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A comp
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M
e
m
o
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b
u
il
t
-
in
se
lf
-
tes
t
(
M
BI
S
T)
h
a
s
b
e
c
o
m
e
a
n
e
ss
e
n
ti
a
l
d
e
sig
n
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fo
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tab
il
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h
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i
q
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e
f
o
r
e
n
su
ri
n
g
th
e
re
li
a
b
il
it
y
a
n
d
q
u
a
li
ty
o
f
e
m
b
e
d
d
e
d
m
e
m
o
ries
in
m
o
d
e
rn
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n
teg
ra
ted
c
ircu
it
s.
Th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
a
n
M
BIS
T
imp
lem
e
n
tatio
n
is
larg
e
ly
d
e
term
in
e
d
b
y
it
s
tes
t
a
l
g
o
rit
h
m
,
wh
ich
d
e
fin
e
s
th
e
se
q
u
e
n
c
e
o
f
m
e
m
o
r
y
o
p
e
ra
ti
o
n
s,
d
irec
tl
y
in
f
lu
e
n
c
i
n
g
b
o
th
tes
t
c
o
m
p
lex
it
y
a
n
d
fa
u
lt
c
o
v
e
ra
g
e
.
De
sig
n
in
g
a
n
e
fficie
n
t
tes
t
a
lg
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ri
th
m
re
q
u
ires
b
a
lan
c
in
g
lo
w
tes
t
c
o
m
p
lex
it
y
with
c
o
m
p
re
h
e
n
siv
e
fa
u
lt
d
e
tec
ti
o
n
.
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is
p
a
p
e
r
p
re
se
n
ts
a
c
o
m
p
re
h
e
n
siv
e
re
v
i
e
w
o
f
M
BI
S
T
tes
t
a
lg
o
rit
h
m
s
fo
r
sta
ti
c
fa
u
lt
d
e
tec
ti
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n
in
sta
ti
c
ra
n
d
o
m
-
a
c
c
e
ss
m
e
m
o
ry
(S
RAM).
T
h
e
re
v
iew
first
su
m
m
a
rize
s
th
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c
h
a
ra
c
teristics
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m
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RAM
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ti
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lt
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t
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re
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e
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ts.
It
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n
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m
p
a
re
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se
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tativ
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tes
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lg
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se
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e
n
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e
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l
t
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n
d
d
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u
r
th
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rm
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re
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t
h
e
e
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io
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o
f
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BIS
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tes
t
a
lg
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rit
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m
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e
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d
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ra
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l
a
d
h
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a
p
p
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to
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n
h
a
n
c
e
d
a
l
g
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rit
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m
s
d
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ri
v
e
d
f
r
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m
e
x
isti
n
g
M
a
rc
h
tes
ts.
Th
e
c
o
m
p
a
ra
ti
v
e
a
n
a
ly
sis
in
d
ica
tes
th
a
t
a
n
1
8
N
-
c
o
m
p
lex
it
y
tes
t
a
lg
o
rit
h
m
is
g
e
n
e
ra
ll
y
re
q
u
ired
to
a
c
h
iev
e
c
o
m
p
lete
d
e
te
c
ti
o
n
o
f
a
ll
u
n
li
n
k
e
d
sta
ti
c
fa
u
l
ts
i
n
S
RAM
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wh
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re
a
s o
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ti
m
ize
d
1
4
N
-
c
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m
p
le
x
i
ty
a
lg
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r
it
h
m
s p
r
o
v
i
d
e
a
n
e
ffe
c
ti
v
e
t
ra
d
e
-
o
ff
b
e
twe
e
n
tes
t
ti
m
e
a
n
d
fa
u
l
t
c
o
v
e
ra
g
e
.
F
i
n
a
ll
y
,
th
e
re
v
iew
i
d
e
n
ti
fi
e
s
c
u
rre
n
t
re
se
a
rc
h
c
h
a
ll
e
n
g
e
s,
i
n
c
lu
d
in
g
e
fficie
n
t
d
e
tec
ti
o
n
o
f
d
y
n
a
m
ic
a
n
d
li
n
k
e
d
m
e
m
o
ry
fa
u
lt
s
a
n
d
t
h
e
d
e
v
e
lo
p
m
e
n
t
o
f
M
BIS
T
a
l
g
o
ri
th
m
s
fo
r
e
m
e
rg
in
g
m
e
m
o
ry
tec
h
n
o
l
o
g
ies
su
c
h
a
s
m
a
g
n
e
ti
c
ra
n
d
o
m
-
a
c
c
e
ss
m
e
m
o
ry
(M
RAM),
h
ig
h
li
g
h
ti
n
g
p
r
o
m
isin
g
d
irec
ti
o
n
s
fo
r
fu
t
u
re
re
se
a
rc
h
.
K
ey
w
o
r
d
s
:
Ma
r
ch
test
alg
o
r
ith
m
MBIST
Me
m
o
r
y
f
a
u
lt c
o
v
e
r
ag
e
SR
AM
Static f
au
lts
T
h
is i
s
a
n
o
p
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n
a
c
c
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ss
a
rticle
u
n
d
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r th
e
CC B
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li
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se
.
C
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p
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uth
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:
Aim
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Z
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Fak
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Keju
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Ko
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Un
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7
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Du
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im
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m
y
1.
I
NT
RO
D
UCT
I
O
N
Me
m
o
r
y
b
u
ilt
-
in
s
elf
-
test
(
B
I
ST)
o
r
MBIST
is
co
m
m
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ly
a
d
o
p
ted
b
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e
s
em
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d
u
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f
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r
m
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m
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test
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[
1
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.
I
t
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r
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ce
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ex
p
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ex
te
r
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test
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s
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d
,
th
u
s
,
p
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d
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a
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t
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aster
m
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to
ex
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test
s
an
d
th
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v
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if
y
th
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test
r
esp
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n
s
es
in
d
ep
en
d
en
tly
[
2
]
–
[
5
]
.
I
t
is
a
v
ital
tech
n
iq
u
e
s
in
ce
th
e
ch
ip
s
ar
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m
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ly
o
cc
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p
ied
b
y
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u
m
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p
to
9
4
%
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th
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t
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tal
ch
ip
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ea
[
6
]
,
[
7
]
.
Su
b
s
eq
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en
tly
,
th
e
q
u
ality
o
f
th
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o
n
-
c
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m
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r
ies
p
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s
a
v
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r
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le
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m
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d
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ch
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s
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f
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wh
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p
to
9
0
%
o
f
o
v
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all
f
a
u
lts
in
th
e
ch
ip
[
8
]
–
[
1
0
]
.
A
te
s
t
u
s
in
g
MBIST
is
co
n
d
u
cted
b
y
p
er
f
o
r
m
in
g
a
s
er
ies
o
f
test
o
p
e
r
a
tio
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s
ca
lled
th
e
test
s
eq
u
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ce
s
,
d
ef
in
e
d
b
y
th
e
ap
p
lied
test
alg
o
r
ith
m
[
1
1
]
.
I
t
ty
p
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co
n
s
is
ts
o
f
a
co
n
tr
o
ller
to
g
en
er
ate
th
e
test
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
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J
E
lec
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g
&
C
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m
p
Sci
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SS
N:
2502
-
4
7
5
2
A
co
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r
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s
ive
r
ev
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f m
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r
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B
I
S
T a
lg
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ith
ms fo
r
S
R
A
M st
a
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fa
u
lt d
etec
tio
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(
A
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n
Za
kwa
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Jid
in
)
401
p
atter
n
s
to
b
e
wr
itten
t
o
th
e
m
em
o
r
y
u
n
d
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test
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th
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x
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r
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lts
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wh
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p
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th
e
m
em
o
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y
to
d
etec
t
an
y
f
ailu
r
e
[
1
2
]
–
[
1
4
]
.
Hen
ce
,
t
h
e
b
u
ilt
-
in
MBIST
cir
cu
itry
p
r
o
v
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d
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f
aster
m
em
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test
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g
th
an
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s
in
g
ex
ter
n
al
test
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s
as
it
elim
in
ates
th
eir
test
laten
cy
[
4
]
,
[
1
5
]
,
[
1
6
]
.
Dif
f
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t
test
alg
o
r
ith
m
s
co
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s
is
t
o
f
d
i
s
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im
ilar
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p
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n
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eq
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ce
s
,
o
f
f
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r
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g
d
if
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e
r
en
t
f
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lt
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v
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n
d
test
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m
p
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ity
.
T
h
e
f
au
lt
co
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ag
e
d
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r
m
in
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s
th
e
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r
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tatic
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an
d
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m
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s
m
e
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(
S
R
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d
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test
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wh
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ch
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b
s
eq
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e
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tly
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ality
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test
.
Me
an
wh
ile,
th
e
co
m
p
lex
ity
o
f
a
test
in
d
icate
s
its
len
g
th
,
wh
ich
d
ir
ec
tly
in
f
l
u
en
ce
s
its
co
s
t:
th
e
h
ig
h
er
th
e
co
m
p
lex
ity
,
th
e
lo
n
g
er
th
e
test
len
g
th
,
an
d
th
e
h
ig
h
er
th
e
test
co
s
t
[
1
7
]
,
[
1
8
]
.
T
h
e
co
m
p
lex
ity
o
f
a
test
alg
o
r
ith
m
ca
n
b
e
eith
er
lin
e
ar
o
r
n
o
n
-
lin
ea
r
[
1
1
]
,
[
1
9
]
.
I
t
ca
n
b
e
ex
p
r
ess
ed
as
m
Np
,
wh
er
e
m
is
th
e
n
u
m
b
er
o
f
test
o
p
er
atio
n
s
in
th
e
s
eq
u
en
c
e,
an
d
N
is
th
e
s
ize
o
f
th
e
m
e
m
o
r
y
u
n
d
e
r
test
(
u
s
u
ally
d
e
f
in
ed
in
th
e
n
u
m
b
er
o
f
wo
r
d
ce
lls
)
.
A
test
alg
o
r
ith
m
i
s
s
aid
to
h
av
e
a
n
o
n
-
lin
ea
r
co
m
p
lex
ity
wh
en
p
is
g
r
ea
ter
th
a
n
1
.
T
wo
ex
am
p
les
o
f
n
o
n
-
lin
ea
r
test
alg
o
r
ith
m
s
ar
e
th
e
Gallo
p
in
g
Patter
n
(
GAL
PAT)
an
d
t
h
e
W
alk
in
g
Patter
n
(
W
AL
PAT)
alg
o
r
ith
m
s
,
with
a
co
m
p
le
x
ity
o
f
4
N2
a
n
d
2
N2
,
r
esp
ec
ti
v
ely
[
1
1
]
,
[
1
2
]
,
[
2
0
]
.
On
th
e
o
th
er
h
a
n
d
,
a
test
alg
o
r
ith
m
’
s
co
m
p
lex
ity
is
co
n
s
id
er
ed
lin
ea
r
wh
e
n
p
eq
u
al
s
1
.
A
lin
ea
r
-
co
m
p
lex
ity
test
alg
o
r
ith
m
ty
p
ically
p
r
o
d
u
ce
s
a
s
ig
n
if
ican
tly
s
h
o
r
t
er
test
tim
e
th
an
a
n
o
n
-
lin
ea
r
co
m
p
lex
ity
test
alg
o
r
ith
m
.
As
s
h
o
wn
in
T
ab
le
1
,
a
test
u
s
in
g
a
lin
ea
r
-
co
m
p
le
x
ity
alg
o
r
ith
m
o
n
a
1
MB
m
em
o
r
y
r
eq
u
ir
es
o
n
ly
1
0
2
.
4
m
s
.
I
n
co
n
tr
ast,
a
test
o
n
th
e
s
am
e
m
em
o
r
y
m
a
y
r
eq
u
ir
e
u
p
to
1
d
ay
to
b
e
co
m
p
let
ed
wh
en
a
n
o
n
-
lin
ea
r
co
m
p
lex
ity
alg
o
r
ith
m
is
u
s
ed
[
8
]
,
[
1
1
]
,
[
2
1
]
.
T
ab
le
1
.
T
h
e
test
co
m
p
letio
n
ti
m
e
o
n
a
1
-
MB m
em
o
r
y
f
o
r
v
a
r
io
u
s
test
co
m
p
lex
ities
Te
st
c
o
mp
l
e
x
i
t
y
N
N
3/
2
N
1
0
2
.
4
m
s
1
.
8
m
i
n
u
t
e
s
1
.
3
d
a
y
Fo
r
th
is
r
ea
s
o
n
,
th
e
in
d
u
s
tr
y
p
r
ef
er
s
a
lin
ea
r
-
c
o
m
p
lex
ity
te
s
t
alg
o
r
ith
m
lik
e
th
e
Ma
r
ch
-
s
er
ies
test
alg
o
r
ith
m
s
[
1
9
]
,
[
2
2
]
.
A
Ma
r
ch
test
alg
o
r
ith
m
co
n
s
is
ts
o
f
a
ce
r
tain
n
u
m
b
e
r
o
f
test
o
p
er
atio
n
s
th
at
m
u
s
t
b
e
ap
p
lied
o
n
ev
er
y
ce
ll
o
f
th
e
m
em
o
r
y
u
n
d
e
r
test
.
I
ts
test
s
eq
u
en
ce
co
m
b
in
es
th
e
f
o
ll
o
win
g
f
o
u
r
p
o
s
s
ib
le
o
p
er
atio
n
s
:
wr
ite
th
e
ce
ll
to
0
(
w0
)
,
wr
ite
th
e
ce
ll
to
1
(
w1
)
,
r
ea
d
f
r
o
m
th
e
ce
ll
an
d
ex
p
e
ctin
g
a
0
(
r
0
)
,
an
d
r
ea
d
f
r
o
m
th
e
ce
ll
an
d
e
x
p
ec
ti
n
g
a
1
(
r
1
)
[
1
1
]
.
Ad
d
itio
n
ally
,
th
ese
test
o
p
er
atio
n
s
m
ay
b
e
ca
r
r
ied
o
u
t
eith
e
r
in
th
e
ascen
d
in
g
(
⇑
)
o
r
d
escen
d
i
n
g
(
⇓
)
m
em
o
r
y
a
d
d
r
ess
o
r
d
er
.
