A Proposed Simulation Model of Automatic Machine For House Paint Selection Using Finite State Automata

International Journal of Computer Applications Technology and Research
Volume 4– Issue 12, 916 - 922, 2015, ISSN: 2319–8656
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A Proposed Simulation Model of Automatic Machine For
House Paint Selection Using Finite State Automata
Emigawaty
Departement of Informatics
STMIK AMIKOM
Yogyakarta, Indonesia
Abstract: One important criterion considered by the public at the time of house selection or property is the aspect of house paint
colors. Principally, the selection of house paint is not exessively complicated, but if the homeowner does not have enough knowledge
about how to make a good combination with the paint color, the consequence is the color of choice is not in accordance with their
expected. This study aims to provide a simulation of how to do a combination of paint color selection using automated machines. The
method used in the design of this model is the Prototype method and blackbox testing to ensure the system is made valid and reliable.
In the mean while, the approach automata models used are Finite State Automata (FSA) has the characteristics due to work by
identifying and capturing the pattern in the compilation process of determining the color of wall paint the house. This paper also
resulted in the identification of input symbols, FSA-NFA diagrams, rules production, NFA, equivalence transition table of FSA-DFA,
and FSA-DFA transition diagram. At the same time, in the design of a prototype, also produced mockup simulation applications in
order to generate automatic machine house paint selection. Thus, problems such as confusion and lack of knowledge of homeowners
against a combination of paint colors can be overcome properly.
Keywords: automatic machine, prototype, finite state automata
1. INTRODUCTION
Along with the high expectations of today's human needs
would be a challenge for developers of information
technology to create models or equipment that can support
daily activities. This is evidenced by the increasing number of
variants of information technology innovation both based
hardware and software which proved quite effective in
helping humans for teaching and learning activities, work,
sports, and other business aspects. One of the areas that affect
the development of the information technology tools is the
property sector. The rise of property business in almost all
regions of the country is certainly a phenomenon as demand
for property is also one of the primary needs of human. The
developers of housing today competing to offer properties
ranging from design models, thematic; to the color selection is
also an important consideration to attract public attention.
The selection of paint color for some people may not be a
priority compared to some other criteria. But not a few people
have a high level of sensitivity to choose the appropriate color
combinations or desired according to the taste or thematic
expected by the owner of the house later. Determine the
combination of colors of paint it takes precision and a good
knowledge before deciding the color of choice. Because if we
are incorrect in choosing and combining these colors is not
likely to result from the combination does not conform to
what is expected.
Automatic machine is one variant of the technology
innovations created to change an activity or process that is the
business of a conventional or to automatic with the goal of
accelerating time activity process itself [1]. One of the
automated machines that began to develop at this time is a
compilation engine automatically selecting paint the walls of
the house. The presence of the house paint compilation engine
is expected to be one solution to simplify the electoral process
and the determination of the color of paint with different
variations. Finite State Automata (FSA) is an abstract
machine in the form of mathematical models of systems with
discrete inputs and outputs that can recognize the simplest
language also known as regular language and can be
implemented in practice. FSA also serves as a model that is
very useful to help recognizing and capturing a pattern in the
data. This model can also receive inputs and produce outputs
that have a finite number of states and can transform from one
state to another based on input and transition functions in it
[2]. FSA on a compilation machine house paint color selection
is the right choice to model the process in this case. After
simulating paint color selection is expected to house the
homeowner will get a selection of color illustrations and
recommendations in accordance with the needs and desires.
In this study, using a model of the application of the concept
of FSA on the implementation of the automatic machine
compilation paint of the house where the automatic machine
has the characteristic assignment by identifying and capturing
the pattern in the compilation process of determining the color
of house paint. Therefore, problems such as confusion and
lack of knowledge of homeowners against a combination of
paint colors can be overcome with good. Moreover, this study
also used some of the conditions that limit to do simulation
and compiling election house paint colors using 3 size
capacities gallon of paint (5kg, 10kg, and 15kg) with color
inputs or raw are: yellow, blue, and red as primary colors,
black and white as a neutral color, green (mixture of blue and
yellow) as the secondary color, purple (mix of blue and red)
as the secondary colors, orange (mix of red and yellow as
secondary colors, while the composition used is 1 to 1.
