The Formal Model of Structure-Independent Databases
Sergey Kucherov, Alexander Sviridov and Svetlana A. Belousova
Department of System Analyses and Telecommunications, Southern Federal University,
44 Nekrasovsky St., Taganrog, Russian Federation
Keywords: Structure-independent Databases, Formal Model, Metadata Manipulation.
Abstract: In this paper we’d like to propose a formal model of structure-independent databases. This formal model
allows to describe and implement not only different SIDB that are implemented on relational technology,
but also the tools of working with them. Model contains set of relations and operations which are basic and
can be supplemented depending on the characteristics and requirements of implementation. To provide the
flexibility structure-independent databases presupposes manipulation of data and metadata structures.
1 INTRODUCTION
In configurable information systems correspondence
to the domain is recorded at the moment of delivery
to the consumer, and this correspondence can be
corrected at any time with minimal costs and
without loss of efficiency of existing configuration
(Rogozov, Degtyarev, 2014; Rogozov, Sviridov, Belikov,
2014)
.
Configurable information systems deal with data
with variable structure – data sets with pre-defined
and strictly fixed structure, which may be modified
in accordance with changes of the domain. The main
differences between data with variable structure and
semistructured data with similar properties are
shown during the work with them:
- For data with variable structure it is required to
identify and record the database schema before using
it.
- Schema of data with variable structure should
be prescriptive, rather than describing, as in the case
of semistructured data.
There are various private approaches to solving
the problem of database flexibility for configurable
information systems that can be generalized to two
major categories: dynamic physical structure of the
database
(Ginige, 2010) and static physical database
structure (
Paley, 2002; Tenzer, 2001).
The conceptual model of structure- independent
database will be considered in section 2.
Due to the fact that all known structure-
independent databases (SIDB) are based on
relational technology, the corresponding
mathematical apparatus will be used for
formalization: theory of relations
(Anderson, 2004),
theory of sets (Kuratowski, 1970) and Codd's
relational algebra
(Codd, 1972.). The formal model of
SIDB will be presented in sections 3-4.
2 CONCEPT OF
STRUCTURE-INDEPENDENT
DATABASE
Static physical database structure provides a new
level of flexibility – work with user data structures
especially on the logical level, that is isolated from
the majority of technical nuances, such as triggers,
indexes, etc., and largely centered on the domain –
on the structure and the links between the stored
data, types of data stored and so on. Thus this
variant of the problem solution of providing
database flexibility for adaptive information systems
is most preferred. Selection of this variant is caused
by difficulties in creating the physical layer in the
absence of exhaustive description of the subject area
and by rising of maintaining and refining cost during
the database usage.
Such decisions can be summarized by the term –
structure-independent database. SIDB – is a database
that is marked by the absence of any impact of
changes at the conceptual or logical data model level
of the domain on physical structure of the tables or
records. SIDB is intended for use within a single
implementation area of information systems
146
Kucherov S., Sviridov A. and A. Belousova S..
The Formal Model of Structure-Independent Databases.
DOI: 10.5220/0005110301460152
In Proceedings of 3rd International Conference on Data Management Technologies and Applications (DATA-2014), pages 146-152
ISBN: 978-989-758-035-2
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

