the solution is found in 2 iterations.
According to the method that was previously used, the number of steps depended on set
MAXSTEP.
2. By assuming that there is a set of numbers, where the solution is found in 3 steps.
According to statistics there are about 40% of such subscribers.
Using the method of n-th LLT in any case the solution is found in 3 iterations.
According to the method that was previously used, the number of steps depended on set
MAXSTEP. And if we set MAXSTEP = 1, the final solution will not be found at all. In
other cases, increasing MAXSTEP, the time is lost on extra steps of the algorithm.
3. Suppose that there is a set of numbers, where the solution is found in n steps.
Using the method of n-th LLT in any case the solution is found in n steps. According
to the method that was previously used, the number of steps depended on set MAXSTEP.
In this case, if set parameter is too small, then the final solution will not be found, only an
intermediate (in this way not all hypothetically connected objects will be found), and if the
set parameter is too large, the search for a solution will take much time.
Thus, the method of n-th LLT allows finding the final solution. Using the
MAXSTEP parameter, the number of steps is limited and a solution will be found faster in
most cases (if the solution is found in 2-6 steps). Using the method previously used, the
MAXSTEP parameter cannot be set small (2 or 3) because about 30% of phone numbers
do not fit in this space, but if the parameter set more than 3, then for about 75 % of
numbers redundant iteration will be made. The method of n-th LLT does not have these
shortcomings.
Solving the Problem of Finding Hypothetically Connected Objects by Means
«Штучний інтелект» 3’2011 325
5Ch
Conclusions
Thus, the above listed results make possible the following important conclusion:
using new algebraic and logical means of modeling of natural language constructions in the
form of a system of equations based on the AFP-language and explicit way of specifying a
finite alphabet operator which underlies method of solving these equations, ensures
realization the property of reversibility of AFP-structures and a wide paralleling of
symbolical information processing. Fundamental research of the algebraic and logical
structure of an natural language as well as algebraic and logical means of its modeling in
the form of AFP-structures of the first, second and the third sort permits to come close to
the solution of the important scientific problem: attain qualitatively new technologies of
symbolical information processing on the basis of the concept of unification and
methods of synthesizing reversible spatial multivalued structures of language systems.
Suchwise, we have investigated implementation of n-th LLT degree finding method
for HCSFP. This allowed to increase speed and accuracy of finding problem solutions by
reducing the number of steps during information processing, due to the formulation of
clear work completion criterion. However, the method allows to stay not bind to a specific
subject domain structure, hence in further it makes sense to investigate the work of the
method for arbitrary objects, for instance, for problems solving in logistics or some objects
of reach transport nodes connecting problems.
In particular, in the works the accent on the concept of neuro-physiologic and neuro-
cybernetic aspects of alive brain mechanisms is made. It is connected with the following
natural neuron structures from nervous cells, i.e. neurons, essentially are highly effective
recognizing systems and, for this reason, is of interest not only for doctors and physio-
logists, but also for the experts designing artificial intelligence systems. However direct
transfer of research results of neuro-physiologists in engineering practice is now impos-
sible because of a lack of an appropriate bioelectronic technology and an element basis,
that has led to development and creation of a set of varieties of artificial neurons realized
on the elements of the impulse technology.
As the corollary, non-adequacy of used principles of coding and element basis to
simulated processes entails a redundancy, complication and non evidence of used
mathematical and engineering means of transformations, loss of a micro level of
parallelism in handling expected fast acting and flexibility of restructuring without
essential modifications of architecture and connections.
Literatura
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cheskogo interfeisa / M. Bondarenko, G. Chetverikov, A. Karpukhin // Proc of the 10th International
Conference KDS – 2003, (Varna, Bulgaria, June 16-26, 2003). – P.78-92
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Г.Г. Четвериков, И.Д. Вечирская, В.А. Лещинский
Решение проблемы обнаружения гипотетически связанных объектов на основе пространственных
многозначных структур
В работе исследованы основные аспекты математического моделирования АКП-структур как
универсальных функциональных преобразователей пространственного типа на основе декомпозиции
многозначных структур, а также был рассмотрен подход к выполнению линейного логического метода
обнаружения преобразования для того, чтобы решить гипотетически связанную проблему подписчиков в
автоматизированной системе сложных вычислений телекоммуникационного предприятия.
Г.Г. Четвериков, І.Д. Вечирська, В.О. Лещинський
Розв’язання проблеми виявлення гіпотетично пов’язаних об’єктів на основі просторових
багатозначних структур
У роботі досліджено основні аспекти математичного моделювання АСП-структур як універсальних
функціональних перетворювачів просторового типу на основі декомпозиції багатозначних структур, а
також був розглянутий підхід впровадження лінійного логічного методу виявлення перетворення, щоб
вирішити гіпотетично зв’язану проблему передплатників в автоматизованій системі складних обчислень
телекомунікаційного підприємства.
Статья поступила в редакцию 04.07.2011.
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