2. LITERATURE REVIEW
2.1 Language Theory
In the process, a clump of computer science has two elements,
namely: First, the model and the fundamental idea of the
theory of computation. Secondly, the so-called engineering
techniques for the system design of the computational model,
both in terms of software and devices severity. Meanwhile,
language and automata theory included in the first element

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that makes this concept as a model and the fundamental idea
of the theory of computation [3].
One theory being unique or singular when it may be good
alternative solution of a phenomenon that exists in a science
discipline. Computer science itself has a very broad scope
ranging from concept, design theory, computer networks,
programming, until the business processes within an
information system. For that was created or constructed
abstract models of the computer system or computing. Model
theory of language has an important function, and generally
how the computing system may be invoked on a software
development and hardware [4].
In studying the theory of language, is identical with an
understanding of formal language, primarily for the benefit of
the design compiler and processing a script or text processor.
By definition, a formal language is a set of sentences in a
language that is raised by a grammar the same [3]. In its
characteristics, that a formal language can be generated by
two or more different grammar. Background that the theory of
language can be called as well as the formal language for
grammar created precedes the generation of each sentence. In
contrast to human language, which is the reverse, while,
grammar was created to formalize the words that live in the
community.
Utdirartatmo [3] wrote that the automata is a system that
consists of several finite state, where the state represents
information regarding the input, and can also be translated as
a reminder mesing. In this case, the input is meant automata
machine is considered as the language that must be
recognized by a machine. Then, the automata machines can
make decisions that recognize or analyze whether the input is
acceptable or not. In line with that rose by Linz [2], that for
modeling hardware is a needed models automaton, which can
also serve as a temporary storage medium and has the
capability to transform an input to an output.
Furthermore, Juarna [5] provide some basic understanding of
the language and automata theory as the basis of a common
understanding of the definition and the main terminology as
follows:
a) Symbol is an abstract entity (such as the definition of a
point in geometry). A letter or a figure is an example of
the symbol.
b) The string is a row of a limited (finite) symbols. For
example, if a, b, and c are three symbols then abcb is a
string that is constructed from the three symbols.
c) If w is a string, the string length is expressed as w | and
defined for the count (number) symbols that make up the
string. For example, if w = abcb then | w | = 4.
d) The empty string is a string with zero fruit symbols.
Empty string ε is expressed by a symbol (or ^) that | ε | =
0. The empty string can be viewed as a symbol of a
vacuum because both are composed of zero fruit
symbols.
e) Alphabet is hinpunan up (finite set) symbols.
2.2 Grammar and Language
Grammar by Ullman [6] is a collection of the sets of variables,
symbols terminal, the initial symbol, which is governed
formally by the rules of production. Historically, teradapat a
mathematician named Noam Chomsky in 1959 performed
clustering or classification level language into four categories,
which became known as Chomsky Hierarcy. The clustering
can be seen in Table 1:
Table 1. Classification Level of Language
Language Automatic Machine Production Rules
Limitation
Regular / Type 3 Finite State Automata
(FSA) covers
Deterministic Finite
Automata (DFA) & Non
Deterministic Finite
Automata (NFA)
α is a variabel symbol.
Maximum β has a
variable symbol that
when there is in the
rightmost position
Context Free / Type 2 Push Down Automata
(PDA)
α is a variable symbol
Context Sensitive /
Type 1
Linier Bounded
Automata
|α| ≤|β|
Unrestricted / Phase
Structure / Natural
Language / Type 0
Turing Machine No Limitation
2.3 Finite State Automata (FSA)
Finite State Automata (FSA) or often also referred to as finite
automata, in principle, not a physical machine but a
mathematical model of a notation or phrase that can receive
input and output is discrete. FSA is part of the machine
automata regular languages, which have a finite number of
states, and can move from one state to another. One
shortcoming of these automata models is that the FSA does
not have the storage allocation so that the ability to remember
is very limited [3].