(medical, economic, etc.) and is able to continue to
operate and save the functionality after any change
in the data model of the domain, which makes it
universal within this area.
Representation of the data structure in the form
of sparse matrix allows to provide the possibility of
its dynamic changing, and direct storage of metadata
in the database allows to make independent physical
and logical levels of implementation. Using these
statements to solve the problem of flexibility of
databases leads to three-dimensional representation
of this database in the basis: "entity-instance-
attribute"
(Kucherov, 2010; Kucherov, 2011) shows that
there is no need in priori domain description for
flexible database – it is ready for use, even if it does
not contain any entity or attribute. A complete
separation of the physical and logical levels of
implementation is achieved.
SIDB should store not only user data but also a
description of their structure. Therefore, SIDB
should contain the relevant subschemas for explicit
storage of both data and metadata. This statement is
also supported by general features of considered
databases for storing user data structures.
An important point is the access to data and
metadata. The principles embodied in the data model
EAV lay in the basis of SIDB. One of the
fundamental principles is to store data in columns
(
Abadi, 2008; Boncz, 2005; Boncz, 1999; Stonebraker,
2005). Unlike traditional storage by rows, which is
the characteristic of table data presentation, data
storage by columns suggests such correspondence:
one line = one value of one attribute of one entity. In
this case the defining of entity and attribute, which
value is stored in the row, is performed not by
naming tables and fields, but making links to the
appropriate tables of entities and attributes. This
makes it possible not only to change the value, but
also other elements: entities and attributes.
Since column-storage is not common form of
data presentation, and the user perceives data in
table form (represented by rows) better, there is a
problem of direct and inverse transformation
between views. It is obvious that operation of
transformation will always be performed by one
algorithm (only the values of the rows will vary).
Thus, it makes sense to identify and include in SIDB
number of mechanisms that provide for the user the
possibility to work with the data presented in
columns in a familiar table form.
SIDB include four main components:
1. Metadata. Set of directories, implemented as
static subschema of tables;
2. Data. Set of directories, implemented as a
static unbound set of similar tables on the number of
data types used.
3. Mechanisms for data processing. They are a
set of parts comprising procedures, functions, and
interfaces for providing to the user the normal
operation mode with table data view.
4. Mechanisms for metadata processing that
constitute set of components, including procedures,
functions, and interfaces for multiple changes of
user data structures described within SIDB.
Generalized conceptual representation of
structurally independent database (
Kucherov, 2009) is
shown in Figure 1.
Figure 1: Conceptual model of structure-independent
database.
SIDB range of users is expanded as compared
with a conventional relational databases, for which it
is allocated only data consumers. Innovation is the
inclusion of developer (database administrator) to
the SIDB users. Metadata manipulation mechanisms
should be available for this category
(Rogozov,
Sviridov, Grishchenko, 2014).
Through these
mechanisms the description and modification of user
data structures is performed. Also it is possible to
organize the interface part of the mechanisms in the
way when changes will be carried out without the
involvement of technical experts.
Based on this concept representation the usage of
SIDB can be introduced as follows:
1. Logical Data Model of the domain that is
defined by one of the classical types, is converted by
means of deterministic procedures of conversion
into the form of its storage in SIDB;
2. Logic level of SIDB is filled with relevant
directories, hierarchies , key values , etc.;
3. SIDB logical model with the help of
deterministic procedures is converted into a
TheFormalModelofStructure-IndependentDatabases
147

relational form. Metadata and data are divided into
relevant tables.
According to this we can mark the main task of
SIDB formalizing – formalization of the structure
and methods of data manipulation and data
structures manipulation (
Rogozov, Sviridov, Kucherov,
2014).
3 FORMAL MODEL OF
STRUCTURE-INDEPENDENT
DATABASE
The structure of considered existing databases can
be generalized to the following basic components:
domain objects; characteristics of domain objects;
relations of characteristics with objects; relations of
objects with objects; object instances; relations of
object instances; data stored in the form of values of
objects characteristics.
We use the following notation:
 object (in object-oriented and graph data
models) , the relation (in relational data
model) = entity;
 characteristic, feature, quality of the object
= attribute.
Based on this, we formulate a mathematical
model of the SIDB structure, which can be
represented as follows
(Kucherov, 2011; Kucherov,
2010):
(1)
where: E – component "entities"; A - component
"attributes"; S - component "entities structure"; L -
component "structure of relations"; R - component
"entity instances"; V - component "data" (or
"attribute values").
Entity. Suppose there are n entities that can be
identified. Then all entities will be described in the
following finite set:

i
eE 
(2)
where
ni ,1
Attribute. Suppose that there is a finite set C of
allowed value area:

n
СССС ,...,,
21

(3)
where Ci – i-th set of allowed values.
Suppose that there is a finite set N of allowed
value area names:

k
nnnN ,...,,
21

(4)
where ni – i-th name of certain allowed value
area. For sets C and N there can be set bijective
correspondence of names ti and areas Cj, called the
set of data types.
),,( FNCT

(5)
where
NCF


,
Tt
i

, – i-th data type.
Then domain Di will be a finite subset of the
named elements of bijective correspondences tj, and
domain name Di will be called as attribute Aj:


jin
tDDDDD 

|,...,,
21
(6)
Thus, the finite set of all attributes stored in
SIDB is represented in the form of pairs:
},{ 
kj
taA
(7)
where aj – certain j-th attribute, tk – the data type
of the attribute.
Structure of Entities. Each entity of the domain
is defined by its name and has the structure in a form
of attributes set. Entities structure can be given in
the following form:
),,( FAES

(8)
S is a binary relation defined on sets E and A
with the relationship graph F, that the projection on
the first component
 1 of the graph F is a subset of
entities having the structure of E' of the set E, and
the projection of the second component
 2 of
relations graph F – is a subset of attributes A' of set
A:
EEEF 

