I
AE
S In
t
er
na
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA)
Vo
l.
13
,
No
.
4
,
Dec
em
b
er
20
24
,
p
p
.
4
5
2
~
4
6
8
I
SS
N:
2722
-
2
5
8
6
,
DOI
:
1
0
.
1
1
5
9
1
/i
jr
a
.
v
13
i
4
.
pp
4
5
2
-
468
452
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:
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ttp
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sto
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g
d
a
ta str
u
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re
s wh
e
n
sim
u
latin
g
a
tes
t
se
t.
K
ey
w
o
r
d
s
:
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lt si
m
u
latio
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atr
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Fau
lt tr
u
th
tab
le
Fau
lt
-
as
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d
r
ess
s
im
u
latio
n
In
-
m
em
o
r
y
c
o
m
p
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tin
g
L
o
g
ic
v
ec
to
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co
m
p
u
tin
g
Sm
ar
t d
ata
s
tr
u
ctu
r
es
T
est tr
u
th
tab
le
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Vlad
im
ir
Hah
an
o
v
Desig
n
Au
to
m
atio
n
Dep
ar
t
m
e
n
t
,
Kh
ar
k
o
v
Natio
n
al
Un
i
v
er
s
ity
o
f
R
ad
io
E
lectr
o
n
ics
Kh
ar
k
o
v
,
Uk
r
ain
e
E
m
ail: h
ah
an
o
v
@
iclo
u
d
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Statem
en
t
o
f
th
e
p
r
o
b
lem
th
e
p
ap
er
is
ad
d
r
ess
in
g
.
Mo
s
t
o
f
th
e
ex
is
tin
g
s
o
lu
tio
n
s
f
o
r
p
r
o
c
ess
in
g
b
ig
d
ata,
in
clu
d
in
g
d
esig
n
a
n
d
v
e
r
if
icatio
n
,
u
s
e
p
o
ten
t
c
o
m
p
u
te
r
s
,
n
etwo
r
k
s
,
an
d
c
o
m
p
u
tin
g
c
en
ter
s
wh
er
e
ar
r
ay
s
o
f
in
f
o
r
m
atio
n
ar
e
s
to
r
e
d
.
Su
ch
s
o
lu
tio
n
s
r
eq
u
ir
e
a
l
o
t
o
f
elec
tr
ical
en
er
g
y
a
n
d
a
r
e
clo
s
e
to
p
o
wer
p
lan
ts
.
Giv
en
th
at
th
e
r
e
will
alwa
y
s
b
e
in
s
u
f
f
icien
t
elec
tr
icity
,
e
v
e
r
y
th
in
g
r
elate
d
t
o
th
e
en
er
g
y
-
i
n
ten
s
iv
e
p
r
o
ce
s
s
in
g
o
f
b
ig
d
ata
will
g
r
ad
u
ally
b
e
co
m
e
a
th
in
g
o
f
th
e
p
ast.
I
n
s
tead
,
th
er
e
is
a
s
tead
y
in
cr
ea
s
e
in
in
-
m
em
o
r
y
co
m
p
u
tin
g
,
wh
ich
will
s
o
lv
e
th
e
p
r
o
b
lem
s
o
f
in
tellig
en
t
p
r
o
ce
s
s
in
g
o
f
b
ig
d
ata
o
n
s
m
ar
t
d
ata
s
tr
u
ctu
r
es
with
o
u
t
p
r
o
g
r
am
m
in
g
alg
o
r
it
h
m
s
an
d
ar
ch
itectu
r
es
f
r
ee
o
f
p
o
te
n
t
p
r
o
ce
s
s
o
r
s
.
On
e
o
f
t
h
ese
co
s
t
-
ef
f
ec
tiv
e
s
o
lu
tio
n
s
is
p
r
o
p
o
s
ed
f
o
r
r
esea
r
ch
:
in
-
m
em
o
r
y
m
o
d
elin
g
an
d
s
im
u
latio
n
o
n
s
m
ar
t
d
ata
s
tr
u
c
tu
r
es
th
at
u
s
e
o
n
ly
r
ea
d
-
wr
ite
tr
an
s
ac
tio
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s
.
T
h
e
s
t
u
d
y
'
s
f
o
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m
u
la
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u
s
e
o
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s
m
ar
t
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ata
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ctu
r
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v
ec
to
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ta
b
le
f
o
r
m
s
o
f
lo
g
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cir
cu
it
d
escr
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n
t
o
o
r
g
an
iz
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in
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m
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b
ase
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n
r
ea
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wr
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t
r
an
s
ac
tio
n
s
[
1
]
f
o
r
s
im
u
latin
g
f
au
lts
as
ad
d
r
ess
es
[
2
]
,
[
3
]
.
E
x
p
er
ts
in
co
m
p
u
ter
tech
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o
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y
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d
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Gar
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p
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o
f
th
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n
N
eu
m
an
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c
h
itectu
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2
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a
n
d
p
o
wer
f
u
l
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ce
s
s
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s
[
4
]
,
[
5
]
.
T
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y
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d
v
o
ca
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ad
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al
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s
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tio
n
s
o
n
m
em
o
r
y
elem
en
ts
ar
e
en
o
u
g
h
[
1
]
,
[
2
]
.
T
h
is
is
th
e
p
r
ac
tical
ess
en
ce
o
f
th
e
p
r
o
p
o
s
ed
s
tu
d
y
.
On
th
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th
er
h
a
n
d
,
in
tellig
en
t
co
m
p
u
tin
g
,
ac
co
r
d
in
g
to
lead
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g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
F
a
u
lts
-
as
-
a
d
d
r
ess
s
imu
la
tio
n
(
V
la
d
imir
Ha
h
a
n
o
v
)
453
ex
p
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ts
,
h
as
a
s
tr
o
n
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en
c
y
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u
s
e
s
m
ar
t
m
em
o
r
y
-
b
ased
d
ata
s
tr
u
ctu
r
es
[
4
]
,
[
6
]
to
p
r
o
ce
s
s
b
ig
d
ata
with
o
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t
p
r
o
g
r
a
m
m
in
g
alg
o
r
it
h
m
s
[
7
]
,
[
8
]
.
At
th
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s
am
e
tim
e
,
s
m
ar
t
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ata
s
tr
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r
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n
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e
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(
ML
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wh
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d
ata
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ab
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cc
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d
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T
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g
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3
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[
4
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to
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lv
e
p
r
o
b
lem
s
d
u
e
to
th
e
s
p
ee
d
o
f
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
at
th
e
l
ev
el
o
f
o
n
e
n
a
n
o
s
ec
o
n
d
[
5
]
.
Her
e
ar
e
w
h
at
h
as
b
ee
n
d
o
n
e
b
ef
o
r
e
ab
o
u
t
th
e
p
r
o
b
le
m
.
Mo
d
els
an
d
alg
o
r
ith
m
s
ar
e
s
tr
o
n
g
ly
in
ter
co
n
n
ec
ted
.
R
ed
u
n
d
an
c
y
o
f
o
n
e
co
m
p
o
n
e
n
t
lead
s
t
o
a
d
e
cr
ea
s
e
in
th
e
o
th
e
r
an
d
v
ice
v
er
s
a.
I
f
an
e
n
g
in
ee
r
wan
ts
a
s
im
p
le
alg
o
r
ith
m
,
h
e
s
h
o
u
ld
u
s
e
th
e
r
ed
u
n
d
an
c
y
a
n
d
s
im
p
licity
o
f
ex
p
licit
d
ata
s
tr
u
ctu
r
es
(
lo
g
ical
v
ec
to
r
s
,
tr
u
th
tab
les
[
1
]
,
[
3
]
,
[
9
]
,
an
d
m
atr
ices)
in
s
tead
o
f
an
aly
tical
[
1
0
]
–
[
1
2
]
,
o
r
g
r
ap
h
[
1
3
]
–
[
1
5
]
m
o
d
els.
Desig
n
an
d
test
in
g
h
a
v
e
b
ee
n
,
ar
e,
a
n
d
will
co
n
tin
u
e
to
b
e
th
e
m
o
s
t
ad
v
an
ce
d
tech
n
o
lo
g
y
f
o
r
b
u
ild
in
g
in
tellig
en
t
co
m
p
u
tin
g
[
1
0
]
,
[
1
6
]
,
th
e
g
o
al
o
f
wh
ich
is
to
cr
ea
te
th
e
cy
b
er
b
r
ain
o
f
h
u
m
an
ity
.
An
u
r
g
en
t
p
r
o
b
lem
is
v
er
if
y
in
g
n
ew
d
i
g
ital
s
o
lu
tio
n
s
u
s
in
g
s
y
s
tem
-
on
-
ch
ip
(
So
C
)
n
u
m
b
e
r
in
g
b
il
lio
n
s
o
f
tr
an
s
is
to
r
s
.
Au
to
m
atic
s
y
n
th
esis
s
y
s
tem
s
o
f
Sy
n
o
p
s
y
s
,
c
ad
en
ce
ca
n
d
e
s
ig
n
a
s
y
s
tem
o
f
an
y
co
m
p
le
x
ity
.
Ho
wev
er
,
t
h
e
q
u
esti
o
n
is
h
o
w
t
o
v
er
i
f
y
s
u
c
h
a
s
y
s
tem
.