Furthermore, as proposed by Ulman [7] that the FSA is a tool
that can be used to design a system, whereby the mechanism
can be applied or implemented on lexical analysis, text-editor,
the network communication protocol, and checks parity,
elevator system, traffic light system, or also the automatic
machine. FSA formally expressed by 5 tuple or M = (Q, Σ, δ,
S, F), where:
Q = set of state / status
Σ = set of symbols input / input / alphabet
δ = transition function
S = the initial state / initial position (initial state)
F = set the final state
Finite State Automata is a machine that can recognize regular
language classes and has the following characteristics:
a) Ribbons inputs contains a series of symbols (string) from
the set of symbols / alphabet,
b) Every time after reading one character, posisir read head
will be in the next symbol,
c) At any time, the FSA is at a certain status,
d) The number of valid status for the FSA is finite.
Based on the function and definition of Finite State Automata
(FSA) and also in terms of its ability to change its state then
this model can dikaslifikasikan into 2 groups: Deterministic
Finite Automata and Non-Deterministic Finite Automata.
2.4 Deterministic Finite Automata (DFA)
At Deterministic Finite Automata (DFA), from a state there is
exactly one next state for each symbol of the input received,
cannot be empty and more than one state. DFA formally
expressed by 5 tuple or M = (Q, Σ, δ, S, F), where Ulman [7]:
Σ = set of symbols
S = the initial state (S ε Q)
F = set the final state (can be more than 1)

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Figure 1. Deterministics Finite Automata (DFA) Machine
DFA configuration in Figure 1 is expressed formally as
follows:
Q = {q0, q1, q2}
Σ = {a, b}
S = q0
F = q2
While the transition of existing functions in Figure 1 are as
follows:
d (q0,a) = q0
d (q0,b) = q1
d (q1,a) = q1
d (q1,b) = q2
d (q2,a) = q1
d (q2,b) = q2
2.5 Non-Deterministic Finite Automata
(NDFA)
In the non-deterministic finite automata of a state there can be
0,1, or more bows out (transition) labeled with the same input
symbol. FSA formally expressed by 5 tuple or M = (Q, Σ, δ,
S, F), where:
Σ = set of symbols
S = the initial state (S ε Q)
F = set the final state (can kebih of 1)
Figure 2. Non-Deterministics Finite Automata (DFA) Machine
2.6 Related Works
1. Melly [8] with the title of paper "Application of Concept
Finite State Automata at Coffee Beverage Maker
Machine Auto". In this study focused on an application
of the concept of FSA in an automatic coffee machine
beverage maker. The method used in this study is the
implementation of formal methods that can be used to
bridge (the formal specification) the manufacture,
development and verification of hardware and software,
which can be used from the initial design to the test
results. The study produced a simulation applications
beverage automatic coffee maker is an application
simulating a machine that can make the process of
making coffee drinks and variations automatically where
the completion of the process used concept of FSA.
Disadvantages of this study are not yet modeled
Equivalence of NFA to DFA thus cannot be
recommended to be developed or translated into the
programming language.
2. Suprihatin [9], titled paper "Finite State Automata for
Parsing Beheading Syllabary In Indonesian". In this
study how decapitated syllables in Indonesian is good
and right, while the FSA itself functions as an abstract
machine, which is used to help design, the parsing
(decapitation) syllable. FSA in its implementation is used
to describe the structure of vowels, consonants, or the
structure of words in Indonesian accordance with
Spelling Enhanced (EYD). The downside of this research
has not been able to show in detail the transition diagram
for each of the components or variables measured.
3. Dihya [10], with paper title "Implementation of the
Transitional Graf Defining Formal Languages". This
study on how to model a formal language with transition
graph and proof when modeled with other modeling.
This is done to determine how the machine answers the
problem decisions based on the input string to provide
the output of 'yes' or 'no'. So that it can be seen how the
issues will be seen run private computing simple
graphical representation of the transition. The downside
of this research is only at the stage of analysis and
produces a transition table, not to the implementation of
an object or case studies, so the validity of this study
cannot be measured.
3. METHODOLOGY
3.1 Prototype Model
Methodology is the unity of methods or rules used by the
work of a science. While the method is a systematic method
or technique to grind. The general objective of this
development is to provide ease in conveying information,
reduce costs and save time, improve control, drive growth,
improve the productivity and profitability of the organization.