I
n
th
e
f
o
r
m
er
ca
s
e,
th
e
test
o
p
er
atio
n
s
will f
ir
s
t b
e
ca
r
r
ied
o
u
t
o
n
th
e
ce
ll
with
t
h
e
b
ase
a
d
d
r
ess
[
2
3
]
–
[
2
5
]
.
A
Ma
r
ch
alg
o
r
ith
m
is
g
en
er
all
y
b
r
o
k
e
n
d
o
wn
in
to
m
u
ltip
le
s
m
aller
g
r
o
u
p
s
ca
lled
th
e
test
elem
en
ts
;
all
th
e
te
s
t
o
p
er
atio
n
s
th
at
b
elo
n
g
to
a
test
elem
en
t
m
u
s
t
b
e
ex
ec
u
ted
to
all
m
e
m
o
r
y
ce
lls
f
ir
s
t b
ef
o
r
e
m
o
v
in
g
o
n
t
o
th
e
f
o
llo
win
g
test
elem
en
ts
.
Fo
r
in
s
tan
ce
,
th
e
Ma
r
ch
X
al
g
o
r
ith
m
[
2
6
]
h
as
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇑
(
r
0
,
w1
)
;
⇓
(
r
1
,
w0
)
;
⇕
(
r
0
)
.
I
n
t
h
is
n
o
tatio
n
,
th
e
test
elem
en
ts
ar
e
s
ep
ar
ated
b
y
s
em
ico
lo
n
s
.
So
,
it
h
as
4
tes
t
elem
en
ts
,
s
tar
tin
g
f
r
o
m
T
E
0
to
T
E
3
.
I
n
T
E
0
(
⇕
(
w
0
)
)
,
all
ce
lls
will
b
e
s
et
to
0
r
eg
ar
d
less
o
f
th
e
m
em
o
r
y
ad
d
r
ess
d
ir
ec
tio
n
.
Nex
t,
in
T
E
1
(
⇑
(
r
0
,
w
1
)
)
,
all
ce
lls
(
s
tar
tin
g
f
r
o
m
th
e
ce
ll
with
th
e
b
ase
m
em
o
r
y
ad
d
r
ess
)
will
b
e
r
ea
d
(
ex
p
ec
tin
g
a
0
at
th
e
o
u
tp
u
t)
an
d
s
et
to
1
.
Af
ter
th
at,
in
T
E
2
(
⇓
(
r
1
,
w
0
)
)
,
all
ce
lls
will
b
e
r
ea
d
(
ex
p
ec
tin
g
a
1
at
th
e
o
u
t
p
u
t
)
an
d
s
et
to
1
,
s
tar
tin
g
f
r
o
m
th
e
ce
ll
with
th
e
f
in
al
m
em
o
r
y
a
d
d
r
ess
.
Fin
ally
,
a
ll
ce
lls
wil
l
b
e
r
ea
d
(
ex
p
ec
tin
g
a
0
at
th
e
o
u
tp
u
t)
in
an
y
ad
d
r
ess
d
ir
ec
tio
n
in
T
E
3
(
⇕
(
r
0
)
)
.
T
h
ese
test
o
p
er
atio
n
s
ar
e
illu
s
tr
ated
in
T
ab
le
2
u
s
in
g
a
s
im
p
le
3
-
ce
ll m
em
o
r
y
.
T
ab
le
2
.
An
illu
s
tr
atio
n
o
f
th
e
Ma
r
ch
X
alg
o
r
ith
m
test
o
p
er
at
io
n
s
Te
st
e
l
e
me
n
t
Te
st
se
q
u
e
n
c
e
I
l
l
u
st
r
a
t
i
o
n
TE
0
⇕
(
w
0
)
TE
1
⇑
(
r
0
,
w
1
)
TE
2
⇓
(
r
1
,
w
0
)
TE
3
⇕
(
r
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
4
3
,
No
.
2
,
Au
g
u
s
t
20
2
6
:
400
-
4
1
2
402
Selectin
g
an
a
p
p
r
o
p
r
iate
test
alg
o
r
ith
m
f
o
r
an
MBIST
co
n
t
r
o
ller
is
o
n
e
o
f
th
e
m
o
s
t
cr
iti
ca
l
d
esig
n
d
ec
is
io
n
s
b
ec
au
s
e
it
d
ir
ec
tly
af
f
ec
ts
b
o
th
test
q
u
ality
a
n
d
p
r
o
d
u
ctio
n
co
s
t.
T
est
al
g
o
r
ith
m
s
with
h
ig
h
co
m
p
lex
ity
(
e.
g
.
,
ex
ce
ed
i
n
g
1
8
N)
g
en
er
ally
ac
h
iev
e
ex
ce
l
len
t
f
au
lt
co
v
er
ag
e
b
u
t
r
eq
u
ir
e
lo
n
g
er
ex
ec
u
tio
n
tim
e,
th
er
eb
y
in
cr
ea
s
in
g
m
an
u
f
ac
tu
r
in
g
co
s
t.
C
o
n
v
e
r
s
ely
,
lo
w
-
co
m
p
lex
ity
alg
o
r
ith
m
s
s
ig
n
if
ican
tly
r
ed
u
ce
test
tim
e
b
u
t
m
a
y
f
ail
to
d
etec
t
ce
r
tain
m
em
o
r
y
f
au
lt
m
o
d
els,
r
esu
ltin
g
in
in
ad
e
q
u
ate
test
q
u
ality
[
2
7
]
,
[
2
8
]
.
C
o
n
s
eq
u
en
tly
,
a
n
e
f
f
ec
tiv
e
MBIST
test
alg
o
r
ith
m
m
u
s
t
ac
h
i
ev
e
a
s
u
itab
le
b
alan
ce
b
etwe
e
n
f
a
u
lt
co
v
e
r
ag
e
an
d
test
co
m
p
lex
ity
.
Ov
er
th
e
p
ast
s
ev
er
al
d
ec
ad
es,
n
u
m
er
o
u
s
Ma
r
ch
-
b
ased
test
alg
o
r
ith
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
t
o
im
p
r
o
v
e
f
au
lt
c
o
v
er
ag
e
w
h
ile
m
in
im
izin
g
test
co
m
p
lex
ity
.
T
h
ese
alg
o
r
ith
m
s
d
if
f
er
in
t
h
eir
test
s
eq
u
en
ce
s
,
d
etec
tab
le
f
au
lt
m
o
d
els,
im
p
lem
en
tatio
n
c
o
m
p
lex
ity
,
an
d
s
u
itab
ilit
y
f
o
r
MBIST
ar
ch
itectu
r
es.
Alth
o
u
g
h
s
ev
e
r
al
s
u
r
v
ey
s
h
av
e
d
is
cu
s
s
ed
m
em
o
r
y
test
in
g
,
a
c
o
m
p
r
e
h
en
s
iv
e
co
m
p
a
r
is
o
n
f
o
cu
s
in
g
o
n
th
e
ev
o
lu
tio
n
o
f
Ma
r
ch
alg
o
r
ith
m
s
,
th
eir
co
m
p
lex
ity
,
f
a
u
lt
co
v
er
ag
e,
a
n
d
d
esig
n
m
et
h
o
d
o
lo
g
ies
r
em
ain
s
lim
ited
.
T
h
er
ef
o
r
e,
th
is
p
a
p
er
p
r
esen
ts
a
co
m
p
r
eh
e
n
s
iv
e
r
ev
iew
o
f
Ma
r
ch
test
alg
o
r
ith
m
s
f
o
r
SR
AM
s
tatic
f
au
lt
d
etec
tio
n
in
MBIST
ap
p
l
icatio
n
s
.
First,
th
e
ch
ar
ac
ter
is
tics
an
d
d
etec
tio
n
r
e
q
u
ir
em
en
t
s
o
f
co
m
m
o
n
s
tatic
SR
AM
f
au
lt
m
o
d
els
ar
e
d
is
cu
s
s
ed
.
Nex
t,
r
ep
r
esen
tativ
e
Ma
r
ch
alg
o
r
ith
m
s
ar
e
s
y
s
t
em
atica
lly
co
m
p
ar
ed
i
n
ter
m
s
o
f
th
eir
test
s
eq
u
en
ce
s
,
co
m
p
u
tatio
n
al
co
m
p
lex
ity
,
a
n
d
f
au
lt
co
v
er
a
g
e.
Su
b
s
eq
u
en
tl
y
,
th
e
m
eth
o
d
s
u
s
ed
to
d
ev
el
o
p
an
d
o
p
tim
ize
th
e
s
e
alg
o
r
ith
m
s
,
in
clu
d
in
g
m
o
d
if
icatio
n
s
o
f
ex
is
tin
g
Ma
r
c
h
test
s
an
d
n
ewly
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
es,
ar
e
r
ev
iewe
d
an
d
an
aly
ze
d
.
Fin
ally
,
cu
r
r
en
t
r
esear
ch
ch
allen
g
es
an
d
f
u
tu
r
e
r
esear
c
h
d
ir
ec
tio
n
s
ar
e
h
ig
h
lig
h
ted
to
s
u
p
p
o
r
t
t
h
e
d
e
v
elo
p
m
e
n
t
o
f
m
o
r
e
ef
f
icien
t
MBIST
alg
o
r
i
th
m
s
f
o
r
e
m
er
g
in
g
m
em
o
r
y
tec
h
n
o
lo
g
ies.
2.
ST
A
T
I
C
F
AU
L
T
M
O
D
E
L
S IN SRA
M
Me
m
o
r
y
f
au
lts
ar
e
g
en
er
ally
c
lass
if
ied
in
to
s
tatic
f
au
lts
an
d
d
y
n
am
ic
f
au
lts
ac
co
r
d
in
g
to
t
h
e
n
u
m
b
er
o
f
test
o
p
er
atio
n
s
r
eq
u
ir
e
d
to
a
ctiv
ate
th
e
f
au
lty
b
eh
av
i
o
r
.
A
s
tatic
f
au
lt
ca
n
b
e
s
en
s
itized
a
n
d
d
etec
ted
u
s
in
g
a
s
in
g
le
m
em
o
r
y
o
p
er
atio
n
,
wh
er
ea
s
a
d
y
n
am
ic
f
a
u
lt
r
eq
u
ir
e
s
a
s
eq
u
en
ce
o
f
two
o
r
m
o
r
e
m
em
o
r
y
o
p
e
r
atio
n
s
f
o
r
ac
tiv
atio
n
an
d
o
b
s
er
v
ati
o
n
[
1
0
]
,
[
2
9
]
.
B
ec
au
s
e
s
tatic
f
au
lts
co
n
s
titu
te
th
e
m
ajo
r
ity
o
f
m
a
n
u
f
ac
tu
r
in
g
-
r
elate
d
d
ef
ec
ts
an
d
ca
n
b
e
d
etec
ted
u
s
in
g
r
elativ
ely
s
im
p
le
test
s
eq
u
en
ce
s
,
th
ey
h
av
e
b
ee
n
ex
ten
s
iv
ely
in
v
esti
g
ated
in
th
e
d
ev
elo
p
m
e
n
t
o
f
MBIST
alg
o
r
ith
m
s
.
Me
m
o
r
y
f
a
u
lts
ca
n
also
b
e
ca
teg
o
r
ized
as
u
n
lin
k
ed
o
r
lin
k
ed
f
au
lts
.
An
u
n
lin
k
ed
f
a
u
lt
o
cc
u
r
s
in
d
ep
e
n
d
en
tly
,
wh
er
e
th
e
f
au
lty
b
eh
a
v
io
r
o
f
o
n
e
m
em
o
r
y
ce
ll
is
u
n
af
f
ec
ted
b
y
o
th
e
r
f
au
lts
p
r
e
s
en
t
in
th
e
m
em
o
r
y
a
r
r
ay
.
I
n
co
n
tr
ast,
a
lin
k
ed
f
au
lt
ar
is
es
wh
en
two
o
r
m
o
r
e
f
au
lts
co
ex
is
t
an
d
in
ter
ac
t
with
o
n
e
an
o
th
er
.
Su
c
h
in
ter
ac
ti
o
n
s
m
ay
alter
,
m
ask
,
o
r
ev
en
co
m
p
en
s
ate
f
o
r
t
h
e
o
b
s
er
v
ab
le
b
eh
a
v
io
r
o
f
in
d
iv
id
u
al
f
au
lts
,
m
ak
in
g
f
au
lt
d
etec
tio
n
co
n
s
id
er
ab
ly
m
o
r
e
ch
allen
g
in
g
[
3
0
]
.
C
o
n
s
eq
u
en
tly
,
test
alg
o
r
ith
m
s
ca
p
ab
le
o
f
d
etec
tin
g
lin
k
e
d
f
au
lts
g
en
er
ally
r
eq
u
ir
e
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
test
s
eq
u
en
ce
s
th
an
th
o
s
e
d
esig
n
ed
s
o
lely
f
o
r
u
n
lin
k
e
d
f
au
lts
.
T
h
is
p
ap
er
co
n
s
id
er
s
9
ty
p
es
o
f
u
n
lin
k
ed
s
tatic
f
au
lts
,
as
d
escr
ib
ed
in
T
ab
le
3
.
Sin
g
le
-
ce
ll
f
au
lts
(
SC
F
)
,
T
F,
R
DF,
I
R
F,
DR
D
F,
an
d
W
DF
ar
e
SC
F
wh
o
s
e
f
au
lt
b
eh
av
io
r
s
o
n
l
y
af
f
ec
t
a
s
in
g
le
v
ictim
ce
ll.
I
n
co
n
t
r
ast,
C
Ftr,
C
Fd
r
d
,
an
d
C
Fwd
ar
e
th
e
Do
u
b
le
-
C
ell
f
au
lts
(
DC
F),
wh
er
e
th
e
f
au
lty
b
e
h
av
io
r
o
b
s
er
v
ed
in
a
v
ictim
ce
ll
(
v
)
d
ep
en
d
s
o
n
th
e
s
tate
o
r
t
h
e
o
p
er
atio
n
s
d
o
n
e
in
its
ag
g
r
ess
o
r
ce
ll
(
a
)
[
2
]
,
[
3
1
]
–
[
3
5
]
.