',')(
1

AAAF 

',')(
2

If
AaEe
ji
 &
are such that the relation S
contains a tuple U, for which
i
eU

)(
1

,
j
aU

)(
2

, than the attribute aj belongs to entity
ei. Unlike traditional relational databases in SIDB
the same attribute can belong to multiple entities.
The Structure of Connections. The data model
of any subject area, made in any of known forms,
should reflect not only a set of entities of the domain
and their structure as a set of attributes, but also the
relationships between individual entities. In SIDB
such links can be formally presented as follows:
),,( FAEL

(9)
L is a ternary relation, defined on the sets E and
A, with the relationship graph F, that the projection
on the first component
 1 of the graph F is a subset
VRLSAEM ,,,,,
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of parent entities having the structure of E' of the set
E, and the projection of the second component
 2 of
graph relations F – is a subset of child entities E' of
the set E, and the projection of the third component
 3 of relations graph F – is a subset of key attributes
A' of set A:
EEEF 

',')(
1

EEEF  '','')(
2

AAAF 

',')(
2

If
AaEee
kji

 &,
such that the relation
L contains a tuple U, for which
i
eU

)(
1

,
j
eU )(
2

,
k
aU )(
3

, entities ei and ej are
linked by the attribute ak. And ei – is the parent
entity, ej – child entity, ak is primary key and ej is
foreign key of entity.
Entity Instances. In the relational model, both
in the physical and logical levels, each instance of a
single entity is uniquely determined by the values of
one tuple (row in the table), with no need to
introduce extra copies of identifying features.
At the same time SIDB storage of entity
instances in the physical layer is carried out not in
the form of sequences of length n, where n – is the
number of attributes of an entity, but in
n'n

triples – ternary tuples, each of which stores value of
one attribute of the entity. Here, the n' refers to the
fact that the triple ni exists if the attribute has the
value ai. With this approach, the value «null» is not
stored and the place for such value them is not
reserved.
Due to these features it is necessary to identify
groups of tuples belonging to one entity instance.
Formally, the identification can be represented as
follows:
),,( FIER 
(10)
R is a binary relation defined on the sets E and I,
with the relationship graph F, that the projection on
the first component
 1 of the graph F is a subset of
parent entities having the instances E' of the set E,
and the projection of the second component
 2 of
relations graph F – is a set I of all instances of all
entities that are stored in database:
EEEF  ',')(
1

IF )(
2

If
Ee
j
 such that the projection of the
second component
 2 of relation graphic F with
selection operator
)(F
j
e

is a subset I' of set I:
IIIF
j
e


','))((
2


then for the entity ej, there is a set


k
iI '
of
instances of amount
'In 
. For entities which do
not have any entities in SIDB
)(
1
R

and
)(
2
R

are
equal to zero.
Data (Attribute Values). As has been noted, in
SIDB data is stored as tuples of fixed length and
structure that regardless of the data type can be
represented as follows:
),,,( FDAIV
i
t

(11)
i
t
V
is a ternary relation, defined on the sets I, A
and D, with the relationship graph F, that the
projection on the first component
 1 of the graph F
is a subset of all entity instances that consist of
attributes type ti, I’’ of the set I, and the projection
of the second component
 2 of relations graph F –
is a subset A' of attributes having type ti of the set A,
and the projection of the third component 3 of
relations graph F – is a subset D’’ of domain set D’
of type ti:
IIIF 

'','')(
1

AAAF 

',')(
2

i
СDDDDF  ',''','')(
3

Relations between Entity Instances. Along
with storing the structure of relationships between
entities there exists the problem of storage of
relations between instances of these entities. In other
words, the first defines the logical data model of the
domain, and the second allows you to create in the
output the separate information entity of the domain,
which in a logical model can be represented by a set
of tables. For example, such a task is to build a
directory that stores information entity "Employee",
which in the logical data model is represented by
two entities "Passport data" and "History of the
salary".
To solve this problem, you can use the relations
(9) as a container for the storage of such relations.
But since the relationship between specific values
are related to the field of data and appear during the
immediate operation of the database, it is advisable
to:
1. Identify specific data type Cn named tk, such
that Ci = I. That is, the allowed value area of this
data type will include all elements of the set I of
entity instances. Than to add this type to the set (3),
and to add name of this type to the set (4). To add
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149

the correspond domain Dn to the set (6). In this case,
Dn= Cn.
2. Use for storage of links between entity
instances the relation (11), where use the desired
type Cn named tk as the attribute type:
),,,( FDAIV
k
t