System development can mean the preparation of a new
system to replace the old system as a whole or improve
existing systems. System development method used is the
method Prototype. Prototype is a method used in a systems
approach to make something quick and gradual program that
can immediately be evaluated by the user. The stages
contained in this prototype method is as follows [11]:
1. Identification of User Needs, at this stage developers and
users meet. User describes the system requirements.
2. Create Prototype; developers began to create a prototype
of the system.
3. Test Prototype, after prototype form testing prototype
user and give criticism or suggestions.
4. Improving Prototype, In This stage developers make
modifications in accordance with the input from the user.
5. Develop Prototype, after evaluation and perfect the
system in accordance with the wishes of the user. Then
the developer completed the final system in accordance
with the insert of the wearer.

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3.2 FSA Formal Specification
Formal specification by definition is a specification or
statement, which is represented in the form of a formal
language with the intention to describe what, should be done
or decided by the software [12]. In the implementation, this
study will use a formal specification in order to make a model
of an object or system behavior using mathematical
approaches such as sets and sequences.
After having a specification, either in the form of formal or
informal, the implementation can be made. Implementation of
the model can be made of conventional or automatic. Making
the manual implementation is only suitable for use in the
design of the level of complexity is not too high. For complex
systems, easy error occurred. The process of making the
implementation is automatically called automatic synthesis.
To guarantee the truth of the synthesis process, the synthesis
process must be substantiated. If a tool for automatic synthesis
and synthesis processes that are used can be proved right then
the results can be said to be "correct by construction".
Usually this is done to a system that departs from a system
specified formally, then performed "refining" in order to
obtain results in more detail, and done repeatedly until it
becomes implementations in the level of abstraction desired
(eg up to level layout transistor). Each step in the refining
process is guarded by a mechanism (for example, by a
theorem prover) so it cannot perform the process of refining
the wrong [12].
4. RESULTS AND DISCUSSION
4.1 Input Symbol Identification
In the design stage and construction of the simulation
modeling of automated machinery house paint color selection
using the FSA, the necessary step towards the identification of
input symbols in advance. This is necessary in order to
provide the initial terms of the initiation of the formal
specification by way of input variables, process variables, and
variable selection. In practice, this study will use a formal
specification that is used to create a model of an object or
system behavior using arithmetic approach such as sets and
sequences.
The following is a formal specification through initiation
illustration of input and output variables:
Tabel 2. Formal Specification of Input Identification
Process Initiate Capacity Selection Compile Process
0 Back to start state j Gallon 5 kg m Red
a Choose green k Gallon 10 kg n Add Red
b Choose light green l Gallon 15 kg o Yellow
c Choose dark green p Add Yellow
d Choose purple q Blue
e Choose light purple r Add Blue
f Choose dark purple s Black
g Choose orange t Add Black
h Choose light
orange
u White
i Choose orange tua v Add White
w Compile
In Table 2 describes the formal specification in the initiation
input variables in the form of a variable to i, and the process
variables, namely m up to w. As for the election process
capacity is represented by the variable j, k, and l. In the
implementation, application built will have an interface to
allow the user or the user selects multiple colors and desired
gallon capacity according to their needs.
4.2 FSA – Non DFA
Figure 3. Diagram of Finite State Automata - NFA
In Figure 3 it can be seen that the Finite State Automata start
work on State S0, in this diagram, there are 9 colors that can
be, namely: green [a] to State S1, light green color [b] to State
S2, dark green color [ c] to State S3, purple [d] to the State
S4, light purple [e] to the State S5, and petunia [f] to State S6.
Then, from State to State S1 to S9 choice for gallon capacity,
ie paint 5kg [j] to State S10, paint 10kg [k] to State S11, and
paint 15kg [l] to State S12. Mathematical model on FSA-NFA
diagram is then translated into the design of the interface by
providing drop down option or combo box for each option.
Transition specification diagram illustrates the process that is
automated election house paint using the concept or theory of
FSA. In principle, the machine is designed to mengikuki
pattern of the flow of paint color selection process is based on
several primary colors or base is then processed according to
color choices finally as an output. Is because each state has
had towards both the source state and state clear objectives,
then it is highly unlikely to happen mistakes or errors in
processing or even have an end result that is not in accordance
with a predetermined scheme. In the mean time, in order to be
able to read and interpret symbols input the formal
specification designed, the FSA granted terminology in the
form of a dictionary of symbols is fixed and redundancy with
other processes.