I
n
ad
d
itio
n
,
ea
ch
SC
F
co
n
s
is
t
s
o
f
2
f
au
lt
p
r
im
itiv
es
(
FP
)
,
wh
ich
in
d
icate
s
its
f
au
lty
ch
a
r
ac
ter
is
tics
u
s
in
g
th
e
<
S
/
V
/
O>
n
o
tatio
n
,
wh
er
e
S
s
h
o
ws
th
e
f
au
lt’s
s
en
s
it
izin
g
o
p
er
atio
n
s
,
V
r
ep
r
esen
ts
th
e
o
b
s
er
v
ed
f
au
lty
s
tate
at
th
e
v
ce
ll,
an
d
O
th
e
r
ea
d
v
alu
e
to
b
e
o
b
s
er
v
ed
at
th
e
o
u
tp
u
t
[
3
6
]
–
[
3
8
]
.
O
ca
n
h
av
e
‘
-
’
as
a
v
alu
e
if
it
is
ir
r
elev
an
t
o
r
is
e
x
p
ec
ted
to
b
e
id
en
tical
to
V
.
Me
an
wh
ile,
a
DC
F
h
as
8
FP
s
s
in
ce
it
d
ep
e
n
d
s
o
n
two
p
o
s
s
ib
le
s
tates
o
f
th
e
a
ce
ll
(
lo
w
o
r
h
ig
h
s
tate)
a
n
d
t
h
e
lo
ca
tio
n
o
f
th
e
a
ce
ll
ca
n
b
e
eith
e
r
b
ef
o
r
e
(
a
<v
)
o
r
a
f
ter
(
a
>v
)
th
e
v
ce
ll
with
in
th
e
m
e
m
o
r
y
.
T
h
er
ef
o
r
e,
th
e
FP
n
o
tati
o
n
f
o
r
a
DC
F
is
<
S
a
;S
v
/
V
/
O
>
a>
v
o
r
<
S
a
;S
v
/
V
/
O>
a<
v
.
T
h
e
FP
o
f
ea
ch
f
au
lt
also
in
d
icate
s
its
d
etec
tio
n
r
eq
u
ir
e
m
en
t,
as
in
th
e
n
ec
ess
ar
y
test
o
p
er
atio
n
s
eq
u
en
ce
to
s
en
s
itize
an
d
d
e
te
ct
it.
An
SAF
<
x/x’
/
-
>
ca
n
b
e
s
en
s
itized
b
y
s
ettin
g
all
m
em
o
r
y
ce
lls
to
x
,
wh
er
e
x
∈
{0
,
1
}.
T
h
en
,
its
f
au
lty
b
eh
av
io
r
ca
n
b
e
d
etec
ted
wh
en
a
r
ea
d
o
p
er
atio
n
f
r
o
m
th
e
af
f
ec
t
ed
v
ce
ll
r
etu
r
n
s
its
co
m
p
lem
en
t
x’
.
A
T
F
<
x’
w
x/
x’
/
-
>
s
en
s
itizatio
n
an
d
d
etec
ti
o
n
is
alm
o
s
t
id
en
tical
to
SA
F
<
x/x’
/
-
>,
b
u
t
all
ce
lls
’
s
tate
s
m
u
s
t
b
e
in
itialize
d
to
x’
b
ef
o
r
e
p
er
f
o
r
m
in
g
th
e
w
x
o
p
er
atio
n
.
R
DF
<r
x/x’
/x’
>
an
d
I
R
F
<r
x/x/x
’
>
ca
n
b
e
s
en
s
itized
an
d
d
etec
ted
b
y
r
ea
d
in
g
f
r
o
m
all
m
e
m
o
r
y
ce
lls
th
at
ar
e
s
et
to
x
-
s
tate.
T
h
ey
h
av
e
id
en
tical
d
etec
tio
n
r
eq
u
ir
em
e
n
ts
as
th
e
SAF
<
x/x’
/
-
>
[
3
4
]
.
Me
an
wh
ile,
a
DR
DF
<r
x/x’
/
x
>
ca
n
b
e
d
etec
te
d
b
y
p
e
r
f
o
r
m
in
g
t
h
e
r
ea
d
o
p
er
atio
n
twice
co
n
s
ec
u
tiv
ely
o
n
ev
er
y
m
em
o
r
y
ce
ll;
th
e
f
ir
s
t
r
ea
d
will
s
en
s
itize
its
f
au
lty
b
e
h
av
io
r
wh
ile
th
e
s
ec
o
n
d
wil
l
d
etec
t
it
at
th
e
o
u
t
p
u
t.
Fin
ally
,
a
W
DF
<
x
w
x/x’
/
-
>
ca
n
b
e
s
en
s
itized
b
y
wr
itin
g
a
n
x
lo
g
ic
to
m
e
m
o
r
y
ce
lls
co
n
tain
i
n
g
x
;
a
r
ea
d
o
p
er
atio
n
th
at
f
o
llo
ws
c
an
d
etec
t
its
f
au
lty
b
eh
av
io
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
co
mp
r
eh
en
s
ive
r
ev
iew
o
f m
emo
r
y
B
I
S
T a
lg
o
r
ith
ms fo
r
S
R
A
M st
a
tic
fa
u
lt d
etec
tio
n
(
A
ima
n
Za
kwa
n
Jid
in
)
403
T
ab
le
3
.
An
SR
AM
’
s
u
n
lin
k
e
d
s
tatic
f
au
lt m
o
d
els’
d
escr
ip
ti
o
n
s
F
a
u
l
t
FP
S
C
F
/
D
C
F
D
e
scri
p
t
i
o
n
I
l
l
u
st
r
a
t
i
o
n
S
t
u
c
k
-
a
t
f
a
u
l
t
(SAF)
<
0
/
1
/
-
>,
<
1
/
0
/
-
>
S
C
F
R
e
g
a
r
d
l
e
ss
o
f
t
h
e
n
e
w
w
r
i
t
t
e
n
v
a
l
u
e
,
a
v
c
e
l
l
’
s
st
a
t
e
r
e
mai
n
s
l
o
w
o
r
h
i
g
h
.
Tr
a
n
s
i
t
i
o
n
f
a
u
l
t
(
TF)
<
0
w
1
/
0
/
-
>
,
<
1
w
0
/
1
/
-
>
S
C
F
A
v
c
e
l
l
f
a
i
l
s
t
o
c
h
a
n
g
e
a
st
a
t
e
(
f
r
o
m
l
o
w
t
o
h
i
g
h
o
r
h
i
g
h
t
o
l
o
w
)
.
R
e
a
d
D
e
st
r
u
c
t
i
v
e
f
a
u
l
t
(
R
D
F
)
<
r
0
/
1
/
1
>
,
<
r
1
/
0
/
0
>
S
C
F
A
r
e
a
d
f
r
o
m
a
v
c
e
l
l
u
n
w
a
n
t
e
d
l
y
c
h
a
n
g
e
s i
t
s
st
a
t
e
a
n
d
r
e
t
u
r
n
s
i
n
c
o
r
r
e
c
t
o
u
t
p
u
t
.
I
n
c
o
r
r
e
c
t
r
e
a
d
f
a
u
l
t
(
I
R
F
)
<
r
0
/
0
/
1
>
,
<
r
1
/
1
/
0
>
S
C
F
A
r
e
a
d
f
r
o
m
a
v
c
e
l
l
r
e
t
u
r
n
s
i
n
c
o
r
r
e
c
t
o
u
t
p
u
t
.
D
e
c
e
p
t
i
v
e
r
e
a
d
d
e
s
t
r
u
c
t
i
v
e
f
a
u
l
t
(
D
R
D
F
)
<
r
0
/
1
/
0
>
,
<
r
1
/
0
/
1
>
S
C
F
A
r
e
a
d
f
r
o
m
a
v
c
e
l
l
u
n
w
a
n
t
e
d
l
y
c
h
a
n
g
e
s i
t
s
st
a
t
e
b
u
t
r
e
t
u
r
n
s
t
h
e
c
o
r
r
e
c
t
o
u
t
p
u
t
.
W
r
i
t
e
d
i
st
u
r
b
f
a
u
l
t
(WDF)
<
0
w
0
/
1
/
-
>
,
<
1
w
1
/
0
/
-
>
S
C
F
A
n
o
n
-
t
r
a
n
s
i
t
i
o
n
w
r
i
t
e
t
o
a
v
c
e
l
l
u
n
e
x
p
e
c
t
e
d
l
y
c
h
a
n
g
e
s
i
t
s st
a
t
e
.
Tr
a
n
s
i
t
i
o
n
c
o
u
p
l
i
n
g
f
a
u
l
t
(
C
F
t
r
)
<
0
;
0
w
1
/
0
/
-
>
a>
v
,
<
0
;
0
w
1
/
0
/
-
>
a<
v
,
<
1
;
0
w
1
/
0
/
-
>
a>
v
,
<
1
;
0
w
1
/
0
/
-
>
a<
v
,
<
0
;
1
w
0
/
1
/
-
>
a>
v
,
<
0
;
1
w
0
/
1
/
-
>
a<
v
,
<
1
;
1
w
0
/
1
/
-
>
a>
v
,
<
1
;
1
w
0
/
1
/
-
>
a<
v
D
C
F
A
v
c
e
l
l
f
a
i
l
s
t
o
c
h
a
n
g
e
a
st
a
t
e
(
f
r
o
m
l
o
w
t
o
h
i
g
h
o
r
h
i
g
h
t
o
l
o
w
)
e
v
e
r
y
t
i
me
i
t
s
a
c
e
l
l
i
s
i
n
a
sp
e
c
i
f
i
c
st
a
t
e
.
or
D
e
c
e
p
t
i
v
e
r
e
a
d
d
e
s
t
r
u
c
t
i
v
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c
o
u
p
l
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n
g
f
a
u
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(
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F
d
r
d
)
<
0
;
r
0
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>
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0
;
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1
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0
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1
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C
F
A
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e
a
d
f
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o
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a
v
c
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l
l
u
n
w
a
n
t
e
d
l
y
c
h
a
n
g
e
s i
t
s
st
a
t
e
b
u
t
r
e
t
u
r
n
s
t
h
e
c
o
r
r
e
c
t
o
u
t
p
u
t
e
v
e
r
y
t
i
me
i
t
s
a
c
e
l
l
i
s
i
n
a
sp
e
c
i
f
i
c
st
a
t
e
.
or
W
r
i
t
e
d
i
st
u
r
b
c
o
u
p
l
i
n
g
f
a
u
l
t
(
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F
w
d
)
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0
;
0
w
0
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1
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>
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0
;
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1
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1
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D
C
F
A
n
o
n
-
t
r
a
n
s
i
t
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o
n
w
r
i
t
e
t
o
a
v
c
e
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l
u
n
e
x
p
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t
e
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l
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c
h
a
n
g
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i
t
s st
a
t
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t
s
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e
l
l
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n
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i
f
i
c
s
t
a
t
e
.
or
I
n
co
n
tr
ast,
s
in
ce
a
DC
F
in
v
o
lv
es
two
co
u
p
lin
g
ce
lls
,
th
eir
d
etec
tio
n
r
eq
u
ir
em
en
ts
ar
e
m
o
r
e
co
m
p
lex
th
an
SC
Fs
.
C
Ftr,
C
Fd
r
d
,
an
d
C
Fwd
o
cc
u
r
r
en
ce
s
ca
n
b
e
s
en
s
itized
an
d
d
etec
ted
b
y
f
o
llo
win
g
th
e
s
am
e
r
u
les as
T
F,
DR
D
F,
an
d
W
D
F,
r
esp
ec
t
iv
ely
.
Ho
wev
er
,
th
e
id
e
n
tical
test
s
eq
u
en
ce
s
m
u
s
t b
e
ca
r
r
ied
o
u
t in
b
o
th
ad
d
r
ess
d
ir
ec
tio
n
s
to
co
v
er
b
o
th
a
>v
a
n
d
a
<v
ca
s
es.
T
ab
le
4
s
u
m
m
a
r
izes
th
e
r
e
q
u
ir
e
d
test
s
eq
u
e
n
c
es
to
s
en
s
itize
an
d
d
etec
t
th
ese
f
au
lts
[
2
7
]
,
[
3
4
]
.
I
n
th
is
tab
le,
th
e
n
ec
ess
ar
y
test
o
p
er
atio
n
s
to
d
etec
t
R
DF
an
d
I
R
F
ar
e
r
ep
r
esen
ted
b
y
SAF
s
in
ce
th
ei
r
d
etec
tio
n
r
e
q
u
ir
em
e
n
ts
ar
e
s
im
ilar
.
F
(
x
)
r
e
p
r
esen
ts
an
y
o
p
er
atio
n
(
s
)
to
ca
u
s
e
th
e
m
em
o
r
y
ce
lls
to
b
e
in
t
h
e
x
-
s
tate.
C
o
n
s
id
er
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w
0
)
;
⇑
(
r
0
,
w1
,
w1
)
;
⇓
(
r
1
,
w
0
,
w0
)
;
⇕
(
r
0
)
.
T
h
is
test
s
eq
u
en
ce
s
h
all
allo
w
th
e
MBIST
o
p
er
atio
n
to
d
etec
t th
e
f
o
llo
win
g
f
au
l
ts
:
−
SAF,
R
D
F,
an
d
I
R
F si
n
ce
it in
clu
d
es n
ec
ess
ar
y
th
e
r
ea
d
o
p
e
r
atio
n
s
(
r
0
in
T
E
1
an
d
T
E
3
,
an
d
r
1
in
T
E
2
).
−
W
DF
s
in
ce
it
p
er
f
o
r
m
s
n
o
n
-
tr
an
s
itio
n
wr
ite
o
p
er
atio
n
s
(
w1
w1
in
T
E
1
an
d
w0
w0
in
T
E
2
)
,
wh
ich
ar
e
im
m
ed
iately
f
o
llo
wed
b
y
a
r
ea
d
o
p
er
atio
n
.