Ho
w
ca
n
a
test
f
o
r
it
b
e
b
u
ilt
to
d
ete
r
m
in
e
its
q
u
alities
in
d
etec
tin
g
lo
g
ical
o
r
p
h
y
s
ical
f
au
lts
?
E
lectr
o
n
ic
d
esig
n
au
to
m
atio
n
(
E
DA
)
ap
p
lies
test
ab
le
d
esig
n
s
tan
d
ar
d
s
to
b
r
ea
k
d
o
wn
a
co
m
p
lex
s
y
s
tem
in
to
th
e
m
ar
k
et'
s
So
C
in
tellectu
al
p
r
o
p
er
t
y
(
IP
)
co
r
es.
T
ests
ar
e
th
en
b
u
ilt
f
o
r
th
ese
m
o
d
u
les,
wh
ic
h
m
u
s
t
b
e
v
er
if
ied
u
s
in
g
f
au
lt
s
im
u
latio
n
alg
o
r
ith
m
s
.
T
y
p
ically
,
t
h
ese
alg
o
r
ith
m
s
u
s
e
co
m
p
ac
t
an
aly
tical
o
r
h
ar
d
war
e
d
escr
i
p
tio
n
lan
g
u
ag
e
(
HDL
)
d
i
g
ital
cir
cu
its
an
d
elem
en
t
m
o
d
els
.
T
h
eir
p
r
o
ce
s
s
in
g
in
v
o
lv
es
th
e
cr
ea
tio
n
o
f
p
o
we
r
f
u
l
c
o
m
p
iler
s
b
ased
o
n
th
e
u
s
e
o
f
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
.
Su
ch
s
im
u
lato
r
s
a
r
e
co
s
tly
an
d
r
eq
u
i
r
e
a
lo
t
o
f
tim
e
an
d
en
er
g
y
[
1
7
]
,
[
1
8
]
.
W
h
at
ca
n
b
e
o
f
f
e
r
ed
in
r
et
u
r
n
?
T
ec
h
n
o
lo
g
ically
s
im
p
le,
ch
ea
p
-
to
-
u
s
e
test
g
en
e
r
ato
r
s
a
n
d
s
im
u
lato
r
s
[
1
9
]
–
[
2
1
]
th
at
c
o
n
s
u
m
e
a
m
in
im
u
m
am
o
u
n
t
o
f
en
er
g
y
[
2
2
]
–
[
2
4
]
.
T
h
e
r
esear
c
h
f
o
r
m
u
la
f
o
r
t
h
is
m
etr
ic
is
t
o
d
ev
elo
p
m
ec
h
an
is
m
s
f
o
r
in
-
m
em
o
r
y
m
o
d
elin
g
an
d
s
im
u
latio
n
o
f
f
au
lts
-
as
-
ad
d
r
ess
es b
ased
o
n
lo
g
ical
v
ec
to
r
s
[
2
1
]
,
[
2
5
]
o
f
cir
cu
it e
lem
en
ts
,
wh
ich
ar
e
p
r
o
ce
s
s
ed
b
ased
o
n
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
[
2
0
]
,
[
2
6
]
.
Fo
r
th
is
p
u
r
p
o
s
e,
r
ed
u
n
d
an
t
s
m
ar
t
an
d
ex
p
licit
d
ata
s
tr
u
ctu
r
es
[
2
0
]
,
[
2
7
]
,
[
2
8
]
h
av
e
b
ee
n
i
n
tr
o
d
u
ce
d
an
d
u
s
e
d
,
s
ig
n
if
ican
tly
r
e
d
u
cin
g
th
e
c
o
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
s
i
m
u
latio
n
alg
o
r
ith
m
s
[
1
]
,
[
1
5
]
,
[
2
9
]
.
L
o
g
ical
v
ec
to
r
s
,
tr
u
th
tab
les,
an
d
lo
g
ical
m
a
tr
ices
r
ep
r
esen
t
s
m
ar
t
d
ata
s
tr
u
ctu
r
es.
On
ly
o
n
e
XOR
o
p
er
atio
n
a
n
d
a
r
ea
d
-
w
r
ite
tr
an
s
ac
tio
n
a
r
e
r
eq
u
ir
e
d
t
o
p
r
o
ce
s
s
th
em
f
o
r
f
au
lt
-
as
-
a
d
d
r
ess
s
im
u
latio
n
.
Ho
wev
er
,
th
is
XOR
o
p
er
atio
n
ca
n
also
b
e
r
e
d
u
ce
d
to
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
o
n
a
lo
g
ical
v
e
cto
r
[
1
]
,
[
1
9
]
.
T
h
e
ef
f
icien
cy
o
f
th
e
s
im
u
latio
n
m
ec
h
an
is
m
is
u
n
p
ar
alleled
,
p
r
o
v
id
in
g
s
im
p
licity
an
d
g
o
o
d
ec
o
n
o
m
ics
o
f
th
e
s
o
lu
tio
n
.
C
o
m
p
u
ter
en
g
in
ee
r
in
g
s
tu
d
en
ts
m
aster
th
is
m
ec
h
an
is
m
in
o
n
e
les
s
o
n
,
4
5
m
in
u
tes.
T
h
e
to
p
ic
o
f
f
au
lt
s
im
u
latio
n
in
t
h
e
E
DA
m
ar
k
et
h
as
b
ee
n
r
ele
v
an
t
f
o
r
7
0
y
ea
r
s
an
d
o
cc
u
p
ies
o
n
e
o
f
th
e
f
ir
s
t
p
lace
s
in
th
e
d
ev
elo
p
m
e
n
t o
f
r
esear
ch
er
s
an
d
co
m
p
a
n
ies.
T
h
e
m
ar
k
et
r
ele
v
an
ce
o
f
t
h
is
to
p
ic
is
d
eter
m
in
ed
b
y
th
e
f
o
llo
win
g
m
etr
ics
[
2
9
]
–
[
3
1
]
:
i
)
t
h
e
d
e
v
elo
p
m
en
t o
f
s
m
ar
t d
ata
s
tr
u
ctu
r
e
s
an
d
ef
f
icien
t a
lg
o
r
ith
m
s
f
o
r
test
in
g
in
cr
ea
s
in
g
ly
co
m
p
lex
co
m
p
u
ter
s
y
s
tem
s
an
d
n
etwo
r
k
s
co
n
s
is
tin
g
o
f
b
illi
o
n
s
o
f
eq
u
iv
alen
t
g
ates
;
ii
)
i
n
v
ar
ian
ce
o
f
s
tr
u
ctu
r
es
an
d
alg
o
r
ith
m
s
co
n
ce
r
n
in
g
tech
n
o
lo
g
ies
an
d
ty
p
e
s
o
f
d
ig
ital
p
r
o
d
u
cts
th
at
ch
an
g
e
r
ap
id
ly
o
v
er
tim
e
[
3
2
]
;
iii
)
t
h
e
f
lex
ib
ilit
y
o
f
d
ata
s
tr
u
ctu
r
es a
n
d
alg
o
r
ith
m
s
will a
llo
w
th
e
p
r
o
ce
s
s
in
g
o
f
a
wid
e
r
an
g
e
o
f
d
ig
itized
tech
n
ical
d
ev
ices
an
d
p
r
o
ce
s
s
es
f
o
r
th
eir
test
in
g
,
v
er
if
icatio
n
,
d
iag
n
o
s
tics
,
an
d
f
au
lt
d
etec
tio
n
[
3
3
]
–
[
3
5
]
;
iv
)
c
o
n
s
id
er
in
g
f
a
u
lts
as
b
ig
d
ata,
alg
o
r
ith
m
s
f
o
r
t
h
eir
an
aly
s
i
s
m
u
s
t
b
e
ef
f
icien
t
in
ter
m
s
o
f
tim
e
an
d
en
e
r
g
y
co
n
s
u
m
p
tio
n
.
T
h
er
ef
o
r
e,
f
au
lt
s
im
u
latio
n
s
h
o
u
ld
b
e
im
p
lem
en
ted
o
n
p
r
im
itiv
e
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
as
in
-
m
em
o
r
y
co
m
p
u
tin
g
with
o
u
t
th
e
u
s
e
o
f
th
e
r
o
b
u
s
t
in
s
tr
u
ctio
n
s
et
o
f
th
e
u
n
iv
er
s
al
p
r
o
ce
s
s
o
r
in
th
e
v
o
n
Neu
m
an
n
ar
c
h
itectu
r
e
[
2
]
,
[
3
6
]
,
[
3
7
]
;
v
)
d
ata
s
tr
u
ctu
r
es
f
o
r
f
au
lt
s
im
u
latio
n
s
h
o
u
ld
b
e
s
im
p
le
an
d
ac
ce
s
s
ib
le
to
co
m
p
u
ter
s
an
d
h
u
m
a
n
s
[
3
6
]
.
Su
ch
id
ea
l
d
ata
s
tr
u
ctu
r
es,
i
n
v
ar
ian
t
in
tim
e,
ar
e
th
e
u
n
ju
s
tly
f
o
r
g
o
tten
tr
u
t
h
tab
le
an
d
its
co
m
p
ac
t
d
er
iv
ativ
e,
th
e
lo
g
ical
v
ec
to
r
.