Where the projection on the first component  1
of the graph F is a subset of all instances of parent
entities Ip of set I, the projection of the second
component
 2 of relations graph F – is a subset A'
of attributes having type ti of the set A, and the
projection of the third component
 3 of relations
graph F – is a subset of instances of child entities Ic
of set I:
IIIF
pp
 ,)(
1

AAAF 

',')(
2

IIIF
cc
 ,)(
3

The developed formalized model is basic and
can be supplemented depending on the extension of
the SIDB domain. On the basis of the model (1)
there can be obtained a variety of different SIDB
implementations depending on the particular
purpose of the developer.
4 FORMAL MODEL OF
METADATA MANIPULATION
MECHANISMS IN SIDB
In classical relational databases to describe the
manipulation methods of data structures the data
definition languages are used (in particular, DDL-
subset of SQL operators – Create, Alter, Drop). In
contrast to this, the way in which SIDB provide the
flexibility along with the physical layer
independence
(Abadi, 2008; Boncz, 2005; Boncz, 1999;
Stonebraker, 2005; Kucherov, 2009)
allows to solve
these problems using data manipulation languages
(in particular, DML-subset SQL operators – Select,
Insert, Update, Delete)
(Kuratowski, 1970).
Manipulation of data structures presupposes the
presence of operations of adding, deleting and
modifying the following components of data
structure: 1. Entities; 2. Attributes; 3. Relations
“entity-attribute”; 4. Relations “entity-entity”.
In SIDB by storing data in columns operations
are performed with the help of the data manipulation
language SQL. Let us examine them in detail.
Entity Adding. To add the entities you should
perform operation of sets union:

ki
eeEEEE ',...,'','''
1


where:
Е = {e1,…,ei} – is a finite set of entities
available in SIDB;
E’ = {ei+1,…,ek} – is a finite non-empty set of
entities to be added;
E’’ = {e1,…,ei,ei+1,…,ek} – is a result finite set
of entities available in SIDB.
Entity Deletion. To remove the entity you
should perform operation of sets difference:

ki
eeEEEE ',...,'','''
1



where:
Е = {e1,…,ei,ei+1,…,ek} – is a finite non-empty
set of entities available in SIDB;
E’ = {e’i+1,…,e’k} – is a finite nonempty set of
deleted entities;
E’’ = {e1,…,ei} – is a result finite set of entities
available in SIDB.
Entity Changing. To change the entity you
should perform two operations - the difference and
the union:

nni
eeEEEE ,...,','''





ini
eeEEEE ''',...,'''''','''''



where:
Е = {e1,…,ei } – is the initial and the resulting
finite non-empty set of entities available in SIDB;
E’ = {e’i-n,…,e’i} – is a finite nonempty set of
entities to be changed;
E’’ = {e1,…,ei-n-1} – is an intermediate finite
set of entities available in SIDB;
E’’’ = {e’’’i-n,…,e’’’i} – is a finite nonempty set
of modified entities.
Creation of “entity-entity” Links. To add
relationships between entities it is needed to perform
operation of sets union:
where:
L = {<e1,e2,a1 >,…,<ei,ek,aj>} – is a finite set
of entity-entity links available in SIDB;
L’ = {<e’i+1,e’k+1,a’j+1>,…,<e’m,en,a’p>} –
is a finite nonempty set of entity-entity links to be
added;
L’’ = {<e1,e2,a1>,…,<ei,ek,aj> ,
<e’i+1,e’k+1,a’j+1>,…, <e’m,en,a’p>} – is the
result set of entity-entity links available in SIDB.



 pnmjki
aeeaeeLLLL ',',',...,',','','''
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Changing the “entity-entity” Links. To change
the connections it is necessary to perform two
operations – the difference and union:



 jkinjnkni
aeeaeeLLLL ',',',...,',','','''