−
Half
o
f
C
Ftr
(
C
Ftr
<0
;0
w1
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-
>
a>
v
,
C
Ftr
<1
;0
w1
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-
>
a<
v
,
C
F
t
r
<0
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w0
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/
-
>
a>
v
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d
C
Ftr
<1
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w0
/1
/
-
>
a>
v
).
−
Half
o
f
C
Fwd
(
C
Fwd
<0
;1
w1
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-
>
a>
v
,
C
Fwd
<1
;1
w1
/0
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-
>
a<
v
,
C
Fwd
<0
;0
w0
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/
-
>
a>
v
,
an
d
C
Fwd
<1
;0
w0
/1
/
-
>
a<
v
).
−
I
t c
an
n
o
t
d
etec
t D
R
DF a
n
d
C
F
d
r
d
s
in
ce
it h
as n
o
co
n
s
ec
u
tiv
e
d
o
u
b
le
-
r
ea
d
o
p
er
a
tio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
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n
esian
J
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&
C
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p
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Vo
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4
3
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2
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Au
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s
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20
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:
400
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4
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Nec
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F
(
x
)
,
w
x
, r
x
,
F
(
x’
)
)
;
o
r
⇕
(
F
(
x’
)
)
;
⇑
(
F
(
x
)
,
w
x
, r
x
,
F
(
x
)
)
;
o
r
⇕
(
F
(
x’
)
)
;
⇑
(
F
(
x
)
,
w
x
)
;
⇕
(r
x
,
…)
;
o
r
⇕
(
F
(
x
)
)
;
⇕
(w
x
, r
x
,
F
(
x’
)
,
F
(
x
)
)
;
o
r
⇕
(
F
(
x
)
)
;
⇕
(
F
(
x’
)
,
w
x
, r
x
,
F
(
x
)
)
;
o
r
⇕
(
F
(
x
)
)
;
⇕
(
F
(
x’
)
,
w
x
)
;
⇕
(r
x
,
…)
;
o
r
⇕
(
F
(
x
)
)
;
⇕
(w
x
, r
x
,
F
(
x
)
)
;
o
r
⇕
(
F
(
x
)
)
;
⇕
(w
x
)
;
⇕
(r
x
,
…)
;
R
e
q
u
i
r
e
d
t
e
s
t
se
q
u
e
n
c
e
s
f
o
r
C
F
w
d
<
x
;
x
w
x
/
x’
/
-
>
a<
v
d
e
t
e
c
t
i
o
n
a
r
e
o
b
t
a
i
n
e
d
b
y
r
e
v
e
r
si
n
g
t
h
e
a
d
d
r
e
ss
o
r
d
e
r
s i
n
t
h
e
t
e
st
se
q
u
e
n
c
e
.
To
d
e
t
e
c
t
C
F
w
d
<
x’
;
x
w
x
/
x’
/
-
>
a>
v
:
⇕
(
F
(
x
)
)
;
⇓
(
F
(
x
)
,
w
x
, r
x
,
F
(
x’
)
)
;
o
r
⇕
(
F
(
x’
)
)
;
⇓
(
F
(
x
)
,
w
x
, r
x
,
F
(
x
)
)
;
o
r
⇕
(
F
(
x’
)
)
;
⇓
(
F
(
x
)
,
w
x
)
;
⇕
(r
x
,
…)
;
o
r
⇕
(
F
(
x’
)
)
;
⇓
(
F
(
x
)
,
w
x
, r
x
,
F
(
x’
));
R
e
q
u
i
r
e
d
t
e
s
t
s
e
q
u
e
n
c
e
s
f
o
r
C
F
w
d
<
x’
;
x
w
x
/
x’
/
-
>
a<
v
d
e
t
e
c
t
i
o
n
a
r
e
o
b
t
a
i
n
e
d
b
y
r
e
v
e
r
si
n
g
t
h
e
a
d
d
r
e
s
s
o
r
d
e
r
s i
n
t
h
e
t
e
st
se
q
u
e
n
c
e
.
3.
RE
VI
E
W
O
F
M
B
I
ST
T
E
ST
AL
G
O
RIT
H
M
S
As
m
en
tio
n
ed
in
s
ec
tio
n
1
,
a
t
est
alg
o
r
ith
m
is
in
d
is
p
en
s
ab
le
in
th
e
MBIST
im
p
lem
en
tatio
n
to
d
ef
in
e
th
e
test
o
p
er
atio
n
s
eq
u
en
ce
to
b
e
ex
ec
u
ted
o
n
to
th
e
m
em
o
r
y
u
n
d
er
test
.
T
h
er
ef
o
r
e,
it
in
f
lu
en
ce
s
two
m
ain
cr
iter
ia
in
a
m
em
o
r
y
test
:
f
au
lt
co
v
er
ag
e
a
n
d
test
co
m
p
lex
ity
.
A
f
au
l
t
co
v
er
ag
e
(
FC
)
d
ef
in
es
th
e
test
q
u
ality
in
ter
m
s
o
f
th
e
n
u
m
b
er
o
f
p
o
s
s
ib
le
f
au
lts
to
b
e
d
etec
ted
d
u
r
in
g
a
test
.
I
t
ca
n
b
e
ca
lcu
lat
ed
b
y
d
i
v
id
in
g
th
e
n
u
m
b
er
o
f
d
etec
tab
le
f
a
u
lts
b
y
th
e
to
tal
f
a
u
lts
,
as
wr
itten
in
(
1
)
.
I
n
t
h
is
s
ec
tio
n
,
th
e
co
v
er
ag
e
o
f
ea
c
h
f
a
u
lt
is
ca
lcu
lated
in
th
e
f
o
llo
win
g
m
an
n
er
s
:
th
e
FC
o
f
ea
ch
SC
F
is
ca
lcu
lated
b
y
d
iv
id
in
g
th
e
n
u
m
b
er
o
f
d
etec
tab
le
FP
s
o
v
er
2
(
s
in
ce
ea
ch
SC
F
c
o
n
s
is
ts
o
f
2
FP
s
)
,
wh
ile
th
e
F
C
o
f
ea
ch
DC
F
is
o
b
tain
ed
b
y
d
iv
id
in
g
th
e
n
u
m
b
er
o
f
d
etec
tab
le
FP
s
o
v
er
8
.
Me
an
wh
i
le,
th
e
test
co
m
p
lex
ity
d
eter
m
in
es
th
e
test
d
u
r
atio
n
;
th
e
h
ig
h
er
t
h
e
co
m
p
lex
ity
,
th
e
lo
n
g
er
it
tak
e
s
f
o
r
a
test
to
co
m
p
lete.
A
lin
ea
r
-
co
m
p
le
x
ity
test
alg
o
r
ith
m
'
s
co
m
p
lex
ity
eq
u
als
th
e
to
tal
n
u
m
b
er
o
f
test
o
p
er
a
tio
n
s
with
in
its
test
s
eq
u
en
ce
m
u
ltip
lied
b
y
t
h
e
s
ize
o
f
th
e
m
em
o
r
y
o
r
N
.
Fo
r
ex
am
p
le,
th
e
co
m
p
lex
ity
o
f
th
e
Ma
r
ch
X
alg
o
r
ith
m
[
2
6
]
eq
u
als
6
N
s
in
ce
it
co
n
s
is
ts
o
f
6
r
ea
d
o
r
wr
ite
o
p
er
atio
n
s
in
its
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇑
(
r
0
,
w1
)
;
⇓
(
r
1
,
w0
)
;
⇕
(
r
0
)
.
=
(
1
)
B
ased
o
n
th
e
liter
atu
r
e,
th
e
cla
s
s
ical
ze
r
o
-
o
n
e
is
th
e
alg
o
r
ith
m
with
th
e
lo
west
co
m
p
lex
ity
(
4
N
)
,
with
th
e
⇓
(
w0
)
;
⇑
(
r
0
)
;
⇑
(
w1
)
;
⇓
(
r
1
)
test
s
eq
u
en
ce
.
Desp
ite
its
lo
w
co
m
p
lex
ity
,
it
h
as
th
e
p
o
o
r
est
f
au
lt
co
v
er
ag
e
am
o
n
g
all
ex
is
tin
g
test
alg
o
r
it
h
m
s
,
wh
er
e
it
ca
n
o
n
ly
d
etec
t
SAF,
R
DF,
I
R
F,
h
alf
o
f
T
F,
an
d
2
5
%
o
f
C
Ftr.
Me
an
wh
ile,
th
e
C
h
ec
k
er
b
o
ar
d
alg
o
r
ith
m
o
f
f
er
s
m
in
o
r
i
m
p
r
o
v
e
m
en
t
in
T
F
an
d
s
o
m
e
C
Fs
d
etec
tio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
co
mp
r
eh
en
s
ive
r
ev
iew
o
f m
emo
r
y
B
I
S
T a
lg
o
r
ith
ms fo
r
S
R
A
M st
a
tic
fa
u
lt d
etec
tio
n
(
A
ima
n
Za
kwa
n
Jid
in
)
405
Fig
u
r
e
1
illu
s
tr
ates
th
e
d
ata
b
ac
k
g
r
o
u
n
d
p
atter
n
s
u
s
ed
b
y
th
e
Z
er
o
-
On
e
an
d
C
h
ec
k
e
r
b
o
a
r
d
alg
o
r
ith
m
s
.
T
h
e
Z
er
o
-
On
e
al
g
o
r
ith
m
u
s
es
a
s
o
lid
d
ata
b
ac
k
g
r
o
u
n
d
,
as
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
.
Me
an
w
h
ile,
th
e
C
h
ec
k
er
b
o
ar
d
alg
o
r
ith
m
u
s
es
a
ch
ec
k
er
b
o
ar
d
d
ata
b
ac
k
g
r
o
u
n
d
,
wh
e
r
e
lo
g
ic
0
s
an
d
1
s
ar
e
alter
n
ated
b
etwe
en
co
n
s
ec
u
tiv
e
ce
lls
,
as sh
o
wn
in
Fig
u
r
e
1
(
b
)
.
(
a)
(
b
)
Fig
u
r
e
1
.
Data
b
ac
k
g
r
o
u
n
d
p
at
ter
n
s
u
s
ed
in
th
e
Z
e
r
o
-
On
e
an
d
C
h
ec
k
er
b
o
ar
d
alg
o
r
ith
m
s
: (
a
)
s
o
lid
d
ata
b
ac
k
g
r
o
u
n
d
an
d
(
b
)
ch
ec
k
e
r
b
o
ar
d
d
ata
b
ac
k
g
r
o
u
n
d
T
h
e
Ma
r
ch
X
alg
o
r
ith
m
[
2
6
]
an
d
th
e
MA
T
S++
alg
o
r
it
h
m
(
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇑
(
r
0
,
w1
)
;
⇓
(
r
1
,
w0
,
r
0
)
)
[
3
9
]
h
av
e
6
N
co
m
p
lex
ity
.
Un
lik
e
th
e
Z
e
r
o
-
On
e
an
d
C
h
ec
k
er
b
o
ar
d
alg
o
r
i
th
m
s
,
b
o
th
o
f
th
ese
alg
o
r
ith
m
s
p
r
o
v
id
e
f
u
ll
co
v
er
ag
e
o
f
T
F
an
d
5
0
%
co
v
er
ag
e
o
f
C
Ftr
[
3
0
]
.
T
h
e
Ma
r
c
h
C
alg
o
r
ith
m
,
with
1
1
N
co
m
p
lex
ity
,
h
as
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇑
(
r
0
,
w1
)
;
⇑
(
r
1
,
w0
)
;
⇕
(
r
0
)
;
⇓
(
r
0
,
w
1
)
;
⇓
(
r
1
,
w0
)
;
⇕
(
r
0
)
[
4
0
]
.
L
ater
,
a
r
ea
d
o
p
er
atio
n
with
in
th
e
test
s
eq
u
en
ce
was
co
n
s
id
er
ed
u
n
n
ec
ess
ar
y
an
d
h
en
ce
r
em
o
v
ed
to
cr
ea
te
a
n
ew
Ma
r
ch
C
-
alg
o
r
i
th
m
with
1
0
N
co
m
p
lex
ity
an
d
th
e
f
o
ll
o
win
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇑
(
r
0
,
w1
)
;
⇑
(
r
1
,
w0
)
;
⇓
(
r
0
,
w1
)
;
⇓
(
r
1
,
w0
)
;
⇕
(
r
0
)
[
4
1
]
.
Fo
r
y
ea
r
s
,
b
o
th
th
e
Ma
r
ch
C
an
d
Ma
r
ch
C
-
alg
o
r
ith
m
s
h
av
e
p
r
o
v
e
n
to
p
r
o
v
id
e
co
m
p
lete
c
o
v
er
ag
e
o
f
SAF,
T
F,
R
DF,
I
R
F,
C
Ftr,
an
d
co
n
v
en
tio
n
al
C
Fs
s
u
ch
a
s
th
e
Static
C
F
(
C
Fs
t)
,
I
d
em
p
o
ten
t
C
F
(
C
f
id
)
,
an
d
I
n
v
er
s
io
n
C
F
(
C
f
in
)
.
Ho
wev
er
,
d
u
e
to
tech
n
o
l
o
g
y
s
ca
lin
g
to
war
d
s
Ver
y
-
Dee
p
Su
b
m
icr
o
n
an
d
n
an
o
m
eter
p
r
o
ce
s
s
es,
n
ewe
r
f
a
u
lts
lik
e
DR
DF,
W
DF,
C
Fd
r
d
,
an
d
C
Fwd
h
a
v
e
em
er
g
ed
an
d
b
ec
o
m
e
m
o
r
e
r
elev
an
t
in
m
o
d
e
r
n
m
em
o
r
ies
[
4
2
]
.
C
o
n
s
eq
u
en
tl
y
,
th
ese
test
alg
o
r
ith
m
s
ar
e
n
o
lo
n
g
er
a
d
eq
u
ate
in
m
em
o
r
y
te
s
tin
g
to
d
etec
t th
ese
n
ew
f
au
lt
s
[
4
3
]
.
Ma
n
y
Ma
r
ch
test
alg
o
r
ith
m
s
with
co
m
p
lex
ities
h
ig
h
e
r
th
an
1
0
N
wer
e
cr
ea
ted
a
n
d
ca
n
d
et
ec
t
s
o
m
e
o
f
th
ese
f
au
lts
,
eith
er
f
u
lly
o
r
p
ar
tially
.