T
h
ey
ar
e
id
ea
l
f
o
r
e
f
f
icien
tly
s
o
lv
in
g
in
-
m
em
o
r
y
co
m
p
u
tin
g
task
s
,
in
clu
d
in
g
b
ig
d
ata
p
r
o
ce
s
s
in
g
[
3
8
]
an
d
f
au
lt
s
im
u
latio
n
;
vi
)
T
h
e
tr
u
t
h
tab
le
s
h
o
u
ld
b
e
elev
ated
to
th
e
r
an
k
o
f
an
i
d
ea
l
in
ter
n
al
m
o
d
el
o
f
a
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
o
r
cir
c
u
it
th
at
is
in
v
a
r
ian
t
co
n
ce
r
n
in
g
d
o
ze
n
s
o
f
lan
g
u
ag
es
d
escr
ib
in
g
h
ar
d
war
e
o
r
s
o
f
twar
e
[
3
7
]
,
[
3
8
]
;
v
ii
)
T
h
e
tr
u
t
h
tab
le
g
en
er
ates
a
co
m
p
lete
s
et
o
f
lo
g
ic
-
f
a
u
lt
co
m
b
in
atio
n
s
f
o
r
a
r
b
itra
r
ily
co
m
p
lex
lo
g
ical
f
u
n
ctio
n
ality
[
1
]
,
[
1
0
]
,
[
1
6
]
.
T
h
u
s
,
co
m
b
in
in
g
in
-
m
em
o
r
y
c
o
m
p
u
tin
g
an
d
s
m
ar
t
d
ata
s
tr
u
ctu
r
es
b
ased
o
n
th
e
tr
u
th
tab
le
m
ay
b
e
a
r
atio
n
al
way
to
s
o
lv
e
d
esig
n
an
d
test
p
r
o
b
lem
s
o
v
er
a
l
o
n
g
tim
e
i
n
th
e
d
e
v
elo
p
m
en
t o
f
g
lo
b
al
c
o
m
p
u
tin
g
[
3
9
]
–
[
4
1
]
.
T
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
an
d
th
e
r
esu
lts
ac
h
iev
ed
.
T
h
e
g
o
al
i
s
to
s
ig
n
if
ican
tly
r
ed
u
ce
th
e
l
aten
cy
an
d
en
er
g
y
co
n
s
u
m
p
tio
n
wh
en
s
i
m
u
latin
g
f
au
lts
-
as
-
ad
d
r
ess
es
u
s
in
g
in
-
m
e
m
o
r
y
co
m
p
u
tin
g
te
ch
n
o
lo
g
y
i
n
lo
g
ical
cir
cu
its
o
f
an
y
d
im
en
s
io
n
b
as
ed
o
n
r
ea
d
-
wr
ite
tr
a
n
s
ac
tio
n
s
o
v
er
s
m
ar
t
d
ata
s
tr
u
ctu
r
es
b
u
ilt
b
ased
o
n
a
lo
g
ical
v
ec
to
r
.
T
h
e
o
b
jectiv
es
o
f
th
is
r
esear
ch
ar
e
to
i
)
i
d
e
n
tify
th
e
co
m
p
o
n
en
ts
o
f
s
m
ar
t
co
m
p
ac
t
d
ata
s
tr
u
ctu
r
es
f
o
r
lo
g
ic
cir
cu
it
f
au
lt
s
im
u
latio
n
;
ii
)
c
r
ea
t
e
a
s
im
u
latio
n
alg
o
r
ith
m
f
o
r
f
a
u
lts
F
o
f
a
lo
g
ical
cir
c
u
it
o
n
an
in
p
u
t
test
s
et
T
b
y
s
y
n
th
esizin
g
d
ed
u
ctiv
e
v
ec
to
r
s
o
f
elem
e
n
ts
f
r
o
m
th
e
ir
lo
g
ical
v
ec
to
r
s
L
,
u
s
in
g
th
e
eq
u
atio
n
D=
T
⨁
L
;
an
d
iii
)
v
er
if
y
th
e
d
ata
s
tr
u
c
tu
r
es
an
d
al
g
o
r
ith
m
s
f
o
r
m
o
d
elin
g
an
d
s
im
u
latio
n
f
au
lts
-
as
-
ad
d
r
ess
es,
u
s
in
g
ex
am
p
les
o
f
lo
g
ic
cir
cu
its
.
W
ith
o
u
t
g
o
in
g
in
to
d
etails,
v
o
n
Neu
m
an
n
'
s
ar
ch
itectu
r
e
[
2
]
co
n
tr
o
ls
an
d
ex
ec
u
tes
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
4
5
2
-
4
6
8
454
th
e
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
.
T
h
er
ef
o
r
e,
it
ca
n
b
e
tr
a
n
s
f
er
r
ed
to
m
em
o
r
y
,
wh
e
r
e
b
ig
d
ata
r
esid
es.
Mo
r
eo
v
e
r
,
th
is
ar
ch
itectu
r
e
ca
n
b
e
u
s
ed
to
s
im
u
late
b
o
th
lo
g
ic
an
d
cir
c
u
its
in
two
m
o
d
es:
g
o
o
d
s
im
u
latio
n
o
f
test
-
as
-
ad
d
r
ess
es
an
d
s
im
u
latio
n
o
f
f
a
u
lt
-
as
-
ad
d
r
ess
es.
T
h
e
d
ev
ice
o
f
co
n
tr
o
l
an
d
ex
ec
u
tio
n
in
co
m
p
u
tin
g
h
as
n
o
t
y
et
b
ee
n
ca
n
ce
led
[
2
]
,
[
1
4
]
,
[
1
9
]
.
2.
F
AULT
S
-
AS
-
ADD
RE
SS
CI
RCUI
T
SI
M
U
L
AT
I
O
N
:
UN
USUAL
AND
S
I
M
P
L
E
E
N
G
I
NE
E
RING
M
E
CH
A
NIS
M
W
h
at
is
n
ew?
F
au
lt
s
-
as
-
ad
d
r
ess
es
s
im
u
latio
n
(
FAAS)
i
s
a
tech
n
iq
u
e
th
at
lev
er
a
g
es
in
p
u
t
f
au
lts
co
m
b
in
atio
n
as
d
ed
u
ctiv
e
v
ec
t
o
r
b
its
ad
d
r
ess
es
th
at
f
o
r
m
d
etec
ted
in
p
u
t
f
au
lts
in
lo
g
ic
ele
m
en
t
o
u
tp
u
t.
FAAS
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
f
o
r
d
ig
ital
cir
cu
it
s
im
u
latio
n
,
wh
er
e
lo
g
ical
v
ec
to
r
s
r
ep
r
esen
t
ele
m
en
ts
as
a
co
m
p
ac
t
f
o
r
m
o
f
th
e
tr
u
th
tab
le.
T
h
e
tr
u
th
tab
le
is
p
r
o
p
o
s
ed
as
a
s
m
a
r
t
d
ata
s
tr
u
ctu
r
e
f
o
r
f
au
lt
s
im
u
latio
n
o
f
i
n
p
u
t
a
n
d
in
ter
n
al
lin
es
o
f
l
o
g
ic
cir
cu
its
.
T
h
e
lo
g
ical
v
ec
t
o
r
in
th
e
tr
u
t
h
tab
le
an
d
th
e
in
p
u
t
test
s
et
ar
e
u
s
ed
to
g
e
n
er
ate
a
d
ed
u
ctiv
e
v
ec
to
r
th
at
d
etec
ts
an
y
co
m
b
in
atio
n
o
f
f
au
lts
in
th
e
cir
cu
it
lin
es
to
its
ex
ter
n
al
o
u
tp
u
ts
.
T
h
e
n
o
v
elt
y
o
f
th
e
FAAS
m
ec
h
an
is
m
is
th
e
Fau
lt
Simu
latio
n
Ma
tr
i
x
ad
d
r
ess
f
illi
n
g
u
s
in
g
d
ed
u
ct
iv
e
v
ec
to
r
s
,
wh
ich
s
im
u
late
a
co
m
b
in
atio
n
o
f
f
a
u
l
ts
as a
n
ad
d
r
ess
.
T
h
e
in
-
m
em
o
r
y
s
im
u
latio
n
u
s
es r
ea
d
-
wr
ite
t
r
an
s
ac
tio
n
s
,
wh
ich
m
ak
es
th
e
FAAS
tech
n
iq
u
e
a
f
r
ee
ce
n
tr
al
p
r
o
ce
s
s
in
g
u
n
it
(
C
PU
)
in
s
tr
u
ctio
n
s
y
s
tem
an
d
co
s
t
-
ef
f
ec
tiv
e
i
n
ter
m
s
o
f
p
o
wer
an
d
tim
e
to
s
im
u
late
f
au
lts
.