Figure 4. Diagram of Finite State Automata - NFA (continued)
Figure 4 is an advanced process flow previously, where the
State S1 to S9 State 5kg choice (j) to State S10, 10kg (k) to
State S11 and 15kg (l) to S12. Furthermore, from State S10,
S11, and S12, if the choice of red (m) to State S13, yellow (o)
to State S14, blue (q) to State S15, black (s) to State S16, and

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white (u ) to State S17. After that, from State S13 add red (n)
to State S18, S19, S20, S24, S25, and S26. Of State S14 add
yellow (p) to State S21, S22, S23, S24, S25, and S26. Of State
S15 add blue (r) to S18, S19, S20, S21, S22, and S23. Of
State S16 add black color (s) to State S19, S22, and S25. Of
State S17 add white (v) to State S20, S23, and S26.
Furthermore, from State S18 to State S26 stirring (w) to State
end S27. From State to State S1 to S27 option ∅
(cancellation) back to S0.
4.3 Rule Production of NDFA
In the domain of language and automata theory, grammar can
also be referred to as Grammar, which is a collection of the
set of variables, symbols terminal (start and an end state), the
initial symbols are constrained by the rules of production.
Furthermore, the production rules in a State Non-
Deterministic Finite Automata (NFA) have produced some
string variables.
NFA Production Rules:
S0 = S
S1 = A S2 = B S3 = C S4 = D
S5 = E S6 = F S7 = G S8 = H
S9 = I S10 = J S11 = K S12 = L
S13 = M S14 = N S15 = O S16 = P
S17 = Q S18 = R S19 = S S20 = T
S21 = U S22 = V S23 = W S24 = X
S25 = Y S26 = Z
S27 = F
Thus,
G = {VT, VN, S, P}
VT = {a,b,c,d,e,f,g,h,I,j,k,l,m,n,o,p,q,r,s,t,u,v,w,∅}
VN =
{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
S = S
P = { S → aA | bB | cC | dD | eE | fF | gG | hH
| iI | ∅,
A → jJ | kK | lL | ∅
B → jJ | kK | lL | ∅
C → jJ | kK | lL | ∅
D → jJ | kK | lL | ∅
E → jJ | kK | lL | ∅
F → jJ | kK | lL | ∅
G → jJ | kK | lL | ∅
H → jJ | kK | lL | ∅
I → jJ | kK | lL | ∅
J → mM | oN | qO | sP | uQ | ∅
K → mM | oN | qO | sP | uQ | ∅
L → mM | oN | qO | sP | uQ | ∅
M → nR | nS | nT | nX | nY | nZ | ∅
N → pU | pV | pW | pX | pY | pZ | ∅
O → rR | rS | rT | rU | rV | rW | ∅
P → tS | tV | tY | ∅
Q → nT | vW | vZ | ∅
R → w | S
S → w | S
T → w | S
U → w | S
V → w | S
W → w | S
X → w | S
Y → w | S
Z → w | S
4.4 Table of Transition Equivalences
Basic concept of Finite State Automata (FSA) provide insight
into fundamental that when a system is in a state of a state that
moves between state-state that no principle can be produced
depends on the input to the system. It is confirmed that the
input (input) is true and valid is crucial for conditioned value
without error. Implementation of this concept can be seen in
modeling compilation or translation of high-level
programming language (high level language) into machine
language equivalent.
From Non-Deterministic Finite Automata (NFA) machine,
which had previously modeled, then the machine can be made
Deterministic Finite Automata (DFA) equivalent. Equivalent
is meant accords or able to accept the same language. In the
case of this study, the transition equivalence can be seen in
Table 4.2. The table contains a description of all State with
input option (input) respectively to the state-state is written.