T
h
e
Ma
r
ch
C
L
alg
o
r
ith
m
,
with
1
2
N
co
m
p
lex
ity
,
h
a
s
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w
0
)
;
⇑
(
r
0
,
w1
)
;
⇕
(
r
1
)
;
⇑
(
r
1
,
w0
)
;
⇓
(
r
0
,
w1
)
;
⇕
(
r
1
)
;
⇓
(
r
1
,
w0
)
;
⇕
(
r
0
)
[
4
4
]
.
I
t
ca
n
f
u
lly
d
etec
t
C
Ftr
an
d
p
a
r
tially
d
etec
t
DR
DF
an
d
C
Fd
r
d
,
b
u
t
it
ca
n
n
o
t
b
e
u
s
ed
to
d
etec
t
W
DF
an
d
C
Fwd
.
Me
an
wh
ile,
th
e
Ma
r
ch
L
R
alg
o
r
ith
m
,
with
1
4
N
co
m
p
lex
ity
,
was
in
itially
p
r
o
p
o
s
ed
to
co
v
er
s
ev
er
al
lin
k
e
d
an
d
u
n
lin
k
e
d
s
tatic
f
au
lts
[
4
5
]
.
I
t
h
as
th
e
f
o
llo
wi
n
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇓
(
r
0
,
w1
)
;
⇑
(
r
1
,
w0
,
r
0
,
w1
)
;
⇑
(
r
1
,
w0
)
;
⇑
(
r
0
,
w1
,
r
1
,
w0
)
;
⇑
(
r
0
)
.
A
r
esear
ch
e
r
claim
s
it
f
u
lly
co
v
er
s
all
u
n
lin
k
ed
s
tatic
SC
F
s
an
d
DC
Fs
[
1
5
]
.
Ho
wev
er
,
it
is
u
n
ab
le
to
d
etec
t
t
h
ese
n
ew
f
au
lts
(
W
DF,
DR
DF,
C
Fwd
,
an
d
C
Fd
r
d
)
;
its
test
s
eq
u
en
ce
in
clu
d
es
n
ei
th
er
d
o
u
b
le
r
ea
d
o
p
er
atio
n
s
to
en
a
b
le
DR
DF
an
d
C
Fd
r
d
d
etec
tio
n
s
n
o
r
th
e
n
o
n
-
tr
an
s
itio
n
o
p
er
atio
n
s
to
d
ete
ct
W
DF
an
d
C
Fwd
[
4
6
]
.
Sev
er
al
1
4
N
-
co
m
p
lex
ity
test
alg
o
r
ith
m
s
ex
is
t
an
d
ar
e
p
r
ef
er
r
ed
b
y
th
e
in
d
u
s
tr
y
to
b
al
an
ce
f
au
lt
co
v
e
r
ag
e
an
d
test
co
m
p
lex
ity
[
3
3
]
.
T
h
e
Ma
r
ch
SR
alg
o
r
ith
m
,
with
⇕
(
w0
)
;
⇑
(
r
0
,
w1
,
r
1
,
w0
)
;
⇑
(
r
0
,
r
0
)
;
⇑
(
w1
)
;
⇓
(
r
1
,
w0
,
r
0
,
w1
)
;
⇓
(
r
1
,
r
1
)
test
s
eq
u
en
ce
,
p
r
o
v
id
es
co
m
p
lete
co
v
er
a
g
e
o
f
DR
DF
b
u
t
o
n
ly
h
alf
o
f
C
Fd
r
d
[
4
7
]
.
A
wo
r
k
was
ca
r
r
ied
o
u
t
in
[
3
3
]
to
m
o
d
if
y
th
e
d
ata
b
ac
k
g
r
o
u
n
d
b
its
u
s
ed
in
th
e
Ma
r
ch
SR
test
s
e
q
u
en
ce
to
estab
lis
h
th
e
m
o
d
if
ied
Ma
r
ch
SR
alg
o
r
ith
m
with
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇑
(r
0
,
w0
,
r
0
,
w1
)
;
⇑
(
r
1
,
r
1
)
;
⇑
(
w1
)
;
⇓
(
r
1
,
w0
,
r
0
,
w0
)
;
⇓
(
r
0
,
r
0
)
.
T
h
e
n
ewly
m
o
d
if
ied
test
s
eq
u
en
ce
co
m
p
letely
d
etec
t
s
all
SC
F,
5
0
%
C
Ftr
an
d
C
Fwd
,
an
d
6
2
.
5
%
co
v
er
a
g
e
o
f
C
Fd
r
d
.
Me
an
wh
ile,
th
e
Ma
r
ch
C
+
alg
o
r
ith
m
was
an
im
p
r
o
v
e
m
en
t
f
r
o
m
th
e
Ma
r
ch
C
-
alg
o
r
ith
m
b
y
a
d
d
in
g
4
r
ea
d
o
p
er
atio
n
s
in
to
th
e
latter
’
s
test
s
eq
u
en
ce
to
b
e
co
m
e
⇕
(
w0
)
;
⇑
(
r
0
,
w1
,
r
1
)
;
⇑
(
r
1
,
w0
,
r
0
)
;
⇓
(
r
0
,
w1
,
r
1
)
;
⇓
(
r
1
,
w0
,
r
0
)
;
⇕
(
r
0
)
[
4
8
]
.
C
o
m
p
ar
ed
to
th
e
latter
,
th
e
f
o
r
m
e
r
o
f
f
e
r
s
co
m
p
lete
d
etec
tio
n
o
f
DR
DF
an
d
C
Fd
r
d
.
Similar
to
th
e
Ma
r
ch
SR
alg
o
r
ith
m
,
it
d
o
es
n
o
t
p
r
o
v
id
e
an
y
d
etec
tio
n
o
f
W
DF
an
d
C
Fwd
.
T
h
e
Ma
r
c
h
AZ
2
alg
o
r
ith
m
,
with
1
4
N
co
m
p
lex
ity
,
h
a
s
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇓
(
w0
,
r
0
)
;
⇑
(
r
0
,
w1
,
w1
,
r
1
)
;
⇑
(
r
1
,
w0
)
;
⇓
(
r
0
,
w1
,
w1
,
r
1
)
;
⇑
(
r
1
)
.
I
t
b
alan
ce
s
test
f
au
lt
co
v
er
ag
e
an
d
co
m
p
lex
ity
b
y
co
v
er
in
g
1
0
0
%
o
f
all
SC
Fs
an
d
7
5
%
o
f
all
DC
Fs
[
2
7
]
.
Me
an
wh
ile,
th
e
Ma
r
ch
AZ
1
alg
o
r
ith
m
,
with
1
3
N
c
o
m
p
lex
ity
,
is
a
lo
wer
c
o
m
p
lex
ity
alter
n
ativ
e
to
th
e
Ma
r
c
h
AZ
2
alg
o
r
ith
m
,
o
f
f
e
r
in
g
a
s
lig
h
tly
lo
wer
C
Ftr
co
v
er
ag
e
(
6
2
.
5
%)
c
o
m
p
ar
e
d
to
th
e
latte
r
[
2
7
]
.
I
t
h
as
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇓
(
w1
)
;
⇑
(
w1
,
r
1
,
r
1
,
w0
)
;
⇑
(
w
0
,
r
0
)
;
⇑
(
r
0
,
w1
,
w1
,
r
1
)
;
⇑
(
r
1
)
.
T
h
e
Ma
r
ch
-
s
if
t
alg
o
r
ith
m
is
a
1
7
N
-
co
m
p
lex
ity
test
alg
o
r
ith
m
th
at
is
co
m
p
o
s
ed
b
y
⇕
(
w0
)
;
⇑
(
r
0
,
w1
)
;
⇓
(
r
1
,
w0
,
r
0
)
;
⇑
(
r
0
,
w1
)
;
⇑
(
r
1
,
w0
)
;
⇓
(
r
0
,
w0
,
r
0
)
;
⇑
(
r
0
,
w1
,
r
1
)
;
⇕
(
r
0
)
test
s
eq
u
en
ce
[
3
1
]
.
Desp
ite
its
test
co
m
p
lex
ity
th
at
is
h
ig
h
er
th
an
a
1
4
N
-
co
m
p
lex
ity
lik
e
th
e
Ma
r
ch
AZ
2
alg
o
r
it
h
m
,
it
o
f
f
er
s
a
lo
wer
o
v
er
all
f
au
lt
co
v
er
ag
e
s
in
ce
it
ca
n
o
n
ly
d
e
tect
h
alf
o
f
th
e
W
D
F,
5
o
u
t
o
f
8
FP
s
o
f
C
Fd
r
d
(
6
3
%),
an
d
2
o
u
t
o
f
8
FP
s
o
f
C
Fwd
(
2
5
%).
T
h
r
o
u
g
h
o
b
s
er
v
atio
n
,
its
test
s
eq
u
en
ce
in
cl
u
d
es
a
n
o
n
-
tr
an
s
itio
n
wr
ite
o
p
er
atio
n
o
n
lo
g
ic
0
(
0
w0
)
at
its
TE
5
.
C
o
n
s
eq
u
en
t
ly
,
it
is
u
n
ab
le
to
d
etec
t
W
DF
<1
w1
/0
/
-
>,
C
Fwd
<X
;1
w1
/
0
/
-
>
a>
v
,
an
d
C
Fwd
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
4
3
,
No
.
2
,
Au
g
u
s
t
20
2
6
:
400
-
4
1
2
406
<X
;1
w1
/0
/
-
>
a<
v
(
wh
er
e
X
r
ep
r
esen
ts
an
y
lo
g
ic
v
alu
e)
.
Me
a
n
wh
ile,
an
1
8
N
-
co
m
p
lex
ity
te
s
t
alg
o
r
ith
m
ca
lled
th
e
Ma
r
ch
-
ee
was e
s
tab
lis
h
ed
with
th
e
f
o
llo
win
g
test
s
eq
u
en
ce
:
⇑
(
w0
)
;
⇑
(
r
0
,
w1
,
r
1
)
;
⇑
(
r
1
,
w0
,
r
0
)
;
⇑
(
r
0
,
w1
)
;
⇓
(
r
1
,
w0
,
r
0
)
;
⇑
(
r
0
,
w0
)
;
⇓
(
r
0
,
w1
,
r
1
)
;
⇑
(
r
1
)
[
4
9
]
.
I
t
p
r
o
v
id
es
a
b
etter
o
v
er
all
f
a
u
lt
co
v
er
a
g
e
th
an
th
e
Ma
r
c
h
-
s
if
t
alg
o
r
ith
m
,
b
u
t
it
ca
n
o
n
ly
d
etec
t
5
0
%
o
f
th
e
W
DF
an
d
2
5
%
o
f
th
e
C
Fwd
d
u
e
to
th
e
s
a
m
e
wea
k
n
ess
f
o
u
n
d
in
th
e
latter
.
An
o
th
er
1
8
N
-
co
m
p
lex
ity
al
g
o
r
ith
m
ca
lled
th
e
Ma
r
ch
L
V,
with
⇕
(
w
0
)
;
⇑
(
r
0
,
w1
,
w1
,
r
1
)
;
⇑
(
r
1
,
w0
,
w0
,
r
0
)
;
⇓
(
r
0
,
r
0
,
w1
,
r
1
)
;
⇓
(
r
1
,
r
1
,
w0
,
r
0
)
;
⇓
(
r
0
)
test
s
eq
u
en
ce
,
p
r
o
v
id
es
b
etter
f
au
lt
co
v
er
ag
e
t
h
r
o
u
g
h
a
f
u
ll d
etec
tio
n
o
f
W
DF a
n
d
5
0
% d
etec
tio
n
o
f
C
Fwd
[
3
2
]
.
T
h
e
Ma
r
ch
MSS
alg
o
r
ith
m
,
a
ls
o
with
1
8
N
co
m
p
le
x
ity
,
h
as
b
ee
n
p
r
o
v
en
to
in
clu
d
e
a
m
i
n
im
al
test
s
eq
u
en
ce
to
co
m
p
letely
co
v
e
r
all
u
n
lin
k
ed
s
tatic
f
au
lts
in
S
R
AM
:
⇕
(
w0
)
;
⇑
(
r
0
,
r
0
,
w1
,
w1
)
;
⇑
(
r
1
,
r
1
,
w0
,
w0
)
;
⇓
(
r
0
,
r
0
,
w1
,
w1
)
;
⇓
(
r
1
,
r
1
,
w0
,
w0
)
;
⇕
(
r
0
)
[
3
4
]
.