T
h
e
ci
r
cu
it
f
a
u
l
t
s
im
u
latio
n
c
o
n
tain
s
n
o
v
elty
p
o
in
ts
:
cir
cu
it
1
is
th
e
d
ed
u
ctiv
e
v
ec
to
r
s
y
n
th
esis
f
o
r
i
n
p
u
t
s
et
a
n
d
lo
g
ic
v
ec
to
r
to
d
etec
t
in
p
u
t
f
au
lts
o
n
elem
e
n
t
o
u
tp
u
t;
cir
cu
it
2
is
th
e
d
ev
elo
p
m
en
t
o
f
a
q
u
ad
r
atic
f
au
lt
s
im
u
latio
n
m
atr
ix
o
f
th
e
cir
cu
it
f
o
r
ev
e
r
y
test
s
et;
cir
cu
it
3
is
th
e
s
im
u
latio
n
o
f
cir
cu
it
lin
es
f
a
u
lts
-
as
-
ad
d
r
ess
es
u
s
in
g
a
s
i
m
u
latio
n
m
atr
ix
a
n
d
d
e
d
u
cti
v
e
v
ec
to
r
s
o
f
lo
g
ic
elem
en
ts
to
o
b
tain
a
v
ec
to
r
o
f
d
etec
ted
f
au
lts
o
n
th
e
in
p
u
t
test
s
et;
an
d
cir
cu
it
4
is
th
e
f
o
r
m
atio
n
o
f
a
tab
le
o
f
d
etec
ted
f
au
lts
to
d
eter
m
in
e
t
h
e
q
u
ality
o
f
th
e
in
p
u
t
s
ets
an
d
th
e
test
.
Alg
o
r
ith
m
s
an
d
d
ata
s
tr
u
ctu
r
es
ar
e
p
r
o
p
o
s
ed
f
o
r
in
-
m
em
o
r
y
s
im
u
latin
g
f
au
lt
-
as
-
ad
d
r
ess
es
an
d
lo
g
ical
s
ch
em
es
o
f
an
y
s
tr
u
ctu
r
al
co
m
p
lex
ity
.
Sm
ar
t
d
ata
s
tr
u
ctu
r
es
h
av
e
th
r
ee
m
ac
r
o
c
o
m
p
o
n
en
ts
:
cir
cu
it
d
escr
ip
tio
n
,
s
im
u
latio
n
m
atr
ix
,
an
d
f
au
l
t
d
etec
tio
n
tab
le.
T
h
e
tr
u
th
tab
l
e
is
th
e
lo
n
g
est
-
liv
ed
m
o
d
el
o
f
th
e
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
;
it
is
m
o
r
e
th
an
1
0
0
y
ea
r
s
o
ld
,
an
d
to
d
ay
,
it
is
p
r
a
ctica
lly
n
o
t
u
s
ed
f
o
r
o
r
g
an
izin
g
co
m
p
u
tatio
n
s
.
Un
d
er
n
ea
t
h
th
e
s
im
p
licity
o
f
th
e
f
o
r
m
o
f
th
e
tr
u
th
tab
le,
wh
ich
is
u
n
d
er
s
tan
d
ab
le
to
h
u
m
an
s
a
n
d
m
ac
h
in
es,
th
er
e
is
an
u
n
d
e
cip
h
er
ed
g
en
o
m
e
o
f
em
er
g
in
g
c
o
m
p
u
tin
g
.
Fau
lt
s
i
m
u
latio
n
alg
o
r
ith
m
s
u
s
e
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
o
n
s
m
ar
t
d
a
ta
s
tr
u
ctu
r
es
in
an
y
So
C
,
f
ield
p
r
o
g
r
am
m
ab
le
g
at
e
ar
r
ay
s
(
FP
GA
)
,
a
p
p
licatio
n
-
s
p
ec
if
ic
in
teg
r
ated
cir
cu
it
(
ASI
C
)
,
o
r
r
e
d
u
ce
d
in
s
tr
u
ctio
n
s
et
co
m
p
u
te
r
(
R
I
SC
-
V
)
m
em
o
r
y
a
n
d
d
o
n
o
t
r
eq
u
ir
e
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
an
d
p
r
e
-
s
y
n
th
esis
o
f
th
e
cir
cu
it
to
b
r
in
g
lo
g
ical
f
u
n
ctio
n
alities
to
a
s
p
ec
if
ic
elem
en
t
b
asis
.
T
h
e
m
ar
k
et
g
o
al
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
to
s
o
lv
e
I
P
-
co
r
e
v
er
if
icatio
n
p
r
o
b
lem
s
b
ased
o
n
in
-
m
e
m
o
r
y
co
m
p
u
tin
g
u
s
in
g
t
h
e
I
E
E
E
1
5
0
0
s
tan
d
ar
d
f
o
r
em
b
ed
d
e
d
co
r
e
test
(
SECT
)
s
tan
d
ar
d
[
2
1
]
.
A
d
ata
s
tr
u
ct
u
r
e
m
etr
ic
is
a
lo
g
ical
v
ec
to
r
o
r
tr
u
t
h
tab
le.
T
h
e
p
r
ac
tical
n
o
v
elty
o
f
th
e
FA
AS
m
ec
h
an
is
m
is
th
e
f
a
u
lt
s
im
u
latio
n
m
atr
i
x
a
d
d
r
ess
f
illi
n
g
u
s
in
g
d
ed
u
ctiv
e
v
ec
to
r
s
,
wh
ich
s
im
u
late
a
co
m
b
in
atio
n
o
f
f
a
u
lts
as
an
ad
d
r
ess
a
s
s
h
o
wn
in
F
ig
u
r
e
1
.
I
t
p
r
o
v
id
es
a
m
o
d
el
o
f
a
good
-
v
alu
e
lin
e
b
eh
a
v
io
r
cir
c
u
it
u
s
in
g
lo
g
ic
v
ec
to
r
s
an
d
a
cir
cu
it
m
o
d
el
f
o
r
f
au
lt
s
im
u
lat
io
n
u
s
in
g
d
ed
u
ctiv
e
v
ec
to
r
s
.
A
q
u
a
d
r
atic
f
au
lt
s
im
u
latio
n
m
atr
i
x
is
p
r
esen
ted
,
w
h
ich
is
f
illed
alo
n
g
th
e
m
ain
d
iag
o
n
al
with
s
in
g
le
v
alu
es
id
en
tify
in
g
f
au
lts
o
f
th
e
cir
cu
it
lin
es.
T
h
r
ee
tr
u
th
tab
les
f
o
r
th
e
s
y
n
th
esis
o
f
th
e
d
ed
u
ctiv
e
v
ec
to
r
ar
e
also
p
r
esen
ted
.
All
th
e
lis
ted
d
ata
s
tr
u
ctu
r
es
ar
e
r
eq
u
ir
ed
to
m
o
d
el
th
e
f
a
u
lt
as
ad
d
r
ess
es
o
n
a
s
in
g
le
in
p
u
t
test
s
et
0
0
1
1
.
T
h
e
r
esu
lt
o
f
a
g
o
o
d
s
im
u
latio
n
is
s
h
o
wn
in
th
e
G
-
lin
e
o
f
th
e
s
im
u
latio
n
m
atr
i
x
.
T
h
e
r
esu
lt
o
f
th
e
f
au
lt si
m
u
latio
n
is
s
h
o
wn
in
th
e
F
-
lin
e
o
f
th
e
s
im
u
latio
n
m
atr
ix
.
Fig
u
r
e
1
.
Fau
lts
-
as
-
ad
d
r
ess
cir
cu
it si
m
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
F
a
u
lts
-
as
-
a
d
d
r
ess
s
imu
la
tio
n
(
V
la
d
imir
Ha
h
a
n
o
v
)
455
T
h
e
r
elatio
n
s
h
ip
T
⨁
L
=D
b
et
wee
n
th
e
test
s
et
T
an
d
th
e
tr
u
th
tab
le
L
o
f
th
e
elem
en
t
f
o
r
m
s
a
d
ed
u
ctiv
e
v
ec
to
r
f
o
r
f
a
u
lt
s
im
u
latio
n
,
u
s
in
g
ad
d
r
ess
es
th
e
tr
u
th
tab
le
o
r
th
e
l
o
g
ic
v
ec
to
r
b
its
.
On
th
e
o
t
h
er
h
an
d
,
a
d
d
r
ess
es
ar
e
u
s
ed
in
th
e
s
im
u
latio
n
m
atr
ix
to
m
ar
k
th
o
s
e
n
-
co
m
b
i
n
atio
n
s
o
f
in
p
u
t
f
a
u
lts
d
etec
ted
at
th
e
elem
en
t'
s
o
u
tp
u
t.
T
h
e
co
lu
m
n
s
o
f
th
e
s
im
u
latio
n
m
atr
i
x
ar
e
tr
ea
ted
as
n
-
r
o
w
ad
d
r
ess
es
to
g
en
er
ate
an
o
u
tp
u
t
r
o
w
o
f
th
e
elem
en
t
v
ia
th
e
d
e
d
u
ctiv
e
v
ec
to
r
.
T
h
er
e
is
n
o
tr
a
n
s
p
o
r
t
o
f
in
p
u
t
f
au
lts
to
t
h
e
o
u
tp
u
t
o
f
th
e
elem
en
t,
On
ly
th
e
1
-
s
ig
n
als
wr
itten
in
th
e
n
o
n
-
in
p
u
t
r
o
w
c
o
o
r
d
in
ates
o
f
th
e
cir
cu
it
s
im
u
latio
n
m
atr
ix
.
T
h
e
s
im
u
latio
n
m
atr
ix
is
in
itially
f
illed
with
1
-
s
ig
n
als
alo
n
g
th
e
m
ain
d
iag
o
n
al.
