FINAL SUBMISSION FORMAT INSTRUCTIONS FOR ...

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15 Αυγ 2012 (πριν από 5 χρόνια)

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SYSTEM DEVELOPMENT BASED ON MODEL
-
DRIVEN
ARCHITEC
TURE

AN EXAMPLE OF CONSTRUCTING

A CENTRALIZED PURCHASING WEBSITE WITH PHP


Yung
-
Hsin

Wang
,

Lan
-
Fon Huang

Department

of Information Management, Ta
tung

University

40
, Sec 3,

Chungshan N. R
d, T
aipei 104, Taiwan
, ROC

y
wang
@
t
t
u.edu.tw



ABSTRACT


This paper aims at
a

study of system development based on the model
-
driven
architecture (MDA).
The MDA
To utilizing the unified modeling language (UML) as
an analytical tool for the system, comply and implement the MDA ar
chitecture, and
then transform the Class Diagram which is created by the UML into the template
related to PHP programming language. Furthermore, the said template would be
transformed into the physically executable codes, and finally, the development
metho
d of this system will be utilized to construct a centralized purchasing website in
an applicable implementation.

Additionally, while referring to the transforming
process of PIM
-
to
-
PSM, we address the relevant method and tools applicable to
rapidly transfo
rm the UML Class Diagram into PHP template so as to dramatically
save the time necessary for thorough
ly

understanding such MDA architecture during
the artificial transformation process as well as
to avoid

the
likely
human errors.


Keyword:
M
odel

D
riven
A
rc
hitecture
,
MDA
,

UML,
PIM
,

PSM
,

PHP


INTRODUCTION

T
he information system
is commonly used to

assist an enterprise organization not
only in resolving problems related to the management, decision and information
processing, but also

in

improv
ing

the oper
ation
al

efficiency and
effectiveness.

However, there are compatible

problems among

various information systems
of
the
legacy

and new systems
. The system logic and platform information are used to be
mingled together during modeling process, which hamper the mod
el reusability when
implementation

platform changed.


The Object management group (OMG) addressed the model
-
driven architecture
(MDA) in
2001
(OMG, 200
1
) pro
vid
ing

a good solution for the development of the
diversified platform
s

and application
s

nowadays.
The
primary goal
of
MDA
is
interoperability between tools and the long
-
term standardization of models for popular
application
domains.

In the MDA architecture, there are two kinds of key models
thereof, one of them is the Platform Independent Model (PIM) t
hat merely describes
the abstract logic of the system, and another model is used to project the system’s
abstract logic onto an implementation platform, which is called the Platform Specific
Model (PSM).


In addition
,
MDA

describes the mapping rules of mod
els transformation
.

Each
transformation needs clear mapping definition.
The develop
ing
constructs on MDA
architecture firstly would model the abstract logic into PIM, and then project PSM to
a certain implement
ation

platform with the PIM
-
to
-
PSM
m
apping,
wh
ich

afterward
would
create the system code through the
m
apping of PSM
-
to
-
Code. All these
relevant
m
a
pping operations can

be done artificially, or done
using

tool
s

with

the
semi
-
automatic or even full
-
automatic transformation
.

C
urrently, there are many
MDA
c
ompliant development tools on the market,
such as

OptimalJ, Coda
gen
Architect, SosyInc Modeller
,
Transformation Engine
,
etc.

to name a few

(Lano, 2005)
.

On the other hand, a famous CASE tool is
Unified Modeling Language (UML)
(OMG,
2003) which
is a kind o
f properly defined, easily expressible, functionally powerful
and generally appli
cable type of modeling language

to

support
ing

the object
-
oriented
analysis and design

from the requirement analysis to the overall developing process of
the software
(
Booch,

R
umbaugh,

&
Jacobson
,

2001
).


Although MDA has been introduced for years

and its theory architecture is favorable
to the developer with many benefits
, there are some misinterpretations in practice of
certain software industries.

The prior studies related to

MDA system development
were mostly aiming at the utilization of Java MDA development tool (e.g.
,

OptimalJ)
on
top of
the Java platform
. However
,
most of

the services, such as
that of
the
dedicated server hosting or the virtual hosts, are provided with the

Open Source
environment (e.g.
,

Apache+PHP+MySQL)

and

very few
are
with the Java platform
.