I
t
ce
r
tain
l
y
p
r
o
v
id
es
f
aster
m
em
o
r
y
test
in
g
th
an
o
th
er
test
alg
o
r
ith
m
s
lik
e:
−
th
e
Ma
r
ch
C
S,
a
2
0
N
-
co
m
p
le
x
ity
alg
o
r
ith
m
with
⇕
(
w0
)
;
⇑
(
w0
,
r
0
,
w
1
,
r
1
)
;
⇕
(
w1
)
;
⇑
(
w
1
,
r
1
,
w
0
,
r
0
)
;
⇓
(
w0
,
r
0
,
w1
,
r
1
)
;
⇓
(
w1
,
r
1
,
w
0
,
r
0
)
;
⇕
(
w0
,
r
0
)
test
s
eq
u
en
ce
[
5
0
]
,
−
th
e
Ma
r
ch
SS
,
a
2
2
N
-
co
m
p
lex
ity
alg
o
r
ith
m
with
⇕
(
w0
)
;
⇑
(
r
0
,
r
0
,
w0
,
r
0
,
w1
)
;
⇑
(
r
1
,
r
1
,
w
1
,
r
1
,
w0
)
;
⇓
(
r
0
,
r
0
,
w0
,
r
0
,
w1
)
;
⇓
(
r
1
,
r
1
,
w1
,
r
1
,
w0
)
;
⇕
(
w
0
)
test
s
eq
u
en
ce
[
5
1
]
,
−
th
e
im
p
r
o
v
e
d
Ma
r
ch
C
+,
a
2
2
N
-
co
m
p
lex
ity
alg
o
r
ith
m
with
⇕
(
w0
)
;
⇑
(
w0
,
r
0
,
w1
,
w1
,
r
1
)
;
⇑
(
w1
,
r
1
,
w0
,
w0
,
r
0
)
;
⇓
(
r
0
,
w0
,
w1
,
w1
,
r
1
)
;
⇓
(
r
1
,
w
1
,
w0
,
w
0
,
r
0
)
;
⇕
(
r
0
)
t
est s
eq
u
en
ce
[
5
2
]
,
−
th
e
im
p
r
o
v
ed
Ma
r
c
h
L
R
,
a
2
2
N
-
co
m
p
lex
ity
alg
o
r
ith
m
with
⇕
(
w0
)
;
⇓
(
r
0
,
w1
)
;
⇑
(
r
1
,
r
1
,
w0
,
w0
,
r
0
,
r
0
,
w
1
,
w1
)
;
⇑
(
r
1
,
w0
)
;
⇑
(
r
0
,
r
0
,
w
1
,
w1
,
r
1
,
r
1
,
w0
,
w0
)
;
⇑
(
r
0
)
test
s
eq
u
en
ce
[
4
6
]
,
a
n
d
−
th
e
Ma
r
ch
R
AW
,
a
2
6
N
-
co
m
p
lex
ity
alg
o
r
ith
m
with
⇕
(
w0
)
;
⇑
(
r
0
,
w0
,
r
0
,
r
0
,
w1
,
r
1
)
;
⇑
(
r
1
,
w1
,
r
1
,
r
1
,
w0
,
r
0
)
;
⇓
(
r
0
,
w0
,
r
0
,
r
0
,
w
1
,
r
1
)
;
⇓
(
r
1
,
w1
,
r
1
,
r
1
,
w0
,
r
0
)
;
⇕
(
r
0
)
test
s
eq
u
en
ce
[
5
3
]
.
A
r
ed
u
ce
d
v
er
s
io
n
o
f
th
e
M
ar
ch
R
AW
alg
o
r
ith
m
,
ca
lled
th
e
Ma
r
ch
R
AW
1
alg
o
r
ith
m
,
is
also
av
ailab
le
with
th
e
f
o
llo
win
g
t
est
s
eq
u
en
ce
:
⇕
(
w0
)
;
⇕
(
w0
,
r
0
)
;
⇕
(
r
0
)
;
⇕
(
w1
,
r
1
)
;
⇕
(
r
1
)
;
⇕
(
w
1
,
r
1
)
;
⇕
(
r
1
)
;
⇕
(
w0
,
r
0
)
;
⇕
(
r
0
)
[
5
3
]
.
W
ith
o
n
ly
1
3
N
co
m
p
lex
ity
,
it o
n
ly
f
o
cu
s
es o
n
d
etec
tin
g
all
SC
Fs
.
T
ab
le
5
s
u
m
m
ar
izes
all
test
al
g
o
r
ith
m
s
r
e
v
iewe
d
in
th
is
s
ec
tio
n
:
F
d
esig
n
ates
t
h
at
a
f
au
lt
i
s
1
0
0
%
o
r
f
u
lly
co
v
e
r
ed
,
H
s
p
ec
if
ies
a
5
0
%
co
v
er
a
g
e,
wh
ile
‘
-
’
r
ep
r
esen
ts
th
e
n
o
n
-
d
etec
tab
ilit
y
o
f
a
f
au
lt.
T
h
is
tab
le
s
h
o
ws
th
at
a
m
in
im
u
m
o
f
1
8
N
co
m
p
lex
ity
is
r
eq
u
i
r
ed
f
o
r
a
test
alg
o
r
ith
m
to
f
u
lly
co
v
e
r
all
u
n
lin
k
ed
s
tatic
f
au
lts
.
I
n
c
o
n
tr
ast,
it
also
d
e
m
o
n
s
tr
ates
th
at
test
alg
o
r
ith
m
s
with
co
m
p
lex
ities
b
elo
w
1
0
N
h
av
e
p
o
o
r
f
a
u
lt
co
v
er
ag
es
a
n
d
c
an
n
o
t
d
etec
t
t
h
o
s
e
n
ew
f
au
lts
in
tr
o
d
u
ce
d
b
y
th
e
n
an
o
m
eter
p
r
o
ce
s
s
tech
n
o
lo
g
y
.
I
n
b
etwe
en
,
s
o
m
e
test
alg
o
r
ith
m
s
p
r
o
v
id
e
g
o
o
d
co
v
er
ag
e
in
m
a
n
y
f
au
lts
b
u
t
ar
e
n
o
ta
b
ly
u
n
ab
le
to
d
ete
ct
W
DF
an
d
C
Fwd
.
Fo
r
ex
am
p
le,
th
e
Ma
r
ch
C
+
alg
o
r
ith
m
o
f
f
er
s
ex
ce
llen
t
d
etec
tio
n
s
o
f
all
f
au
lts
ex
c
ep
t
W
DF
an
d
C
Fwd
.
Me
an
wh
ile,
th
e
Ma
r
ch
AZ
2
a
lg
o
r
ith
m
,
with
1
4
N
co
m
p
lex
it
y
,
d
eliv
er
s
th
e
b
est
co
v
e
r
ag
e
o
f
all
tar
g
eted
f
a
u
lts
am
o
n
g
all
b
elo
w
1
8
N
-
co
m
p
lex
ity
test
alg
o
r
ith
m
s
(
with
8
3
.
3
%
o
f
th
e
o
v
er
all
f
a
u
lt
co
v
er
a
g
e)
,
th
u
s
o
f
f
e
r
in
g
th
e
b
est b
alan
ce
b
etwe
en
t
h
e
m
em
o
r
y
test
in
g
’
s
co
m
p
lex
ity
an
d
f
au
lt c
o
v
er
ag
e
.
T
ab
le
5
.
MBIST
test
alg
o
r
ith
m
s
’
co
m
p
lex
ities
an
d
f
au
lt c
o
v
er
ag
es
Te
st
a
l
g
o
r
i
t
h
m
C
o
m
p
l
e
x
i
t
y
F
a
u
l
t
c
o
v
e
r
a
g
e
S
A
F
TF
R
D
F
I
R
F
D
R
D
F
W
D
F
C
F
t
r
C
F
d
r
d
C
F
w
d
To
t
a
l
Ze
r
o
-
O
n
e
4
N
F
H
F
F
-
-
2
5
%
-
-
2
5
%
M
A
TS+
+
6
N
F
F
F
F
-
-
H
-
-
3
3
%
M
a
r
c
h
X
6
N
F
F
F
F
-
-
H
-
-
3
3
%
M
a
r
c
h
C
-
10
N
F
F
F
F
-
-
F
-
-
4
4
%
M
a
r
c
h
C
L
12
N
F
F
F
F
H
-
F
H
-
5
8
%
M
a
r
c
h
A
Z
1
13
N
F
F
F
F
F
F
6
3
%
7
5
%
7
5
%
8
1
%
M
a
r
c
h
LR
14
N
F
F
F
F
-
-
F
-
-
4
4
%
M
a
r
c
h
S
R
14
N
F
F
F
F
F
-
F
H
-
6
1
%
M
o
d
i
f
i
e
d
M
a
r
c
h
S
R
14
N
F
F
F
F
F
F
H
6
3
%
H
6
9
%
M
a
r
c
h
C
+
14
N
F
F
F
F
F
-
F
F
-
7
2
%
M
a
r
c
h
A
Z
2
14
N
F
F
F
F
F
F
7
5
%
7
5
%
7
5
%
8
3
%
M
a
r
c
h
-
si
f
t
17
N
F
F
F
F
F
H
7
5
%
6
3
%
2
5
%
6
7
%
M
a
r
c
h
-
ee
18
N
F
F
F
F
F
H
F
F
2
5
%
8
1
%
M
a
r
c
h
LV
18
N
F
F
F
F
F
F
F
F
H
8
9
%
M
a
r
c
h
M
S
S
18
N
F
F
F
F
F
F
F
F
F
1
0
0
%
M
a
r
c
h
C
S
20
N
F
F
F
F
F
F
F
F
F
1
0
0
%
M
a
r
c
h
S
S
22
N
F
F
F
F
F
F
F
F
F
1
0
0
%
I
mp
r
o
v
e
d
M
a
r
c
h
C
+
22
N
F
F
F
F
F
F
F
F
F
1
0
0
%
I
mp
r
o
v
e
d
M
a
r
c
h
LR
22
N
F
F
F
F
F
F
F
F
F
1
0
0
%
M
a
r
c
h
R
A
W
26
N
F
F
F
F
F
F
F
F
F
1
0
0
%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
co
mp
r
eh
en
s
ive
r
ev
iew
o
f m
emo
r
y
B
I
S
T a
lg
o
r
ith
ms fo
r
S
R
A
M st
a
tic
fa
u
lt d
etec
tio
n
(
A
ima
n
Za
kwa
n
Jid
in
)
407
4.
RE
VI
E
W
O
F
T
E
S
T
AL
G
O
RIT
H
M
G
E
N
E
RA
T
I
O
N
M
E
T
H
O
DS
B
ased
o
n
th
e
liter
atu
r
e
r
ev
iew,
v
ar
io
u
s
way
s
ca
n
b
e
u
tili
ze
d
to
cr
ea
te
a
n
ew
test
alg
o
r
ith
m
.
I
n
m
em
o
r
y
test
in
g
’
s
ea
r
ly
d
a
y
s
,
class
ical
tes
t
alg
o
r
ith
m
s
lik
e
th
e
Z
er
o
-
On
e,
C
h
ec
k
er
b
o
a
r
d
,
GAL
PAT,
an
d
W
AL
PAT
wer
e
co
n
s
id
er
ed
th
e
ad
-
h
o
c
test
s
s
in
ce
n
o
f
o
r
m
al
f
au
lt
m
o
d
els
wer
e
estab
lis
h
ed
at
th
at
p
er
io
d
[
4
2
]
.
As
m
en
tio
n
ed
ea
r
lier
,
Z
er
o
-
O
n
e
an
d
C
h
ec
k
er
b
o
ar
d
alg
o
r
ith
m
s
p
r
o
d
u
ce
s
h
o
r
t
m
em
o
r
y
test
in
g
with
v
e
r
y
p
o
o
r
f
au
lt
co
v
er
a
g
es,
wh
er
ea
s
GAL
PAT
an
d
W
AL
PAT
alg
o
r
ith
m
s
o
f
f
er
h
ig
h
er
f
au
lt
co
v
e
r
ag
e
b
u
t
r
e
q
u
ir
e
an
ex
ten
s
iv
e
test
d
u
r
atio
n
d
u
e
to
t
h
eir
n
o
n
-
lin
ea
r
c
o
m
p
lex
ity
,
wh
ich
ca
u
s
es th
e
test
co
s
t to
ar
is
e
as we
ll.
Ma
n
y
Ma
r
ch
test
alg
o
r
ith
m
s
,
e.
g
.
,
t
h
e
Ma
r
ch
C
an
d
MA
T
S++,
wer
e
cr
ea
ted
b
ased
o
n
th
e
test
alg
o
r
ith
m
g
e
n
er
atio
n
b
y
s
im
u
l
atio
n
(
T
AGS)
tech
n
i
q
u
e,
o
win
g
to
th
e
estab
lis
h
m
en
t o
f
m
em
o
r
y
f
au
lt m
o
d
els in
th
e
1
9
8
0
s
[
4
2
]
.
T
h
is
tech
n
iq
u
e
cr
ea
tes
m
u
ltip
le
tem
p
lates
c
o
n
tain
in
g
all
p
o
s
s
ib
le
co
m
b
in
atio
n
s
o
f
r
ea
d
an
d
wr
ite
o
p
er
atio
n
s
at
v
ar
io
u
s
s
tag
es;
it
s
tar
ts
at
th
e
f
ir
s
t
s
tag
e
with
a
1
N
-
co
m
p
lex
ity
tem
p
late
co
n
tain
in
g
a
w
r
ite
o
p
er
atio
n
.
Af
ter
th
at,
th
e
c
o
m
p
lex
ities
o
f
t
h
e
tem
p
lates
will
g
r
ad
u
ally
in
cr
ea
s
e
at
ea
ch
s
tag
e.
E
ac
h
tem
p
late’
s
f
au
lt
co
v
er
ag
e
is
d
eter
m
in
ed
at
ea
ch
s
tag
e
th
r
o
u
g
h
an
aly
s
e
s
u
s
in
g
a
f
au
lt
s
im
u
lato
r
lik
e
th
e
R
AM
s
im
u
lato
r
f
o
r
e
r
r
o
r
s
cr
ee
n
in
g
(
R
AM
SES)
.
Ad
d
itio
n
ally
,
all
a
n
aly
ze
d
tem
p
lates
th
at
d
o
n
o
t
s
h
o
w
an
y
f
a
u
lt
co
v
er
ag
e
im
p
r
o
v
em
e
n
t
f
r
o
m
th
e
p
r
ev
i
o
u
s
s
tag
e
ar
e
r
em
o
v
ed
f
r
o
m
f
u
r
th
er
an
aly
s
is
.
T
h
e
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
a
tem
p
late
co
n
tain
in
g
th
e
test
s
eq
u
en
ce
p
r
o
v
id
i
n
g
1
0
0
%
c
o
v
er
ag
e
o
f
th
e
t
ar
g
eted
f
au
lts
is
p
r
o
d
u
ce
d
o
r
th
e
m
ax
im
u
m
test
len
g
th
is
r
ea
c
h
e
d
[
1
1
]
.
T
h
e
T
AGS
p
r
o
ce
s
s
f
lo
w
is
d
ep
icted
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
A
n
ew
Ma
r
ch
test
alg
o
r
ith
m
g
en
er
atio
n
f
lo
w
u
s
in
g
T
AGS
An
o
th
er
way
to
cr
ea
te
a
n
e
w
test
a
lg
o
r
ith
m
is
th
e
FP
-
b
ased
g
en
er
atio
n
m
eth
o
d
,
w
h
ich
was
s
u
cc
ess
f
u
lly
u
s
ed
to
estab
lis
h
th
e
Ma
r
ch
SS
an
d
th
e
Ma
r
c
h
MSS
alg
o
r
ith
m
s
[
3
4
]
,
[
4
2
]
,
[
5
1
]
.