T
h
e
lin
e
f
au
lts
d
etec
ted
o
n
th
e
test
s
e
t
o
f
cir
cu
its
ar
e
d
eter
m
in
ed
b
y
th
e
in
v
er
s
e
o
f
th
e
g
o
o
d
v
alu
es
o
f
lin
es
G,
wh
ich
h
av
e
1
-
v
alu
es
in
th
e
m
atr
ix
r
o
w
co
r
r
esp
o
n
d
in
g
to
th
e
o
u
t
p
u
t o
f
th
e
last
c
ir
cu
it e
lem
en
t.
T
h
e
d
ed
u
ctiv
e
v
ec
to
r
is
o
b
tain
ed
b
y
th
e
XOR
-
r
elatio
n
s
b
etwe
en
th
e
test
s
et
an
d
th
e
l
o
g
ical
v
ec
to
r
in
th
r
ee
tab
le
o
p
er
atio
n
s
.
T
h
e
ad
v
an
ta
g
e
o
f
th
e
p
r
o
p
o
s
ed
FAAS
m
ec
h
an
is
m
is
th
e
p
r
e
d
ictab
le
co
m
p
lex
ity
o
f
t
h
e
alg
o
r
ith
m
an
d
th
e
m
em
o
r
y
co
n
s
u
m
p
ti
o
n
f
o
r
s
to
r
in
g
d
ata
s
tr
u
ctu
r
es
wh
en
s
im
u
latin
g
a
test
s
et,
d
eter
m
in
ed
b
y
th
e
f
o
r
m
u
la
Q
=
N
2
+
∑
(
Y
i
+
n
i
=
1
D
i
)
,
wh
er
e
N,
n
ar
e
n
u
m
b
er
o
f
lin
es a
n
d
elem
en
ts
in
th
e
cir
cu
it
an
d
Y,
D
ar
e
a
s
et
o
f
lo
g
ical
an
d
d
e
d
u
ctiv
e
v
ec
to
r
s
.
C
o
n
s
tr
u
ctio
n
o
f
th
e
r
ec
o
d
in
g
m
atr
ix
[
1
]
b
y
tak
in
g
a
C
ar
tesi
an
⨁
-
s
q
u
ar
e
o
n
th
e
ad
d
r
ess
es
o
f
th
e
tr
u
th
tab
le
f
r
o
m
n
-
v
a
r
iab
les
ac
co
r
d
i
n
g
to
th
e
f
o
r
m
u
la:
H=
A
⨁
A
=
⨁
2
.
Ad
d
r
ess
es
ac
t
a
s
te
s
t
s
e
ts
T
an
d
c
o
m
b
in
atio
n
s
o
f
lo
g
ic
f
au
lts
F.
T
h
e
r
esu
ltin
g
m
atr
ix
is
a
co
n
s
tan
t
f
o
r
a
ll
lo
g
ical
f
u
n
ctio
n
s
f
r
o
m
n
-
v
ar
iab
les.
T
h
er
e
ar
e
s
ev
er
al
m
o
d
if
icatio
n
s
to
th
e
r
e
co
d
in
g
m
at
r
ix
co
n
s
tr
u
ctio
n
.
N
ex
t,
a
s
im
p
le
r
ec
u
r
s
iv
e
m
ec
h
a
n
is
m
f
o
r
b
u
ild
in
g
a
r
ec
o
d
in
g
m
atr
ix
b
ased
o
n
p
r
ed
ictio
n
is
p
r
o
p
o
s
ed
.
Fo
u
r
s
eq
u
en
tial
o
p
e
r
atio
n
s
ar
e
p
e
r
f
o
r
m
ed
o
n
th
e
f
o
u
r
q
u
ad
r
a
n
ts
o
f
th
e
m
atr
ix
:
H
i
+
1
1
=
H
i
;
H
i
+
1
2
=
2
+
H
i
;
H
i
+
1
3
=
H
i
+
1
2
;
H
i
+
1
4
=
H
i
+
1
1
.
T
h
e
co
n
s
tr
u
ctio
n
o
f
a
m
at
r
ix
o
f
an
y
d
im
e
n
s
io
n
s
tar
ts
f
r
o
m
0
:
H
0
1
=
0
.
An
o
th
er
m
ec
h
a
n
is
m
f
o
r
r
ec
u
r
s
iv
ely
co
n
s
tr
u
ctin
g
a
r
ec
o
d
in
g
m
atr
ix
u
s
es
co
m
p
u
tatio
n
al
h
is
to
r
y
:
H
i
1
=
H
i
−
1
;
H
i
2
=
2
n
–
1
–
H
i
1
;
H
i
3
=
H
i
2
;
H
i
4
=
H
i
1
.
T
h
e
co
m
p
u
tati
o
n
al
co
m
p
lex
ity
o
f
b
o
th
m
ec
h
an
is
m
s
f
o
r
co
n
s
tr
u
ctin
g
a
r
ec
o
d
i
n
g
m
atr
ix
f
o
r
a
lo
g
ical
f
u
n
ctio
n
f
r
o
m
n
-
v
ar
iab
les
is
eq
u
al
to
2
n
+
1
.
T
h
e
d
ata
s
tr
u
ctu
r
es r
ef
lectin
g
th
e
r
ec
u
r
s
iv
e
g
en
e
r
at
io
n
o
f
t
h
e
m
atr
ix
a
r
e
s
h
o
wn
i
n
Fig
u
r
e
2
.
Fig
u
r
e
2
.
Sy
n
th
esis
o
f
H
-
m
atr
i
x
r
ec
o
d
i
n
g
T
h
e
p
r
ac
tical
u
s
e
o
f
th
is
H
-
m
atr
ix
is
th
e
r
ap
id
co
n
s
tr
u
ctio
n
o
f
a
d
ed
u
ctiv
e
v
ec
to
r
b
y
r
ec
o
d
in
g
th
e
co
o
r
d
in
ates
o
f
th
e
lo
g
ic
v
ec
to
r
o
n
th
e
d
ec
im
al
co
d
es
o
f
a
s
t
r
in
g
with
a
n
u
m
b
er
d
eter
m
in
e
d
b
y
th
e
test
in
p
u
t
s
et.
An
ex
am
p
le
o
f
a
d
ed
u
ctiv
e
v
ec
to
r
c
o
n
s
tr
u
ctio
n
u
s
es
lo
g
ic
v
ec
to
r
0
1
1
1
,
n
=2
,
test
s
et
1
0
.
C
o
n
s
id
er
th
e
m
atr
ix
o
f
two
v
ar
iab
les
o
n
a
s
tr
in
g
n
u
m
b
e
r
2
(
T
=1
0
)
,
wh
ich
is
eq
u
al
to
2
3
0
1
.
R
ec
o
d
in
g
th
e
co
o
r
d
in
ates
o
f
a
lo
g
ical
v
ec
to
r
g
iv
es
a
d
ed
u
ctiv
e
v
ec
to
r
:
D=
L
H
T
=
2
=
0111
2301
=
1011
.
Usi
n
g
an
H
-
m
atr
ix
r
ec
o
d
in
g
to
s
y
n
th
esize
d
ed
u
ctiv
e
v
ec
to
r
s
s
p
ee
d
s
u
p
lo
g
ic
cir
c
u
it
f
au
lt
s
im
u
latio
n
s
b
y
3
0
%.
On
e
r
ec
o
d
in
g
m
atr
ix
f
o
r
an
elem
en
t w
ith
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
v
ar
iab
les is
n
ee
d
e
d
to
s
y
n
th
esize
d
ed
u
ctiv
e
v
ec
to
r
s
o
f
a
lo
g
ical
cir
cu
it.
3.
DATA S
T
RUC
T
UR
E
S F
O
R
L
O
G
I
C
E
L
E
M
E
NT
A
ND
C
I
RCUI
T
F
AU
L
T
S
I
M
UL
AT
I
O
N
Vec
to
r
-
lo
g
ical
d
esig
n
an
d
te
s
t
co
m
p
u
tin
g
is
a
p
r
o
ce
s
s
o
r
-
f
r
ee
in
-
m
em
o
r
y
So
C
I
P
-
co
r
e
test
in
g
m
ec
h
an
is
m
b
ased
o
n
r
ea
d
-
w
r
ite
tr
an
s
ac
tio
n
s
o
n
lo
g
ical
v
ec
to
r
s
an
d
th
eir
d
er
iv
ativ
es.
A
m
ec
h
an
is
m
is
a
co
m
m
u
n
icatin
g
r
elatio
n
s
h
ip
b
etwe
en
th
e
r
e
d
u
n
d
an
cy
o
f
d
at
a
s
tr
u
ctu
r
es
an
d
th
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
alg
o
r
ith
m
s
f
o
r
t
h
eir
p
r
o
ce
s
s
in
g
wh
en
an
in
c
r
ea
s
e
in
o
n
e
o
f
th
em
lead
s
to
a
d
ec
r
ea
s
e
in
th
e
o
th
er
an
d
v
ice
v
er
s
a.
Me
ch
an
is
m
s
f
o
r
m
o
d
e
lin
g
,
s
im
u
latio
n
,
a
n
d
test
in
g
d
ig
ital
p
r
o
jects
ar
e
p
r
o
p
o
s
ed
.