T
herefore
,

the objective
of

this study
is to
present MDA
-
based system development
on the
Open Source environment
.


In this paper, we will demonstrate how to produce
a PIM starting from UML system
analysis as well as how to accomplish the m
apping
of
PIM
-
to
-
PSM

transformation

and then the final execution code of PHP. To validate the feasibility of our
MDA
-
based system development, we shall establish a centralized p
urcha
sing website

focusing

on

PHP
realization

u
nder an Open Source environment

and

investigate some

related problems while using the MDA under the Open Source environment

(
Apache+PHP+MySQL

in this study)
.

Besides, since there is no MDA compliable
transformation

tool available

for PHP, this study works up a method and propose a
tool that can fast transform the UML Class Diagram into a PHP code template. This
saves the time needed in understanding the MDA mapping rule during artificial
transformation process and a
voids manual transformation error that the code quality
can be assured.


In the rest of this

paper
,
we

shall

have a brief review of

the
related techniques
describ
ing

the
UML and the MDA architecture along with the introduction to the PHP
developing environ
ment
. We

then describe the case example
of

this study and
its
system analysis
.

System
implementation with PHP

as well as the method and tool

for
PIM
-
to
-
PSM transform
ation will be presented. Finally,

conclusion of this
study is
made including future work su
ggestions
.


BRIEF
REVIEW

OF

REL
A
TED
TECHNIQUES

The UML has integrated the new thought, method
o
logy and technology of software
engineering field
;

without limitation to support the analysis and design of
object
-
oriented, instead it even can support overall s
oftware development process
starting from the requirement analysis
. T
herefore
,

it is a kind of properly defined,
easily expressible, functionally powerful and generally applicable type of modeling
language. In the MDA architecture, UML is applicable to pla
y a role of system
analysis, which is able to specifically
define various features of PIM.


UML (Unified Modeling Language)

The UML

is the result of a successful unification of the many object
-
oriented
analysis and design notations which arose during the
1980s and 1990s. In 1994 work
began on unifying the widely
-
used OMT

(Object
M
odeling Technique)

and Booch

et
al

s

methods

into what became UML, with OOSE also integrated in 1995

(
Booch
,

Rumbaugh,

&
Jacobson
, 2001)
.

From version 1.1 UML was endorsed by the

Object
Management Group (OMG), representing many companies and
organizations
, as a
standard for
object
-
oriented analysis and design, and it has now become the primary
notation in this field. A major revision of UML, to version 2.0, was published in 2004

(
Lano, 2005)
.


UML 2.0 defines thirteen types of diagrams, divided into three categories

where

s
ix
diagram types represent static application structure
,

three represent general types of
behavior
,

and four represent different aspects of interactions

(OMG, 20
03)
:



Structure Diagrams include the Class Diagram, Object Diagram, Component
Diagram, Composite Structure Diagram, Package D
iagram, and Deployment
Diagram.



Behavior Diagrams include the Use Case Diagram (used by some methodologies
during requirements gathe
ring); Activity Diag
ram, and State Machine Diagram.



Interaction Diagrams, all derived from the more general Behavior Diagram,
include the Sequence Diagram, Communication Diagram, Timing Diagram, and
Interaction Overview Diagram
.


Model Driven
Architecture
(
MDA)

The Unified Modeling Language (UML) organized by the Object Management Group
(OMG) has specified the standard Model Notations which is utilized to describe the
system design by the system development personnel. While modeling the system with
UML, exc
ept reducing the communication misunderstandings by means of the
common communication symbols, the model information also can be used to identify
the relevant designs to make sure whether it meets the system requirements or not;
furthermore
,

it will greatl
y facilitate the successive system maintenance, or assist the
new project members to have a better understanding on the current systematic design.
However, it is a little bit regretful that UML documentation is merely acting as a
reference to the developin
g personnel upon the system development period
;

so it is
helplessly to promote the speed of system development.


Thus,

OMG addressed the software development standard of Model
-
driven
Architecture (MDA) in 2001. In the MDA architecture, there are two kinds
of key
models thereof, one of them is the Platform Independent Model (PIM) that merely
describes the abstract logic of the system, and another model is used to project the
system’s abstract logic onto an implementation platform, which is called the Platfor
m
Specific Model (PSM). While modeling the system in the past, it is usually modeling
the PSM information directly; however, it will result in a difficulty for the system to
transform the implementation platform in the future.
Since

that
the system’s abstr
act
logic has been tied closely with the information of the implementation platform
already, and in this way the repetitious usage of model information will become
impossible, it is required to produce PSM again according to the new implementation
platform

as well as the wastage of resources
. Th
is is an
actual

reason why the MDA
would like to independently ex
tr
act the abstract logic from the system and make it as
the PIM.