 jkijki
aeeaeeLLLL ''',''',''',...,''',''','''''','''''
111
where:
L = {<e1,e2,a1>,…,<ei,ek,aj>} – the original
and the result finite nonempty set of entity- attribute
links available in SIDB;
L’ = {<e’i-n,e’k-n,a’j-n>,…,<e’i,e’j,a’k>} –
finite nonempty set of entity-attribute links to be
changed;
L’ = {<e’i-n,e’k-n,a’j-n>,…,<e’i,e’j,a’k>} –
intermediate finite set of entity-attribute links
available in SIDB;
L’’’ = {<e’’’i-n,e’’’k-n,a’’’j-n>,…,
<e’’’i,e’’’j,a’’’k>} – final nonempty modified
entity-attribute links.
5 CONCLUSIONS
So the formal model of structure-independent
database was proposed and developed
(Kucherov,
2011; Kucherov, 2010)
, based on the theory of
relations, set theory and Codd's relational algebra.
As part of a formal model of structure-independent
databases are available: SIDB structure model,
model of operations on metadata (user data
structures), model of operations on user data.
Formal model allows to describe and implement
not only different SIDB that are implemented on
relational technology, but also the tools of working
with them. Considered in model set of relations, sets
and operations are basic and can be supplemented
depending on the characteristics and requirements of
implementation.
The result set of SIDB models must be
implemented according to known database
technologies. To ensure the feasibility in the form of
various particular structure independent databases,
which satisfy the requirements of the particular
configurable information system, it is required to
develop an appropriate design method.
ACKNOWLEDGEMENTS
The research is performed within the government
mandate № 0110021005901621. Theme № 213.01-
11/2014-17 "Development of methods for data
warehouse creation in configurable information
systems and mechanisms for their implementation".
REFERENCES
Abadi, D.J., 2008. ColumnStores vs. RowStores: How
Different Are They Really? Proceedings of the ACM
SIGMOD International Conference on Management of
Data, Vancouver, BC, Canada.
Anderson, J., 2004. Discrete mathematics and
combinatorics. Moscow: Publishing House of
Williams
Boncz, P., 1999. MIL primitives for querying a fragmented
world. VLDB Journal, 8 (2)
Boncz, P., 2005. MonetDB/X100: Hyper-pipelining query
execution. In CIDR.
Codd, E.F., 1972. Relational Completeness of Data Base
Sublanguages. In: R. Rustin (ed.) Database Systems:
Prentice Hall and IBM Research Report RJ 987 , San
Jose, California.
Ginige, A., 2010. Meta-design paradigm based approach
for iterative rapid development of enterprise WEB
applications. Proceedings of the Fifth International
Conference on Software and Data Technologies,
ICSOFT, Volume 2.
Kucherov, S.A., 2009. Structure independent database
SIDB for web-oriented systems development in
automated directory systems. Collected materials
«Science Week 2010" V.2. - Taganrog Univ Tsure ,
Kucherov, S.A., 2010. Way a formal representation of
metamodels. Actual problems of information systems
and processes – SFU-publishing. Taganrog.
Kucherov, S.A., 2011. Formalized model of structurally
independent databases. Structure and manipulation
Informatization and Communication , № 3 (2011)
Kucherov, S.A., 2011. The method of constructing
structure-independent databases using relational
technology. New Technology, Information
Technology, № 2.
Kuratowski, K., 1970. Set Theory: Translation from
English. MI briefly edited Taimanov. Mostowski –
Mir.
Kutcherov, S.A., 2010. Purpose-driven approach for
flexible structure-independent database design.
Proceedings of the Fifth International Conference on
Software and Data Technologies, ICSOFT, Volume 1.
Paley, D., 2002. Modeling of quasistructured data. Open
Systems, 2002.
Rogozov Y., Degtyarev A., 2014. The basic foundation of
software framework for configuration underwater
acoustic information systems with dynamic structure.
Information and Communication Technology for
Education (ICTE-2013). Publisher: WIT
Press.Southampton, Boston, Vol. 1.
Rogozov Y., Sviridov A., Belikov A., 2014. Approach to
CASE-tool building for configurable information
system development. Information and Communication
TheFormalModelofStructure-IndependentDatabases
151

Technology for Education (ICTE-2013). Publisher:
WIT Press. Southampton, Boston, Vol. 1.
Rogozov Y., Sviridov A., Grishchenko A., 2014. The
method of data manipulation operations
representation as a structure in structure-independent
databases oriented on configurable information
system development. Information and Communication
Technology for Education (ICTE-2013). Publisher:
WIT Press. Southampton, Boston, Vol. 1.
Rogozov Y., Sviridov A., Kucherov S., 2014. The method
of configuring dynamic databases. Information and
Communication Technology for Education (ICTE-
2013). Publisher: WIT Press. Southampton, Boston,
Vol. 1.
Stonebraker, M., 2005. C-Store: A Column-Oriented
DBMS. In VLDB.
Tenzer, A. 2001. Database – is object storage.
Computerpress.
DATA2014-3rdInternationalConferenceonDataManagementTechnologiesandApplications
152