T
h
e
o
b
ject
o
f
t
h
e
s
tu
d
y
is
to
d
esig
n
a
n
d
test
c
o
m
p
u
tin
g
b
ased
o
n
v
ec
to
r
-
lo
g
i
c
m
ec
h
an
is
m
s
lo
ca
ted
in
m
e
m
o
r
y
to
s
av
e
en
er
g
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
4
5
2
-
4
6
8
456
an
d
d
esig
n
tim
e.
T
h
e
s
u
b
ject
o
f
th
e
r
esear
ch
is
v
ec
to
r
-
lo
g
ic
al
in
-
m
em
o
r
y
co
m
p
u
tin
g
f
o
r
s
o
lv
in
g
th
e
p
r
o
b
lem
s
o
f
m
o
d
elin
g
,
test
in
g
,
an
d
v
e
r
if
icatio
n
o
f
d
ig
ital
p
r
o
jects
b
ase
d
o
n
v
ec
to
r
-
lo
g
ical
m
o
d
els
o
f
th
e
I
P
-
co
r
e
So
C
in
Fig
u
r
e
3
.
Her
e,
all
c
o
m
p
u
tin
g
co
m
p
o
n
en
ts
ar
e
co
m
p
letely
n
e
w
an
d
f
o
c
u
s
o
n
th
e
E
DA
m
a
r
k
et
o
f
co
s
t
-
ef
f
ec
tiv
e
en
g
in
ee
r
in
g
s
o
lu
tio
n
s
.
T
h
er
e'
s
n
o
p
o
ten
t
C
PU
h
er
e,
n
o
t
ev
en
R
I
SC
-
V.
On
ly
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
an
d
o
n
e
v
ec
to
r
XOR o
p
er
atio
n
ar
e
ea
s
ily
co
n
v
e
r
ted
to
tr
a
n
s
ac
tio
n
s
.
Fig
u
r
e
3
.
Vec
to
r
lo
g
ic
d
esig
n
an
d
test
co
m
p
u
tin
g
in
m
e
m
o
r
y
T
h
e
v
e
ct
o
r
-
l
o
g
i
c
c
o
m
p
u
ti
n
g
e
q
u
ati
o
n
T
⊕
L
⊕
F
=
0
is
u
s
ed
t
o
s
o
l
v
e
a
ll
te
s
tin
g
p
r
o
b
le
m
s
.
I
t
d
e
f
i
n
es
th
e
r
ela
ti
o
n
s
h
i
p
s
b
etw
ee
n
t
h
e
s
am
e
c
o
m
p
o
n
e
n
t
f
o
r
m
a
ts
(
tes
t
,
l
o
g
ic
,
f
a
u
lts
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All
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[
2
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.
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m
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s
all
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wh
ile
it is
m
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co
m
p
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n
d
tech
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lo
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ically
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b
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b
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f
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f
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t'
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h
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t
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=
(
x
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.
Activ
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⨁
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lt
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e.
Sin
ce
th
e
tr
u
th
tab
le
is
th
e
co
m
p
lete
s
et
o
f
co
n
d
itio
n
al
if
s
tatem
en
ts
(
in
ea
ch
v
ar
ia
b
le
m
etr
ic)
tr
an
s
lated
in
to
th
e
tab
le
o
f
o
r
d
er
ed
ad
d
r
ess
es
o
f
th
e
b
its
o
f
th
e
l
o
g
ical
v
ec
to
r
.
C
ir
cu
it
d
escr
ip
tio
n
(
ci
r
cu
it
in
p
u
t
s
et
d
ata)
co
n
tai
n
s
in
f
o
r
m
atio
n
ab
o
u
t
t
h
e
r
elatio
n
s
h
ip
s
b
etwe
en
th
e
s
ch
em
atic
elem
en
ts
(
th
e
n
u
m
b
er
o
f
in
p
u
ts
o
f
ea
ch
elem
e
n
t
an
d
th
eir
n
u
m
er
ical
id
en
tifie
r
s
)
an
d
lo
g
ical
an
d
d
ed
u
ctiv
e
v
ec
to
r
s
f
o
r
p
er
f
o
r
m
in
g
th
e
cir
cu
it
f
au
lt
s
im
u
la
tio
n
.
Simu
latio
n
m
atr
ix
(
m
at
r
ix
o
f
cir
cu
it
f
au
lt
s
im
u
latio
n
o
n
in
p
u
t
s
et)
r
ef
er
s
to
q
u
ad
r
atic
m
atr
ix
o
f
th
e
s
ch
em
atic
s
tr
u
ctu
r
e
f
o
r
s
tu
ck
-
at
-
f
au
lts
s
im
u
latio
n
o
f
in
p
u
t,
in
ter
n
al,
an
d
o
u
tp
u
t
lin
es,
d
im
en
s
io
n
,
o
f
th
e
n
u
m
b
e
r
o
f
lin
es
o
f
th
e
cir
cu
it,
d
eter
m
in
ed
b
y
1
-
v
alu
es
o
f
th
e
co
o
r
d
in
ates
o
f
th
e
m
ain
d
iag
o
n
al.
I
t
is
d
esig
n
ed
to
m
o
d
el
cir
cu
it
f
au
lts
as
ad
d
r
ess
e
s
b
y
u
s
in
g
d
ed
u
ctiv
e
v
ec
to
r
s
o
f
lo
g
ic
elem
en
ts
to
o
b
tain
a
v
ec
to
r
o
f
f
au
lts
to
b
e
d
etec
ted
o
n
th
e
in
p
u
t
s
et.
E
n
d
-
to
-
en
d
n
u
m
b
e
r
in
g
o
f
s
ch
em
atic
lin
es
m
ak
es
tr
ac
in
g
s
tr
u
ctu
r
al
f
ea
tu
r
es
(
r
ec
o
n
v
e
r
g
en
ce
f
a
n
o
u
ts
)
ea
s
y
in
f
au
lt
an
aly
s
is
b
ased
o
n
a
s
im
u
latio
n
N
-
s
q
u
ar
ed
m
atr
ix
.
T
h
e
tab
le
f
o
r
test
–
d
etec
ted
cir
cu
it
f
au
lts
co
n
tain
s
in
teg
r
al
in
f
o
r
m
atio
n
ab
o
u
t
th
e
f
au
lts
d
etec
ted
o
n
ea
ch
i
n
p
u
t
s
et
an
d
an
ass
ess
m
en
t
o
f
th
e
q
u
ality
o
f
th
e
in
p
u
t
s
et
an
d
th
e
test
.
I
t
is
u
s
ed
to
v
alid
ate
th
e
test
an
d
f
in
d
f
a
u
lts
in
th
e
d
ig
ital d
ev
ice.
T
h
e
f
o
r
m
u
la
f
o
r
s
im
u
latin
g
s
tu
ck
-
at
-
f
au
lts
o
f
cir
c
u
it
lin
es
is
as
f
o
llo
ws:
f
r
o
m
th
e
in
p
u
t
s
et
o
n
th
e
e
x
ter
n
al
i
n
p
u
ts
an
d
n
u
m
b
er
ed
N
-
lin
es
o
f
t
h
e
cir
cu
it
is
s
y
n
th
esized
N
2
s
im
u
latio
n
m
atr
ix
f
illed
with
1
-
co
o
r
d
in
ates
d
iag
o
n
ally
to
o
b
tain
a
v
ec
to
r
o
f
d
etec
ted
f
a
u
l
ts
o
n
th
e
N
-
lin
es
o
f
th
e
cir
cu
it
b
y
c
o
n
s
tr
u
ctin
g
a
m
atr
ix
o
f
d
ed
u
ctiv
e
v
ec
to
r
s
f
r
o
m
th
e
m
-
n
u
m
b
er
o
f
f
u
n
ctio
n
al
elem
en
ts
o
f
th
e
cir
cu
it,
b
ased
o
n
lo
g
ical
v
ec
to
r
s
an
d
b
in
ar
y
s
ets
at
th
e
in
p
u
t
s
o
f
t
h
e
elem
e
n
ts
,
af
ter
wh
ich
ea
ch
o
u
tp
u
t
o
f
t
h
e
s
ch
em
atic
elem
en
t
is
s
im
u
lat
ed
b
y
th
e
s
eq
u
en
tial
p
r
o
ce
s
s
in
g
o
f
th
e
co
m
b
in
atio
n
o
f
lin
es
o
f
th
e
s
im
u
latio
n
m
atr
ix
at
t
h
e
elem
e
n
t
in
p
u
ts
a
s
ad
d
r
ess
es
o
f
t
h
e
ce
lls
co
r
r
esp
o
n
d
in
g
t
o
th
e
co
r
r
esp
o
n
d
in
g
d
ed
u
ctiv
e
v
ec
to
r
s
,
af
ter
wh
ich
a
d
is
ju
n
ctio
n
o
p
e
r
atio
n
is
p
er
f
o
r
m
e
d
o
n
th
o
s
e
lin
es
o
f
th
e
s
im
u
latio
n
m
atr
ix
th
at
b
elo
n
g
to
th
e
ex
ter
n
al
in
ter
f
ac
e
o
u
tp
u
ts
o
f
th
e
cir
cu
it,
i
n
o
r
d
er
to
o
b
tai
n
an
in
teg
r
al
∨
-
v
ec
to
r
o
f
th
e
s
im
u
latio
n
,
th
e
1
-
co
o
r
d
in
ates
o
f
wh
ich
ar
e
f
u
r
t
h
er
d
eter
m
in
ed
b
y
th
e
in
v
er
s
e
v
alu
es
o
f
th
e
lin
es
o
f
th
e
v
ec
to
r
o
f
th
e
g
o
o
d
s
im
u
latio
n
to
o
b
tain
th
e
v
ec
t
o
r
o
f
test
ed
f
au
lts
o
n
th
e
in
p
u
t
b
in
a
r
y
s
et.