I
n
th
is
m
eth
o
d
,
all
r
eq
u
ir
ed
test
o
p
e
r
atio
n
s
eq
u
en
ce
s
to
d
etec
t
in
ten
d
ed
f
a
u
l
ts
ar
e
id
en
tifie
d
b
ased
o
n
th
ei
r
FP
s
.
Fro
m
h
er
e,
a
n
ew
test
s
eq
u
en
ce
is
d
ev
elo
p
ed
to
p
r
o
v
id
e
o
p
tim
u
m
d
etec
t
io
n
o
f
th
ese
f
au
lts
.
Fo
r
ex
am
p
le,
s
ix
p
r
o
p
o
s
itio
n
s
wer
e
estab
lis
h
ed
wh
en
cr
ea
tin
g
th
e
Ma
r
ch
MSS
alg
o
r
ith
m
to
g
u
ar
an
tee
its
co
m
p
lete
d
etec
tio
n
o
f
all
u
n
lin
k
ed
s
tatic
f
au
lts
in
S
R
AM
.
Fo
r
i
n
s
tan
ce
,
to
en
s
u
r
e
its
co
v
er
ag
e
o
f
DR
DF
an
d
C
Fd
r
d
,
its
test
s
eq
u
en
ce
m
u
s
t
in
clu
d
e
at
least
two
(
r
0
,
r
0
)
s
eq
u
en
ce
s
an
d
two
(
r
1
,
r
1
)
s
eq
u
en
ce
s
,
o
n
e
o
f
ea
c
h
m
u
s
t
h
av
e
an
a
d
d
r
ess
o
r
d
er
th
at
is
th
e
o
p
p
o
s
ite
o
f
t
h
e
o
t
h
er
:
it
m
u
s
t
c
o
n
tain
at
least
o
n
e
⇑
(
…,
r
x
,
r
x
,
…)
an
d
o
n
e
⇓
(
…,
r
x
,
r
x
,
…)
.
An
au
to
m
atio
n
to
o
l
was
u
s
ed
to
d
ev
elo
p
4
9
n
ew
test
s
eq
u
e
n
ce
s
co
n
tain
in
g
1
8
r
ea
d
o
r
wr
ite
o
p
er
atio
n
s
,
a
m
o
n
g
wh
ich
th
e
Ma
r
ch
MSS
alg
o
r
it
h
m
test
s
eq
u
en
ce
was
r
ec
o
g
n
i
ze
d
to
p
r
o
v
id
e
th
e
b
est
f
au
lt
c
o
v
er
ag
e,
d
etec
tin
g
all
u
n
lin
k
ed
s
tatic
f
au
lts
in
SR
AM
[
3
4
]
.
Fu
r
th
er
m
o
r
e
,
m
an
y
test
alg
o
r
i
th
m
s
wer
e
g
en
er
ated
f
r
o
m
im
p
r
o
v
in
g
an
o
t
h
er
ex
is
tin
g
test
alg
o
r
ith
m
.
On
o
n
e
h
an
d
,
m
an
y
o
f
th
ese
alg
o
r
ith
m
s
wer
e
cr
ea
ted
b
y
ex
ten
d
in
g
th
ei
r
in
itial
test
s
eq
u
en
ce
s
th
r
o
u
g
h
ad
d
itio
n
al
test
o
p
er
atio
n
s
.
Fo
r
ex
am
p
le,
th
e
Ma
r
ch
C
+
alg
o
r
ith
m
r
esu
lted
f
r
o
m
a
d
d
in
g
f
o
u
r
r
ea
d
o
p
er
atio
n
s
in
to
th
e
Ma
r
ch
C
-
alg
o
r
ith
m
s
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
,
th
u
s
en
ab
lin
g
th
e
DR
DF
an
d
C
Fd
r
d
d
etec
tio
n
s
[
4
8
]
.
Me
an
wh
ile,
th
e
im
p
r
o
v
e
d
M
ar
ch
L
R
was
cr
ea
ted
b
y
ad
d
in
g
8
n
ew
test
o
p
er
atio
n
s
i
n
to
th
e
Ma
r
ch
L
R
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
4
3
,
No
.
2
,
Au
g
u
s
t
20
2
6
:
400
-
4
1
2
408
alg
o
r
ith
m
’
s
test
s
eq
u
en
ce
,
r
esu
ltin
g
in
th
e
co
m
p
lete
d
etec
tio
n
o
f
DR
DF,
C
Fd
r
d
,
W
DF,
a
n
d
C
Fwd
,
wh
ich
ar
e
u
n
d
etec
tab
le
b
y
t
h
e
Ma
r
ch
L
R
alg
o
r
ith
m
[
4
6
]
.
Desp
ite
en
h
an
cin
g
th
e
f
a
u
lt
co
v
er
a
g
e,
t
h
is
m
eth
o
d
h
as
a
d
r
awb
ac
k
:
it
u
n
d
o
u
b
ted
ly
i
n
cr
ea
s
es
th
e
test
co
m
p
lex
ity
s
in
ce
ex
tr
a
test
o
p
er
atio
n
s
ar
e
in
v
o
lv
ed
in
d
etec
tin
g
m
o
r
e
f
a
u
lts
.
On
th
e
o
th
er
h
an
d
,
a
wo
r
k
p
r
o
p
o
s
ed
in
[
3
3
]
o
p
tim
izes
th
e
d
ata
b
ac
k
g
r
o
u
n
d
u
s
ed
in
th
e
Ma
r
ch
SR
alg
o
r
ith
m
’
s
test
s
eq
u
e
n
ce
w
h
ile
k
ee
p
in
g
its
co
m
p
lex
ity
u
n
c
h
an
g
ed
,
as
s
h
o
w
n
in
Fig
u
r
e
4
.
C
o
m
p
ar
e
d
to
th
e
Ma
r
ch
SR
’
s
test
s
eq
u
en
ce
,
th
e
m
o
d
if
ied
Ma
r
c
h
SR
’
s
test
s
eq
u
en
ce
in
clu
d
es
n
o
n
-
tr
a
n
s
itio
n
wr
ite
o
p
er
atio
n
s
in
its
T
E
1
an
d
T
E
3
to
en
a
b
le
th
e
d
etec
tio
n
s
o
f
W
DF a
n
d
C
Fwd
,
wh
ic
h
ar
e
u
n
d
etec
tab
le
b
y
th
e
f
o
r
m
er
.
Ho
wev
er
,
it
h
as
s
ev
er
al
lim
itatio
n
s
:
it
f
o
cu
s
es
o
n
ly
o
n
en
ab
l
in
g
SC
F
d
etec
tio
n
an
d
ca
n
e
n
ab
le
W
DF
an
d
C
Fwd
d
etec
tio
n
s
o
n
ly
wh
en
th
e
i
n
p
u
t
test
s
eq
u
en
ce
i
n
clu
d
es
d
o
u
b
le
-
r
ea
d
o
p
er
atio
n
s
[
5
4
]
.
T
h
er
ef
o
r
e,
th
e
wo
r
k
d
o
n
e
in
[
2
7
]
im
p
r
o
v
ed
i
t
b
y
ad
d
in
g
s
ev
er
al
m
o
r
e
s
tep
s
to
r
ea
r
r
an
g
e
th
e
test
o
p
er
ati
o
n
s
an
d
o
p
tim
i
zin
g
th
e
test
ad
d
r
ess
es
to
en
ab
le
an
d
r
em
o
v
e
r
ed
u
n
d
an
cies
in
DC
F
d
etec
tio
n
s
.
I
t
r
esu
lted
in
th
e
Ma
r
ch
AZ
2
alg
o
r
ith
m
,
with
1
4
N
co
m
p
lex
i
ty
,
d
er
iv
ed
b
y
m
o
d
if
y
i
n
g
th
e
ex
is
tin
g
Ma
r
ch
L
R
alg
o
r
ith
m
’
s
test
s
eq
u
en
ce
,
as
d
ep
icted
in
Fig
u
r
e
5
.
Af
ter
ad
ju
s
tin
g
th
e
lat
ter
’
s
d
ata
b
ac
k
g
r
o
u
n
d
,
th
e
ad
d
r
ess
o
r
d
er
s
ar
e
o
p
tim
ized
b
y
r
ev
er
s
in
g
its
T
E
4
’
s
ad
d
r
ess
d
i
r
ec
tio
n
(
f
r
o
m
⇑
t
o
⇓
)
to
elim
in
ate
d
u
p
licated
test
elem
en
t
an
d
DC
F
d
etec
tio
n
r
ed
u
n
d
an
cies.
Fin
ally
,
s
ev
er
a
l
test
o
p
er
atio
n
s
ar
e
r
ea
r
r
an
g
ed
to
en
ab
le
W
DF
an
d
C
F
wd
d
etec
tio
n
s
.
T
h
e
Ma
r
ch
AZ
2
alg
o
r
ith
m
d
eliv
e
r
s
th
e
b
est
co
v
er
ag
e
o
f
th
e
t
ar
g
eted
f
au
lts
am
o
n
g
all
test
alg
o
r
ith
m
s
with
a
co
m
p
lex
ity
lo
wer
th
an
1
8
N
.
Fig
u
r
e
3
.
T
h
e
Ma
r
ch
C
+
cr
ea
ti
o
n
b
y
ad
d
in
g
f
o
u
r
r
ea
d
o
p
er
ati
o
n
s
in
to
th
e
Ma
r
c
h
C
-
alg
o
r
ith
m
’
s
test
s
eq
u
en
ce
Fig
u
r
e
4
.
T
h
e
m
o
d
if
ied
Ma
r
c
h
SR
alg
o
r
ith
m
th
at
is
d
er
iv
ed
f
r
o
m
th
e
Ma
r
c
h
SR
alg
o
r
ith
m
’
s
d
ata
b
ac
k
g
r
o
u
n
d
o
p
tim
izatio
n
Fig
u
r
e
5
.
T
h
e
cr
ea
tio
n
o
f
t
h
e
Ma
r
ch
AZ
2
alg
o
r
ith
m
f
r
o
m
t
h
e
m
o
d
if
icatio
n
o
f
th
e
Ma
r
ch
L
R
alg
o
r
ith
m
Desp
ite
t
h
e
s
ig
n
if
ican
t
p
r
o
g
r
e
s
s
in
b
alan
cin
g
test
co
m
p
lex
it
y
an
d
s
tatic
f
au
lt
co
v
e
r
ag
e,
co
n
s
id
er
ab
le
o
p
p
o
r
tu
n
ities
r
em
ain
to
im
p
r
o
v
e
th
e
ef
f
icien
cy
an
d
ca
p
ab
ilit
y
o
f
m
em
o
r
y
test
in
g
.
E
x
is
tin
g
Ma
r
ch
alg
o
r
ith
m
s
,
s
u
ch
as M
ar
ch
AZ
2
(
1
4
N)
an
d
Ma
r
ch
MSS (
1
8
N)
,
p
r
o
v
i
d
e
e
x
ce
llen
t c
o
v
er
ag
e
o
f
u
n
lin
k
ed
s
tatic
f
au
lts
b
u
t a
r
e
g
en
er
ally
in
s
u
f
f
icien
t
f
o
r
d
et
ec
tin
g
m
o
r
e
co
m
p
lex
f
au
lt
ty
p
es,
in
clu
d
in
g
lin
k
ed
s
tatic
f
au
lts
an
d
d
y
n
am
ic
f
au
lts
.
Acc
o
r
d
in
g
to
t
h
e
liter
atu
r
e,
co
m
p
r
eh
en
s
iv
e
d
y
n
am
i
c
f
au
lt
d
etec
tio
n
ty
p
ically
r
e
q
u
ir
es
s
u
b
s
t
an
tially
h
ig
h
er
test
co
m
p
lex
ity
,
as
d
e
m
o
n
s
tr
ated
b
y
alg
o
r
ith
m
s
s
u
ch
as
Ma
r
ch
SL2
4
(
2
4
N)
[
5
5
]
,
Ma
r
ch
FR
DD
(
3
8
N)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
co
mp
r
eh
en
s
ive
r
ev
iew
o
f m
emo
r
y
B
I
S
T a
lg
o
r
ith
ms fo
r
S
R
A
M st
a
tic
fa
u
lt d
etec
tio
n
(
A
ima
n
Za
kwa
n
Jid
in
)
409
[
2
]
,
an
d
Ma
r
ch
L
SD
(
7
5
N)
[
5
5
]
.
C
o
n
s
eq
u
en
tly
,
f
u
tu
r
e
r
esea
r
ch
s
h
o
u
ld
f
o
cu
s
o
n
d
ev
el
o
p
i
n
g
lo
w
-
co
m
p
lex
ity
test
alg
o
r
ith
m
s
ca
p
ab
le
o
f
d
e
tectin
g
d
y
n
a
m
ic
f
au
lts
wh
ile
m
ain
tain
in
g
h
ig
h
f
au
lt
co
v
e
r
ag
e
an
d
s
h
o
r
t
test
ex
ec
u
tio
n
tim
e
.
Pro
m
is
in
g
d
i
r
ec
tio
n
s
in
clu
d
e
o
p
tim
izin
g
ex
is
tin
g
Ma
r
ch
alg
o
r
ith
m
s
t
h
r
o
u
g
h
r
ed
u
n
d
an
c
y
r
ed
u
ctio
n
,
o
p
e
r
atio
n
r
e
o
r
d
er
i
n
g
,
o
r
h
y
b
r
id
test
s
tr
ateg
ies,
as d
em
o
n
s
tr
ated
in
r
ec
en
t
s
tu
d
ies
[
5
6
]
,
[
5
7
]
.
I
n
ad
d
itio
n
t
o
im
p
r
o
v
in
g
SR
AM
test
in
g
,
f
u
r
th
er
r
esear
ch
is
n
ee
d
ed
to
estab
lis
h
f
au
lt
m
o
d
els
an
d
MBIST
alg
o
r
ith
m
s
f
o
r
em
er
g
in
g
m
em
o
r
y
tech
n
o
lo
g
ie
s
.