In addition to the definition of two
m
odels, MDA has also described the
m
appings of
f
our models. These four
m
appings comprise

(Lee, 2003)
:



PIM to PIM
:
PIM
-
to
-
PIM: This
m
apping takes place while defining the PIM of
the system. It is not a
n

easy work at all to design a very stable system
, which

needs to be constructed by a progressive
-
based
method. And the implicit
meaning of this progressive process is the PIM
-
to
-
PIM transformation.



PIM
-
to
-
PSM: This
mapping

occurs when the PIM of the system has already been
accomplished, and is ready to be projected onto one certain implementation
platform.



PSM
-
to
-
PSM: This
mapping

takes place while defining the PSM of the system.
Because each implementation platforms may have individual characteristic, so
we might need to have a fine adjustment the PSM projected by the PIM so as to
reveal the advantage of su
ch platform
. T
he action of this fine adjustment belongs
to the PSM
-
to
-
PSM transformation.



PSM
-
to
-
PIM: This
mapping

takes place while
r
efining a certain Legacy System.
The application system development for an enterprise often can only be
integrated with th
e Legacy System, and a common method generally utilizes
Adapting Method to set up a communication interface, that is, setting up a
Message Oriented Middleware (MOM) server in
-
between new system and old
system for information exchange. Additionally, there i
s another integration
method, that is, utilizing the reverse engineering to reversely transform the PIM
which is created by the old system, and after modification, it could be
re
-
implemented to a new platform again
. T
his particular process is PSM
-
to
-
PIM
tr
ansformation.


Figure 1

shows the
clear

mapping steps
(Wu, 2005)
. Note that the model
transformations from PIM to PSM and from PSM to the Code can be done
artificially,
or done with
CASE tools

with

semiautomatic or even full
-
automatic transformation
.

At pr
esent
MDA Tools may
be
categorized

into Open Source Tools and Commercial
Tools

as w
e list
ed some in

Table

1
.


T
he advantages
of using tools include s
horten
ing

the cycle of system development
,
i
mprove
d

the system quality
, r
educe
d
cost of system development
,

r
educe
d

difficulty
in the operation of heterogeneous platform transformation
, and i
ncrease
d

repetitive
usage of models.




Figure

1
:

MDA
mapping steps of PIM, PSM,
and
Code

Table
1
:

MDA Tools List

Open Source Tools

Commercial Tools

MOFScript (Eclipse p
lugin)

ArcStyler

(MDA tool from Interactive
Objects)

MTF

(IBM Model Transformation
Framework)

MCC (Model Component Compiler,

J2EE)

ATL (Eclipse plugins)

OptimalJ
(PSM transformations,
integrated UML tool)

MTL Engine (Integrates with Netbeans
MDR and Ecl
ipse EMF)

Xactium XMF Mosiac

(model
-
based
mapping, generation and execution tool)

ModFact (MOF Repository and QVT
-

like engine)

SosyInc (Modeler and Transformation
Engine)

GMT (Generative Model Transformer)

Model
-
in
-
Action

(code generation and
model to m
odel transformation)

KMF (Kent Modelling Framework)

MetaEdit+ (modeling and

metamodeling tool)

OpenArchitectureWare (template
-
based
generator framework)

MDWorkbench (text and model
transformation toolset)

OpenMDX

(integrates with several

tools, J2EE, .N
et)

iQgen 3.0 (template
-
based generator)

AndroMDA (J2EE code generation)

Rational Rose

XDoclet (attribute based code

generation tool for J2EE)

Power Designer


Middlegen (database driven code
generator)

Together



PHP
D
evelop

E
nvironment

PHP (recursive
acronym for

PHP

Hypertext Preprocessor

) is a widely
-
used Open
Source general
-
purpose scripting language that is especially suited for Web
development and can be embedded into HTML. PHP is mainly focused on server
-
side
scripting, so you can do anything an
y other CGI program can do, such as collect
ing

form data, generat
ing

dynamic page content, or send
ing

and receiv
ing

cookies. But
PHP can do much more. There are three main areas where PHP scripts are used,
s
erver
-
side scripting,
c
ommand
-
line scripting
,

a
nd

w
riting desktop applications
.