Table 3. Equivalency Transition from NFA to DFA
4.5 FSA- DFA Transition Diagram
Figure 5. Finite State Automata – NFA Transition Diagram
In Figure 5 can be explained that the FSA began work on the
State S0, from S0 option A to S1, b to S2, c to S3, d to S4, e
to S5, f to S6, g to S7, h to S8, i to S9, j - z State to an empty
({}). Then, from the State S1 to S9 to S10 option j, k and l to
S11 to S12, to a - i and m - z State to an empty ({}).

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Furthermore, from State S10, S11, and S12 option m to S13, o
to S14, q to S15, s to S16 and u to S17, for a - l, n, p, r, t, v - z
to State empty ,
Afterwards, from State to State S13 option n new ({SA18,
S19, S20, S24, S25, S26}). For a - v, x - z to State empty.
From State S14 selection to p ({S21, S22, S23, S24, S25,
S26}). For a - o, q - z to State empty. From State S15
selection to r ({S19, S20, S21, S22, S23}). For a - q, s - z to
State empty. State S16 selection of t to ({S19, S22, S25}). For
a - s, v - z to State empty. From State S17 to choice v ({S20,
S23, S26}). For a - v, w - z to State empty. Of the newly
formed State 5 w option to S27. For a - v, x - z to State empty.
And for all the existing state S0 option other than 0 to S0.
4.6 Application Prototype
Figure 6. Prototype of Paint Color Selection: Green
Figure 6 illustrates the main interface where the user can
immediately make paint color selection, and also the capacity
of gallons of paint in accordance with the wishes or needs. In
this example, the user make the selection with the green color
gallon capacity is 5kg, and a button to execute the process of
mixing paint.
Figure 7. Prototype of Automated Paint Mixing Process: Green
Meanwhile, in Figure 7 can be seen that the application
displays the information about the process through simulation
where the system will demonstrate the process of stirring or
mixing paint, the color blue (the portion of the composition
50%) plus Yellow (the portion of the composition of 50%) to
produce a green color.
Figure 8. Prototype of Automated Paint Mixing Final Result:
Green
Figure 8 is a display end result of the process of stirring or
mixing colors to produce a green color. In this application
also displays the composition of each color to help users
determine the proportion of each paint.
4.7 Prototype Testing
As an important part of assessing the success of a design
prototype, so in this study is also testing a system to produce
valid and reliable. There are several methods in testing of the
prototype as black box testing, white box testing, or usability
testing. But in this study using black box testing, the testing
model by observing the process inputs (input) and output
(output) in the system software to ignore what is going on in
the system.
Tabel 4. Blackbox Prototype Testing
No Indicators Scenario Expected Output Obtained
Output
1 Form
Design
User run
applications from
the beginning to the
end (to get the paint
color desirably)
 Colors
selection
form
 Paint mixing
process form
 Result paint
selection
form
 Acceptable
 Acceptable
 Acceptable
2 Navigatio
n
User run
applications from
color desirably)
Button process
abd navigation
system for each
forms
Acceptable
3 Respon User run
applications from
color desirably)
Duration of
response of
applications
ranging from
input to final
results
Acceptable
4 Transition
Diagram
User run
applications from
color desirably)
Concurrence
between output
with grammar
and FSA
Transition
Diagram -
NDFA
Acceptable

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5. CONCLUSION
Based on the problems and objectives of this study, it can be
delivered several conclusions as follows:
1. This research resulted in Diagram Finite State Automata
- Non Deterministic Finite State Automata, Production
Rules, Transition Equivalence, and Diagrams Finite State
Automata - Deterministic Finite State Automata, also
designed a prototype of an automatic machine simulation
application selection of paint house as one of the models
implementation.
2. Based on the results of the testing of a prototype
application, it can be seen that the concept of Finite State
Automata (FSA) used in designing an automatic machine
simulation application selection with house paint to
generate a grammar (grammar) to produce nine color
options can house paint proved successful according to
the research objectives.
REFERENCES
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Automata (FSA) Pada Mesin Pembuat Kopi Otomatis.
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[2] Linz, P. (2001). An Introduction to Formal Language
and Automata . John and Bartlett Publisher.
[3] Utdirartatmo, F. (2005). Teori Bahasa dan Otomata.
Yogyakarta: Graha Ilmu.
[4] Kelley, D. (1999). Otomata dan Bahasa-bahasa
Formal. Prenhanindo.
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