Fau
lts
-
as
-
ad
d
r
e
s
s
es
s
im
u
latio
n
is
a
tech
n
iq
u
e
th
at
lev
er
a
g
es
in
p
u
t
f
au
lt
co
m
b
in
atio
n
s
as
th
e
ad
d
r
ess
es
o
f
d
ed
u
ctiv
e
v
ec
to
r
b
its
,
wh
ich
f
o
r
m
s
th
e
o
u
tp
u
t v
ec
t
o
r
o
f
th
e
d
etec
ted
in
p
u
t f
a
u
lts
in
a
lo
g
ic
elem
en
t.
T
h
e
m
o
d
el
o
f
d
etec
ted
lin
e
f
au
lt is
r
ep
r
esen
ted
b
y
a
1
-
s
ig
n
al
in
th
e
s
im
u
latio
n
m
atr
ix
,
an
d
t
h
e
f
au
lt th
at
was n
o
t d
etec
ted
is
n
o
ted
b
y
a
0
-
s
ig
n
al.
4.
I
NP
UT
D
AT
A
M
O
DE
L
S F
O
R
L
O
G
I
CAL A
NAL
YSI
S
I
n
p
u
t
d
ata
m
o
d
els
f
o
r
l
o
g
ical
p
r
o
ce
s
s
in
g
ca
n
b
e
r
ep
r
esen
t
ed
in
Fig
u
r
e
4
.
Nu
m
b
er
1
is
th
e
s
et
o
f
co
m
p
ac
t
u
n
s
tr
u
ctu
r
ed
d
ata
r
e
q
u
ir
in
g
co
m
p
le
x
an
d
s
eq
u
e
n
tial
in
p
u
t
p
r
o
ce
s
s
in
g
[
4
2
]
.
Nu
m
b
er
2
is
th
e
b
i
n
ar
y
v
ec
to
r
o
f
u
n
itar
y
-
en
co
d
ed
d
ata
th
at
u
s
es
co
m
p
lex
p
r
o
ce
s
s
o
r
r
eg
is
ter
v
ar
iab
les
t
o
p
r
o
ce
s
s
p
a
ir
s
o
f
in
p
u
t
v
ec
to
r
s
in
p
ar
allel.
Nu
m
b
er
3
is
th
e
a
d
d
r
ess
es
f
o
r
m
ed
b
y
th
e
c
o
lu
m
n
s
o
f
th
e
in
p
u
t
m
atr
ix
o
f
u
n
ita
r
y
-
en
c
o
d
ed
d
ata
to
p
er
f
o
r
m
r
ea
d
-
wr
ite
in
-
m
em
o
r
y
tr
an
s
ac
tio
n
s
o
n
t
h
e
b
its
o
f
th
e
lo
g
ical
v
ec
to
r
(
with
o
u
t
t
r
ad
itio
n
al
p
r
o
ce
s
s
o
r
lo
g
ic)
with
p
ar
allel
an
aly
s
is
o
n
th
e
co
lu
m
n
s
o
f
d
ata
as
a
d
d
r
ess
es.
Her
e,
th
e
v
ec
to
r
L
=
0
1
1
0
1
0
0
1
is
an
XOR
f
u
n
ctio
n
o
f
th
r
ee
v
ar
iab
les
th
at
f
o
r
m
a
d
d
r
ess
es
f
r
o
m
th
e
d
ata
to
b
e
a
n
aly
ze
d
.
T
h
e
lo
n
g
e
r
th
e
lo
g
ical
v
ec
to
r
len
g
th
,
th
e
g
r
ea
ter
th
e
d
e
g
r
ee
o
f
p
ar
allelis
m
wh
en
p
r
o
ce
s
s
in
g
b
ig
d
ata
as
ad
d
r
ess
es.
L
o
g
ical
v
ec
to
r
s
d
o
n
o
t
n
ee
d
to
b
e
r
e
d
u
ce
d
t
o
th
e
lo
g
i
c
o
f
th
e
p
r
o
ce
s
s
o
r
u
s
in
g
r
ath
e
r
co
m
p
lex
s
y
n
th
esis
.
I
n
-
m
e
m
o
r
y
co
m
p
u
tin
g
b
ased
o
n
lo
g
ic
v
ec
to
r
s
is
f
r
ee
f
r
o
m
s
y
n
th
esis
an
d
tr
ad
itio
n
al
C
PU
l
o
g
ic,
r
ep
lace
d
b
y
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
(
6
0
0
p
s
laten
cy
)
,
wh
ich
ar
e
n
o
t
in
f
er
io
r
in
s
p
ee
d
to
th
e
ar
ith
m
etic
lo
g
ic
u
n
it
(
AL
U
)
[
3
8
]
.
At
th
e
s
am
e
tim
e,
in
-
m
em
o
r
y
c
o
m
p
u
tin
g
h
as
h
alf
th
e
p
o
wer
co
n
s
u
m
p
tio
n
wh
en
p
r
o
ce
s
s
in
g
b
ig
d
ata
c
o
m
p
ar
e
d
to
a
p
r
o
ce
s
s
o
r
[
3
9
]
.
T
wo
d
ata
p
r
o
ce
s
s
in
g
o
p
tio
n
s
r
ep
r
esen
t f
au
lt
-
as
-
ad
d
r
ess
s
im
u
latio
n
tech
n
iq
u
es
as sh
o
wn
i
n
Fig
u
r
e
5.
−
T
ec
h
n
iq
u
e
1
.
Use
th
e
co
l
u
m
n
s
o
f
th
e
S
-
m
atr
ix
s
im
u
latio
n
alo
n
g
th
e
in
p
u
t
lin
es
o
f
th
e
e
lem
en
t
as
th
e
ad
d
r
ess
es
o
f
th
e
d
ed
u
ctiv
e
v
ec
to
r
b
its
,
wh
ich
f
o
r
m
th
e
c
o
o
r
d
in
ates
o
f
th
e
v
ec
to
r
o
f
th
e
f
au
lts
to
b
e
d
etec
ted
o
n
th
e
o
u
tp
u
t
lin
e
Y
i
,
j
=
D
x
j
.
Fo
r
th
is
ex
am
p
le,
it
wo
u
l
d
b
e
12
=
100001000100
.
Her
e,
ea
ch
1
-
u
n
it
is
d
ef
in
ed
b
y
ad
d
r
ess
1
0
0
in
th
e
tr
u
t
h
tab
le
o
f
th
e
d
ed
u
ctiv
e
v
ec
to
r
,
wh
er
e
D
(
1
0
0
)
=
1
.
T
h
is
tech
n
iq
u
e
is
im
p
lem
e
n
ted
in
t
h
e
FAAS e
n
g
in
e
f
o
r
cir
cu
it f
a
u
lt si
m
u
latio
n
.
−
T
ec
h
n
iq
u
e
2
.
Dis
tr
ib
u
te
all
c
o
lu
m
n
s
o
f
th
e
S
-
m
atr
ix
o
f
th
e
s
im
u
latio
n
with
th
e
in
p
u
t
n
u
m
b
er
s
o
f
th
e
cir
cu
it
lin
es
to
th
e
ad
d
r
ess
es
o
f
th
e
d
e
d
u
ctiv
e
v
ec
to
r
tr
u
th
t
ab
le,
an
d
th
en
g
e
n
er
ate
th
e
1
-
co
o
r
d
in
ates
o
f
th
e
f
au
lt
v
ec
to
r
to
b
e
test
ed
o
n
th
e
o
u
tp
u
t
lin
e
u
s
in
g
th
e
n
u
m
b
er
s
o
f
th
e
lin
es
eq
u
iv
alen
t
t
o
th
e
co
lu
m
n
s
,
if
th
e
co
lu
m
n
o
f
t
h
e
tr
u
th
ta
b
le
is
co
v
er
ed
b
y
th
e
1
-
co
o
r
d
in
ate
o
f
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ty
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I
SS
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:
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I
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I
n
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R
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b
&
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u
to
m
,
Vo
l
.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
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5
2
-
4
6
8
460
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o
f
b
it
r
ec
o
d
i
n
g
ar
e
r
e
p
r
esen
ted
b
y
d
ec
im
al
ad
d
r
es
s
co
d
es,
wh
ich
ar
e
o
b
tain
ed
b
y
XOR
in
ter
ac
tio
n
o
f
th
e
in
p
u
t
b
in
ar
y
test
s
et
T
an
d
th
e
co
lu
m
n
s
o
f
th
e
tr
u
th
t
ab
le
L
:A=T
⨁
L
o
f
an
y
f
u
n
ctio
n
ality
f
r
o
m
th
e
n
-
v
ar
iab
les.