The Apache HTTP Server Project is an effort to develop and maintain an open
-
source
HTTP server for modern operating systems including

UNIX and Windows
. The goal
is to provide a secure, efficient and extensible server that pr
ovides HTTP services in
sync with the current HTTP standards

(
The Apache Software Foundation
,
2008
)
.


On the other hand,
MySQL, the most popular Open Source SQL database
management sy
stem, is developed, distributed and supported by MySQL

AB. MySQL
AB is a
commercial company, founded by the MySQL developers. It is a second
generation Open Source company that unites Open Source values and methodology
wi
th a successful business model.

Its d
atabase
s
erver is very f
ast, reliable, and easy to
use.

In addition,
My
SQL Server works in cli
ent/server or embedded systems.


D
ESCRIPTION AND SYSTEM ANALYSIS OF THE CASE EXEMPLE

W
e
now proceed to
describe the case example and system analysis process in this
study, a
s well as
describe how to utilize the UML tool to construct
the system models.


Requirement
S
cenarios

A company usually performs the purchasing operation for some consumable materials
;

however, diverse purchasing method not only wastes the manpower, but also
nonnegotiable with manufacturers for the sake of quantity
. To resolve this problem,
therefore it is necessary to draw up a plan for constructing a centralized purchasing
website so as to accumulate all the requirements of users and also allow the
purchasing personnel to purchase batch by batch.


The principle of

the system construction is hoping to develop a new system under a
condition which won’t influence the current system at all, in addition, also hoping to
have a
n

across
-
platform function ability and the flex
ibility for future modification
.

T
herefore
,

they
select to develop the relevant system with the PHP language under the
Open Source environment along with a consideration that it is no need to rewrite all
related programs while proc
eeding the future modification
. Then

they decide to utilize
the MDA archit
ecture in order to preserve the featu
res of current system, such as

easy
maintenance and modification.


System
R
equirement
A
nalysis

While a user addresses a purchasing requirement, if
it

has already existed in the
system requirement list, then the system w
ould add
-
on the require
d
quantity directly.
However, if such user’s requirement does

not

exist in the system requirement list,
then the said user can add a requirement by

self, and meanwhile also record the
purchasing items and the starting/closing time of

such collective purchasing operation.

The requirement analys
is process is shown in Figure 2
.


Figure 2
:

T
he requirement analysis process


Constructing
S
ystem
M
odel (PIM) with UML

In nine diagrams of UML, we adopt two of the most common diagrams as the
an
alytical tools for the system. These two are Class
diagram

and
Sequence

Diagram,
which we will
descri
be

respectively
as follows:




Class Diagram

The Class Diagram describes the quiescent structure of category in the system. It not
only defines the
s
ystem Cl
ass, indicat
ing

the association between Class
es
, such as
correlation, dependence, aggregation
,

etc., but also compris
es

the Class’ internal
architecture (the attribute and operation of the Class).


For example, Employee class has five attributes ID, Name,
Dept, Tel and email. And
there is one
method

Employee(
) in it. Employee class and Cart class is a one
-
many
association.

If all attributes, methods and correlation of the class have been
accomplished, then we will acquire a complete series of Class Diagram
as shown in
Figure 3.


Figure 3
:

Class
d
iagram

of
case example




Sequence Diagram

The Sequence Diagram represents the dynamic cooperative relationship among
objects
.

I
t emphasizes the transferring sequence of the information of objects
. T
he
Collaboration
D
iagram describes the synergistic relationship among objects
;

however,
similar to Sequence Diagram, the Collaboration
D
iagram can show the dynamic
cooperative relationship among objects. In addition to the presentation of information
exchange, Collaboration

diagram also can show objects as well as the relationship
thereof. If it needs to emphasize the time and sequence, then adopt the Sequence
Diagram; but if it is important to emphasize the hierarchical relationship, then it is
required to select the Collab
oration
D
iagram.


If we utilize the Sequence Diagram to present this case example, there are altogether
five

objects, in the illustration
. I
f someone would like to add a new purchasing item,
the user will see all the purchasing items after entering into th
e User's Interface, and
after the verification procedure, ha can immediately add
-
on the purchasing items. Its
related objects and Messages are organized in Figure 4.