Ad
v
an
ce
d
n
o
n
-
v
o
latile
m
em
o
r
ies,
s
u
ch
as
Ma
g
n
eto
r
esis
tiv
e
R
AM
(
MR
AM
)
,
r
esis
tiv
e
R
AM
(
R
R
AM
)
,
p
h
ase
-
ch
an
g
e
m
em
o
r
y
(
PC
M)
,
an
d
Fer
r
o
elec
tr
ic
R
AM
(
Fe
R
AM
)
,
ex
h
ib
it
o
p
er
atin
g
p
r
in
cip
les
an
d
f
ailu
r
e
m
ec
h
an
is
m
s
th
at
d
if
f
er
f
u
n
d
am
e
n
tally
f
r
o
m
th
o
s
e
o
f
co
n
v
en
tio
n
al
SR
AM
.
Fo
r
ex
a
m
p
le,
MRAM
s
to
r
es
in
f
o
r
m
a
tio
n
u
s
in
g
m
ag
n
etic
tu
n
n
el
ju
n
ctio
n
s
in
s
tead
o
f
ch
ar
g
e,
r
esu
ltin
g
in
u
n
iq
u
e
f
au
lt
b
eh
av
i
o
r
s
th
at
ca
n
n
o
t
b
e
ad
eq
u
ately
r
ep
r
esen
te
d
b
y
c
o
n
v
en
tio
n
al
SR
AM
f
au
lt
m
o
d
els.
As
a
r
esu
lt,
th
e
d
ev
elo
p
m
en
t
o
f
co
m
p
r
eh
e
n
s
iv
e
f
au
lt
m
o
d
els,
ef
f
icien
t
t
est
alg
o
r
ith
m
s
,
an
d
d
ed
icate
d
MBIST
ar
c
h
itectu
r
es
f
o
r
t
h
ese
em
er
g
i
n
g
m
em
o
r
ies
r
em
ain
s
a
n
im
p
o
r
tan
t
r
esear
ch
d
ir
ec
tio
n
.
Fu
r
th
er
m
o
r
e
,
in
teg
r
atin
g
ad
ap
tiv
e
test
in
g
tech
n
iq
u
es,
m
ac
h
in
e
lear
n
in
g
,
o
r
a
r
tific
ial
in
tellig
en
ce
in
t
o
MBIST
d
esig
n
m
ay
p
r
o
v
id
e
ad
d
itio
n
al
o
p
p
o
r
tu
n
ities
to
o
p
tim
ize
test
g
en
er
atio
n
,
im
p
r
o
v
e
f
au
lt
d
ia
g
n
o
s
is
,
an
d
r
ed
u
ce
o
v
er
all
test
in
g
co
s
t f
o
r
f
u
tu
r
e
h
ig
h
-
d
e
n
s
ity
m
em
o
r
y
s
y
s
tem
s
.
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ted
a
co
m
p
r
eh
en
s
iv
e
r
ev
iew
o
f
MBIST
alg
o
r
ith
m
s
f
o
r
d
etec
tin
g
u
n
li
n
k
ed
s
tatic
f
au
lts
in
SR
AM
.
T
h
e
r
ev
iew
ex
am
in
ed
t
h
e
ch
a
r
ac
ter
is
tics
an
d
d
etec
tio
n
r
e
q
u
ir
em
e
n
ts
o
f
m
ajo
r
s
tatic
f
au
lt
m
o
d
els
an
d
an
aly
ze
d
r
ep
r
esen
tativ
e
Ma
r
ch
test
alg
o
r
ith
m
s
in
ter
m
s
o
f
th
eir
test
s
eq
u
en
ce
s
,
co
m
p
u
tatio
n
al
co
m
p
lex
ity
,
an
d
f
au
lt
co
v
er
ag
e.
T
h
e
co
m
p
ar
is
o
n
d
em
o
n
s
tr
ates
th
at
th
e
ef
f
ec
tiv
en
ess
o
f
an
MBIST
im
p
lem
en
tatio
n
is
lar
g
ely
d
ete
r
m
in
ed
b
y
th
e
s
elec
ted
test
alg
o
r
ith
m
,
wh
ich
d
ir
ec
tly
in
f
l
u
en
ce
s
test
q
u
ality
,
ex
ec
u
tio
n
tim
e,
a
n
d
m
an
u
f
a
ctu
r
in
g
co
s
t.
T
h
e
r
ev
iewe
d
liter
atu
r
e
in
d
icate
s
th
at
lo
w
-
co
m
p
lex
ity
Ma
r
c
h
alg
o
r
ith
m
s
(
1
0
N
o
r
b
elo
w)
p
r
o
v
id
e
f
ast
test
in
g
b
u
t
ar
e
u
n
a
b
le
to
d
etec
t
s
ev
er
al
im
p
o
r
tan
t
s
tatic
f
au
lt
m
o
d
els.
C
o
n
v
er
s
ely
,
co
m
p
lete
d
etec
tio
n
o
f
all
u
n
lin
k
ed
s
tatic
f
au
lts
g
en
er
ally
r
eq
u
ir
es
a
m
in
im
u
m
test
co
m
p
lex
ity
o
f
1
8
N,
as
a
ch
iev
ed
b
y
alg
o
r
ith
m
s
s
u
ch
as
Ma
r
ch
MSS.
T
o
b
r
id
g
e
t
h
e
g
ap
b
etwe
en
test
in
g
ef
f
icien
cy
an
d
f
au
lt
co
v
er
ag
e
,
n
u
m
er
o
u
s
o
p
tim
ized
Ma
r
ch
alg
o
r
ith
m
s
with
co
m
p
lex
ities
r
an
g
in
g
f
r
o
m
1
0
N
to
1
8
N
h
av
e
b
ee
n
p
r
o
p
o
s
ed
.
Am
o
n
g
th
ese,
th
e
Ma
r
ch
AZ
2
alg
o
r
ith
m
p
r
o
v
id
e
s
o
n
e
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
tr
ad
e
-
o
f
f
s
b
y
ac
h
ie
v
in
g
1
4
N
co
m
p
lex
ity
w
h
ile
d
etec
ti
n
g
all
s
tate
co
u
p
lin
g
f
au
lts
(
S
C
Fs
)
an
d
ap
p
r
o
x
im
ately
7
5
% o
f
d
y
n
am
ic
co
u
p
lin
g
f
au
lts
(
DC
Fs
)
,
m
ak
in
g
it a
n
att
r
ac
tiv
e
ca
n
d
id
ate
f
o
r
p
r
ac
tical
MBIST
im
p
lem
en
tatio
n
s
.
Alth
o
u
g
h
s
ig
n
if
ican
t
p
r
o
g
r
es
s
h
as
b
ee
n
ac
h
iev
ed
in
SR
AM
test
in
g
,
s
ev
er
al
r
esear
ch
ch
allen
g
es
r
em
ain
.
Fu
tu
r
e
s
tu
d
ies
s
h
o
u
ld
f
o
cu
s
o
n
d
e
v
elo
p
in
g
lo
w
-
c
o
m
p
lex
ity
alg
o
r
ith
m
s
ca
p
a
b
le
o
f
d
etec
tin
g
b
o
t
h
s
tatic
an
d
d
y
n
am
ic
f
au
lt
m
o
d
els
with
o
u
t
s
u
b
s
tan
tially
in
cr
ea
s
in
g
test
tim
e.
I
n
ad
d
itio
n
,
th
e
em
er
g
e
n
ce
o
f
ad
v
an
ce
d
m
em
o
r
y
tech
n
o
l
o
g
ies,
in
clu
d
in
g
MRAM,
R
R
AM
,
PC
M,
an
d
FeR
AM
,
n
ec
ess
itat
es
th
e
d
ev
elo
p
m
e
n
t
o
f
n
ew
f
au
lt
m
o
d
els
an
d
co
r
r
esp
o
n
d
in
g
MB
I
ST
alg
o
r
ith
m
s
tailo
r
ed
t
o
th
eir
u
n
iq
u
e
f
ailu
r
e
m
ec
h
an
is
m
s
.
Fu
r
th
er
m
o
r
e
,
in
teg
r
atin
g
in
tellig
en
t
o
p
tim
izat
io
n
tech
n
iq
u
es
an
d
ad
a
p
tiv
e
test
s
tr
ateg
ies
in
to
MBIST
ar
ch
itectu
r
es
r
ep
r
esen
ts
a
p
r
o
m
is
in
g
d
ir
ec
tio
n
f
o
r
ac
h
iev
in
g
h
i
g
h
er
f
a
u
lt
co
v
er
ag
e,
s
h
o
r
ter
test
d
u
r
atio
n
,
an
d
im
p
r
o
v
ed
test
in
g
ef
f
icien
cy
in
n
ex
t
-
g
en
er
atio
n
m
em
o
r
y
s
y
s
tem
s
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
g
r
atef
u
lly
ac
k
n
o
wled
g
e
th
e
f
in
an
cial
s
u
p
p
o
r
t
p
r
o
v
id
ed
b
y
th
e
Mi
n
is
tr
y
o
f
Hig
h
er
E
d
u
ca
ti
o
n
Ma
lay
s
ia
(
MO
HE
)
th
r
o
u
g
h
th
e
Fu
n
d
a
m
en
tal
R
esear
ch
Gr
an
t
Sch
em
e
(
FR
GS
)
u
n
d
er
Gr
an
t
No
.
FR
GS
/1
/2
0
2
4
/TK
0
7
/UT
E
M/0
2
/1
7
.
T
h
e
au
th
o
r
s
also
e
x
p
r
ess
th
eir
s
in
ce
r
e
ap
p
r
ec
iatio
n
to
Un
iv
er
s
iti
T
ek
n
ik
al
Ma
lay
s
ia
Me
lak
a
(
UT
eM
)
a
n
d
Un
i
v
er
s
iti
Ma
lay
s
ia
Per
lis
(
Un
iMAP)
f
o
r
th
eir
co
n
tin
u
o
u
s
s
u
p
p
o
r
t
an
d
f
ac
ilit
ies p
r
o
v
id
ed
th
r
o
u
g
h
o
u
t
th
is
r
esear
ch
.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
A
.
W
o
j
c
i
e
c
h
o
w
s
k
i
,
K
.
M
a
r
c
i
n
e
k
,
a
n
d
W
.
A
.
P
l
e
sk
a
c
z
,
“
C
o
n
f
i
g
u
r
a
b
l
e
M
B
I
S
T
p
r
o
c
e
ss
o
r
f
o
r
e
m
b
e
d
d
e
d
me
mo
r
i
e
s
t
e
st
i
n
g
,
”
i
n
2
0
1
9
MIXD
E
S
-
2
6
t
h
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
r
e
n
c
e
“
Mi
x
e
d
D
e
s
i
g
n
o
f
I
n
t
e
g
r
a
t
e
d
C
i
r
c
u
i
t
s
a
n
d
S
y
st
e
m
s,”
I
EEE,
J
u
n
.
2
0
1
9
,
p
p
.
3
4
1
–
3
4
4
,
d
o
i
:
1
0
.
2
3
9
1
9
/
M
I
X
D
ES.2
0
1
9
.
8
7
8
7
1
6
1
.
[
2
]
R
.
W
a
n
g
,
Z.
H
u
a
n
g
,
G
.
C
a
i
,
a
n
d
Z
.
Y
u
,
“
A
b
u
i
l
t
-
i
n
s
e
l
f
-
t
e
st
c
i
r
c
u
i
t
b
a
s
e
d
o
n
M
a
r
c
h
F
R
D
D
a
l
g
o
r
i
t
h
m
f
o
r
F
i
n
F
ET
m
e
m
o
r
y
,
”
i
n
Ad
v
a
n
c
e
s i
n
T
r
a
n
sd
i
sc
i
p
l
i
n
a
ry
En
g
i
n
e
e
ri
n
g
,
v
o
l
.
3
5
,
2
0
2
3
,
p
p
.
4
3
7
–
4
4
7
,
d
o
i
:
1
0
.
3
2
3
3
/
A
TD
E
2
3
0
0
6
9
.
[
3
]
T.
S
.
N
g
u
a
n
K
o
n
g
e
t
a
l
.
,
“
A
n
e
f
f
i
c
i
e
n
t
M
a
r
c
h
(
5
n
)
F
S
M
-
b
a
se
d
mem
o
r
y
b
u
i
l
t
-
i
n
se
l
f
t
e
s
t
(
M
B
I
S
T)
a
r
c
h
i
t
e
c
t
u
r
e
,
”
i
n
2
0
2
1
I
EEE
Re
g
i
o
n
a
l
S
y
m
p
o
s
i
u
m
o
n
Mi
c
ro
a
n
d
N
a
n
o
e
l
e
c
t
r
o
n
i
c
s
(
R
S
M)
,
I
EEE,
A
u
g
.
2
0
2
1
,
p
p
.
7
6
–
79
,
d
o
i
:
1
0
.
1
1
0
9
/
R
S
M
5
2
3
9
7
.
2
0
2
1
.
9
5
1
1
6
0
2
.
[
4
]
S
.
M
.
U
.
Q
u
t
a
i
b
a
K
h
a
saw
n
e
h
,
“
R
e
d
u
c
i
n
g
t
h
e
p
r
o
d
u
c
t
i
o
n
c
o
s
t
o
f
sem
i
c
o
n
d
u
c
t
o
r
c
h
i
p
s
u
s
i
n
g
(
p
a
r
a
l
l
e
l
a
n
d
c
o
n
c
u
r
r
e
n
t
)
t
e
st
i
n
g
a
n
d
r
e
a
l
-
t
i
me
m
o
n
i
t
o
r
i
n
g
,
”
S
o
u
t
h
e
r
n
M
e
t
h
o
d
i
s
t
U
n
i
v
e
r
si
t
y
,
2
0
1
9
.
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
s
:
/
/
sc
h
o
l
a
r
.
smu
.
e
d
u
/
e
n
g
i
n
e
e
r
i
n
g
_
e
l
e
c
t
r
i
c
a
l
_
e
t
d
s/
3
2
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