T
h
is
is
th
e
th
eo
r
eti
ca
l
ess
en
ce
o
f
th
e
s
y
n
th
esis
o
f
th
e
b
it
-
r
ec
o
d
in
g
m
atr
ix
.
T
h
e
r
esu
lts
o
f
t
h
e
X
OR
in
ter
ac
tio
n
o
f
th
e
in
p
u
t
b
in
ar
y
test
v
ec
to
r
s
(
T
=0
0
0
0
,
0
1
1
1
)
an
d
2
=1
6
co
lu
m
n
s
o
f
th
e
tr
u
th
tab
le
f
o
r
m
th
e
0
an
d
7
r
o
ws
o
f
t
h
e
b
it
-
r
ec
o
d
in
g
m
atr
ix
to
g
en
er
ate
a
d
ed
u
ctiv
e
v
ec
to
r
.
E
ac
h
tab
le
s
h
o
ws
th
e
r
esu
lt
o
f
th
e
XOR
s
u
m
m
atio
n
o
f
th
e
te
s
t
s
et
T
an
d
th
e
s
tan
d
ar
d
tr
u
th
tab
le
L
.
T
h
e
u
p
p
er
p
ar
t
o
f
ea
c
h
ta
b
le
is
r
e
p
r
esen
te
d
b
y
th
e
r
ec
o
d
in
g
v
ec
to
r
o
b
tai
n
ed
t
o
c
o
m
p
ile
t
h
e
H
-
m
at
r
ix
.
T
h
e
b
i
n
ar
y
-
d
ec
im
al
co
d
e
o
f
th
e
test
s
et
f
o
r
m
s
th
e
co
r
r
esp
o
n
d
i
n
g
s
tr
in
g
o
f
th
e
r
ec
o
d
in
g
m
atr
ix
.
Kn
o
win
g
th
e
r
ec
o
d
in
g
v
ec
t
o
r
H
0111
it
is
ea
s
y
to
o
b
tain
th
e
d
ed
u
ctiv
e
v
ec
to
r
D
b
y
ex
ec
u
tin
g
th
e
f
o
r
m
u
la:
f
r
o
m
th
e
test
s
et
T
=0
1
1
1
as
th
e
b
it
ad
d
r
ess
o
f
th
e
lo
g
ical
v
ec
to
r
L
0111
=
1
,
th
e
s
tate
o
f
t
h
e
elem
e
n
t'
s
o
u
tp
u
t
is
d
eter
m
in
e
d
Y=
1
,
XOR
-
s
u
m
m
atio
n
o
f
wh
ich
with
all
th
e
b
its
o
f
th
e
lo
g
ical
v
ec
to
r
L
=
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
g
i
v
es
a
v
ec
to
r
o
f
ac
tiv
ity
A=
Y
⨁
L
=0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
,
to
wh
ich
th
e
H
-
v
ec
to
r
o
f
th
e
r
ec
o
d
in
g
o
f
th
e
b
its
o
n
th
e
test
s
et
T
=0
1
1
1
is
ap
p
lied
to
o
b
tai
n
th
e
d
ed
u
ctiv
e
v
ec
to
r
D=
A
H
=
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
wh
o
s
e
b
its
ar
e
alr
ea
d
y
wr
itten
to
th
e
b
in
ar
y
-
d
ec
im
al
ad
d
r
ess
es
s
ta
n
d
ar
d
.
T
h
e
H
-
m
atr
ix
o
f
b
it
r
ec
o
d
in
g
is
th
e
k
ey
to
co
n
s
tr
u
ctin
g
a
m
atr
ix
o
f
d
ed
u
ctiv
e
v
ec
to
r
s
o
f
a
n
y
lo
g
ic
.
Fig
u
r
e
8
.
T
r
u
th
tab
le
s
y
n
th
esis
o
f
th
e
H
-
m
atr
ix
lin
e
f
o
r
d
e
d
u
c
tiv
e
v
ec
to
r
cr
ea
tio
n
I
t
is
p
r
o
p
o
s
ed
to
u
s
e
a
tr
u
th
tab
le
to
s
y
n
th
esize
th
e
d
ed
u
ctiv
e
v
ec
to
r
o
f
a
f
u
n
ctio
n
al
elem
en
t
in
Fig
u
r
e
9
b
ased
o
n
a
lo
g
ical
v
ec
to
r
an
d
a
g
iv
e
n
b
in
a
r
y
in
p
u
t
s
et
f
o
r
its
u
s
e
in
s
im
u
latin
g
s
tu
ck
-
at
-
f
au
lts
in
a
d
ig
ital
cir
cu
it.
T
h
e
f
o
r
m
u
la
f
o
r
d
ed
u
ctiv
e
v
ec
to
r
m
o
d
elin
g
is
as
f
o
llo
ws.
T
h
e
in
p
u
t
b
in
ar
y
s
et,
as
th
e
ce
ll
ad
d
r
ess
o
f
th
e
lo
g
ical
v
ec
to
r
,
co
n
tain
s
th
e
o
u
tp
u
t
s
tate
o
f
th
e
elem
en
t,
th
e
co
n
ca
ten
atio
n
o
f
wh
ich
with
th
e
Fig
u
r
e
8
.
T
r
u
th
tab
le
s
y
n
th
esis
o
f
th
e
H
-
m
atr
ix
lin
e
f
o
r
d
e
d
u
c
tiv
e
v
ec
to
r
cr
ea
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
F
a
u
lts
-
as
-
a
d
d
r
ess
s
imu
la
tio
n
(
V
la
d
imir
Ha
h
a
n
o
v
)
461
in
p
u
t
b
in
ar
y
f
o
r
m
s
an
in
p
u
t
-
o
u
tp
u
t
s
tate
v
ec
to
r
f
o
r
XOR
in
ter
ac
tio
n
with
all
th
e
co
lu
m
n
s
o
f
th
e
tr
u
th
tab
le
to
s
y
n
th
esize
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e
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tab
le,
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o
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ce
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u
r
e
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ascen
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e
r
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b
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a
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y
ad
d
r
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es o
f
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ar
ia
b
les is
ap
p
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to
o
b
tain
a
d
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e
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ec
to
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i
n
th
e
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er
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Fig
u
r
e
9
.
Gen
e
r
atio
n
o
f
th
e
d
e
d
u
ctiv
e
v
ec
to
r
f
o
r
an
elem
e
n
t
v
ia
a
tr
u
th
tab
le
Data
s
tr
u
ctu
r
es
f
o
r
lo
g
ic
c
ir
cu
it
f
au
lt
s
im
u
latio
n
ar
e
r
ep
r
esen
ted
b
y
th
e
f
o
llo
win
g
m
ac
r
o
-
co
m
p
o
n
en
ts
:
c
ir
cu
it
d
escr
ip
ti
o
n
an
d
s
im
u
latio
n
m
atr
ix
.
T
h
e
f
au
lt
d
etec
tio
n
tab
le
c
o
n
s
is
ts
o
f
i
)
id
e
n
tifie
r
s
o
f
th
e
in
p
u
t
-
o
u
tp
u
t
o
f
th
e
cir
cu
it
an
d
lo
g
ic
elem
en
ts
,
wh
ich
to
g
eth
er
m
ak
e
u
p
th
e
in
ter
f
ac
e
o
f
th
e
cir
cu
it;
ii)
a
m
atr
ix
o
f
lo
g
ical
v
ec
to
r
s
th
at
d
ef
in
e
th
e
f
u
n
cti
o
n
ality
o
f
ea
c
h
elem
en
t
o
f
th
e
cir
cu
it;
iii)
a
m
atr
ix
o
f
d
ed
u
ctiv
e
v
ec
to
r
s
th
at
f
o
r
m
lis
ts
o
f
in
p
u
t
f
au
lts
to
b
e
d
etec
ted
at
t
h
e
o
u
tp
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t
o
f
ea
c
h
elem
en
t
o
f
th
e
c
ir
cu
it;
iv
)
v
ec
to
r
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f
b
in
ar
y
g
o
o
d
b
eh
av
io
r
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it
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es
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th
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at
o
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in
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u
t,
in
ter
n
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an
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o
u
tp
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t
lin
es;
v
)
q
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ad
r
atic
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atr
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(
2
o
f
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e
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u
m
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o
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it
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s
)
f
o
r
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im
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latio
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it
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in
p
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t
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y
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et,
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r
e
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o
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el
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d
vi
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e
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av
io
r
.
N
ex
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a
cir
c
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it
as
in
Fig
u
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1
0
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wh
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ata
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ith
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:
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latio
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illed
with
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ates
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ased
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lated
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m
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atio
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im
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im
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at
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o
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o
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tain
a
n
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te
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al
∨
−
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th
e
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im
u
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ates
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wh
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e
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p
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lts
o
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th
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in
p
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b
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s
et
.
T
h
ese
ca
n
b
e
s
ee
n
in
Fig
u
r
e
1
1
.
Fig
u
r
e
1
0
.
C
ir
cu
it f
o
r
s
im
u
lati
o
n
o
f
f
au
lts
Evaluation Warning : The document was created with Spire.PDF for Python.