Figure 4
:

Sequence
d
iagram

of
case example


SYSTEM

IMPLEMENTATION

AND
PIM
-
TO
-
PSM
TRANSFO
RM TOOL

W
e
now

present

the implementation of MDA system, with an example to construct a
centralized purchasing website with PHP languages, and identify the PIM
-
to
-
PSM
transformation for MDA Class as well as the rules and relationship upon the process
of Co
de transformation. In addition, the prototype system demonstration is utilized to
expound both the operational interface and application of the present study
development system along with the transformation tools for the PHP program
languages in the proces
s of PIM
-
to
-
PSM transformation.


The
A
pplication
R
elated to PIM
-
to
-
P
S
M
T
ransformation

In this paper

we only set forth the Employee Class as the descriptive example. Firstly,
it is required to utilize the Class Diagram as the transformation basis in system
analysis process, but the general transformation tools
currently
used are only covering
the languages of Java
, C++,

.NET
,

etc., and at the time being there is no one has ever
utilized any transformation tool related to PHP yet. However, the process of
PI
M
-
to
-
PSM translation without

tool
assistance can only be transformed step by step,
wherein the primary operations comprising
v
ariable
d
eclar
ation

and
f
unction
definition
, e.g.

attributes

ID, Name, Dept, Tel, Email and Employee method

of
the
Employee Class
;

t
herefore
,

we do need a

class which is able to comprise all variables

and

the

function
. T
he transform
ation
result is
as
shown in Figure 5.


Employee

Class Diagram

(PIM)

Employee

template

(PSM)


class Employee

{

var $ID;

var $N
ame;

var $Dept;

var $Tel;

var $Email;

function Employee()

{

}

}

Figure 5
: T
ransfer UML

c
lass
d
iagram

(PIM) to
template

(PSM)


Transforming
T
emplate into PHP
Code

After being transformed into template (PSM), it is available for us to see the embryo
of PHP
program syntax, and the next step is to transform the template into the PHP
programming language (
Code
) that could be run physically. Due to the fact that there
is no any available tool currently, its transformation process must be performed
manually
. The

transform
ed
result can be refere
nce
d
as that shown in

Figure 6.


Employee

template

(PSM)

Employee

PHP

(
Code
)

class Employee

{

var $ID;

var $Name;

var $Dept;

var $Tel;

var $Email;

function Employee()

{

}

}

class Employee

{

var $ID;

var $Name;

var $Dept;

v
ar $Tel;

var $Email;

function Employee($ID)

{

settype($this
-
>$ID,”String”)

獥瑴y灥⠤瑨楳
-
>$Name,”String”)

獥瑴y灥⠤瑨楳
-
>$Dept,”String”)

獥瑴y灥⠤瑨楳
-
>$Tel,”String”)

獥瑴y灥⠤瑨楳
-
>$Email,”String”)

}

}

Figure 6
:

T
ransfer
template

(PSM) to PHP
C
ode


Demon
stration and description of the prototype system

The other Class Diagrams will be processed repeatedly
with
the above
-
mentioned
method

and
will be transformed into the template (PSM) one by one, then
retransformed again into PHP program (C
ode
), along with
the setting for MySQL
database
. I
n this way we will gradually accomplish the prototype of the centralized
Employee

ID:String

Name:String

Dept:String

Tel:String

Email:String

Employee()

purchasing website system.
I
mplement
ing

a centralized purchasing requirement
website according to the MDA architecture is actually able to fulfill all

advantages
emphasized by MDA in the process of development
. F
or instance, the system codes
can be generated from the model so that it is possible to shorten the cycle of the
system development
. I
n addition, due to th
at

MDA can be directly projected from t
he
PIM of the system to the PSM on a certain implement
ation

platform and then
to
creat
e

all related code
s in order to save the manpower

and

cost while improv
ing

the system
quality at the same time.


The functions of prototype system are described as follow
s (refer to Figures 7 and 8)
:

1.

While entering into the system, the user can easily find out the detailed
requirement lists
;

if he wants to add
-
on the order, he might just input the quantity
along with employee's account number then.

2.

If he finds there is no
available item
s

meet his requirement, he might add
-
on a
new item by himself.

3.

The purchasing personnel is allow
ed

to check the historical records, and performs
the purchasing operation based on the statistical results of such requirements.



Figure 7
:

Demo
nstration of the prototype system
--
New Requirement



Figure
8
:

Demonstration of the prototype system
--
History List


PSM
-
to
-
PIM
A
uto
-
T
ransformation
U
tilities

In order to shorten the time spent in the system development, this paper aims at the
PHP program d
evelopment platform, addressing the CASE tool which is applicable to
the MDA transform
ation
, and for the time being it is able to process the PIM
-
to
-
PSM
transformation
;
thereat in addition to the saving of the programming time, for any one
who is not too f
amiliar to the MDA architecture will still be able to enjoy all the
advantages of MDA. Furthermore
,

it is capable of reducing the human errors and
hence ensuring the quality of the codes accordingly.

The PSM to PIM
mapping

process is shown in Figure 9
.


Th
e class, variable and function of UML class diagram to PHP template mapping
rules are shown in Table 2.
The transform
ing

program provided in this paper is
applicable to transform the diagram of UML Class into the PHP template
automatically
. The

operation
i
s
descri
bed

as follows:

1.

Open the file transformation interface
.

2.

Input both the variable and function of such class diagram
.

3.

Press the PSM button
,

then the PHP template will be generated at once.



Figur
e
9
: PIM to PSM

m
apping
p
rocess


Table 2
:

UML class d
iagram to PHP template mapping rules

UML

class diagram

(PIM)

PHP

template
(PSM)

C
lass name

class

C
lass name

{

}

V
ariable name

var

$
V
ariable name
;

F
unction name

function

F
unction name
()

{

}




Figure
10
:

Tools

for
t
ransf
orming

PIM to PSM


C
ONCLUS
ION

Th
e environment for the individual case according to this study is utilizing the
revision of MySQL 5 as the
object relational

database along with th
e PHP software
program platform
. We

summarize

the specific steps for modeling analysis of user’s
interface wit
h UML upon the application system development, as we
ll

as program
template for transforming the Class Diagram into user’s interface and control class.
A
t
final
,
we
set forth a
case example implementation of
a

centralized purchasing website
,
wherein it is a
n identified example comprising the three modeling processes and
transformation of the entire MDA.


The primary results of th
is
study comprise

the following
:



Address the specific
principle
s and procedures
for

each stage in MDA
concerning UML system

analysi
s,
Class Diagram establishment and its
transformation into PIM, PSM and Code
.



Complete a

case implementation

demonstration that s
ummarize
s

detailed
operation
al

procedure in the
MDA
-
based

system development

with
database,
application
program
and user interf
ace, covering
modeling and

transformation
from levels of
PIM

to

PSM to Code
.



Provide

CASE transformation tool

for PHP program complying with the MDA
transformation, which can assist to rapidly create template upon the PIM
-
to
-
PSM
transformation process.


Du
ring

th
e

process of this study, it is found that there are still a lot of
topic
s
deserved

further investigation
on the UML
m
odeling a
nd

the MDA
model
transformation. Thus
,
the following list some of our
suggestions for

future
work
:



In the case example of
a

centralized purchasing website, there is no discussion
related to the transformation method

concer
n
ing

user’s interface transformation
;

therefore, how to proceed
with
the transformation of the user interface has
become an expected issue.



This study has ai
med at the transformation from the Class Diagram to user’s
interface, wherein it is utilizing the Class Diagram and the Sequence Diagram as
the assistance in the analysis
of
transformation process
. T
herefore
,

whether
there
are
other kind of
UML D
iagram
s

ca
n be used to

assist
such

transformation
analysis would become another interesting issue for future study.



As to the PHP program development platform, we are addressing the CASE tool
complying with the MDA transformation, which is merely applicable in the
p
rocess of the PIM
-
to
-
PSM transformation
. However,

there
is

still a big gap in
the process of the PSM
-
to
-
Code transformation, and hence how to upgrade the
code of template to be directly used and save the manual programming time as
well as promote the effic
iency of system development in the process of UML

m
odeling and the transformation should
also
be
challenging
.


A
CKNOWLEDGEMENT

Financial support of
p
ortions of this work
by Tatung University, Taipei, Taiwan under
grant No. B9
6
-
N0
1
-
0
44

is gratefully acknowl
edged
.


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