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Octo
b
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20
26
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p
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.
4
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[
1
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T
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[
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[
5
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[
6
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.
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I
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15
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No
.
5
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Octo
b
er
20
26
:
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9
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-
4
9
7
9
4970
C
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1
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Pr
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s
t
c
a
s
e
s
[
1
2
]
.
M
o
r
e
o
v
e
r
,
s
t
a
t
i
c
s
l
i
c
i
n
g
a
p
p
r
o
a
c
h
e
s
n
o
t
o
n
l
y
s
i
m
p
l
if
y
s
o
f
t
w
ar
e
m
a
in
t
e
n
an
c
e,
b
u
t
a
l
s
o
s
u
p
p
o
r
t
s
e
c
u
r
i
t
y
an
a
ly
s
i
s
,
d
e
b
u
g
g
in
g
,
a
n
d
p
er
f
o
r
m
an
c
e
o
p
t
im
i
z
a
t
i
o
n
[
1
3
]
.
I
t
s
ab
i
l
i
ty
to
p
r
o
v
id
e
a
c
o
m
p
l
e
te
v
i
e
w
o
f
d
ep
en
d
en
c
i
e
s
w
i
th
o
u
t
p
r
o
g
r
a
m
ex
e
cu
t
i
o
n
m
a
k
e
s
i
t
h
ig
h
ly
s
u
i
ta
b
l
e
f
o
r
ex
t
r
a
c
t
in
g
m
o
d
e
r
n
s
o
f
t
w
a
r
e
d
e
s
i
g
n
r
eq
u
ir
e
m
en
t
s
[
1
4
]
.
Dy
n
am
ic
s
licin
g
tech
n
iq
u
es
h
av
e
tr
ad
itio
n
ally
b
ee
n
em
p
l
o
y
ed
as
b
ac
k
en
d
m
ec
h
an
is
m
s
f
o
r
p
r
o
g
r
am
d
eb
u
g
g
in
g
,
f
au
lt lo
ca
lizatio
n
,
an
d
au
to
m
ated
p
r
o
g
r
am
r
e
p
air
[
1
5
]
,
[
1
6
]
.
Ho
wev
er
,
it h
as b
e
en
wid
ely
o
b
s
er
v
e
d
th
at
s
tate
-
of
-
th
e
-
ar
t
d
y
n
a
m
ic
s
licin
g
tech
n
iq
u
es
f
ac
e
s
ig
n
if
ican
t
ch
allen
g
es
in
ter
m
s
o
f
ef
f
icien
cy
an
d
s
ca
lab
ilit
y
[
1
7
]
.
T
h
ese
tech
n
i
q
u
es
ten
d
to
s
u
f
f
er
as
ex
ec
u
tio
n
s
ize
an
d
th
e
n
u
m
b
er
o
f
ex
ec
u
ted
in
s
tr
u
ctio
n
s
in
cr
ea
s
e,
lead
in
g
to
h
ig
h
r
u
n
ti
m
e
o
v
er
h
ea
d
[
1
8
]
,
[
1
9
]
.
An
o
n
-
d
em
an
d
r
e
-
ex
ec
u
tio
n
-
b
ased
d
y
n
a
m
ic
s
licin
g
s
tr
ateg
y
was
p
r
o
p
o
s
ed
in
[
2
]
,
wh
e
r
e
s
lices
ar
e
p
r
o
g
r
ess
iv
ely
co
n
s
tr
u
cted
b
y
r
ep
ea
ted
ly
e
x
ec
u
tin
g
t
h
e
p
r
o
g
r
am
to
ac
q
u
ir
e
d
ep
en
d
en
c
y
in
f
o
r
m
atio
n
.
T
h
e
ap
p
r
o
ac
h
co
m
p
a
r
es
o
n
-
d
em
an
d
r
e
-
e
x
ec
u
tio
n
with
ex
ec
u
te
-
o
n
ce
p
a
r
ad
ig
m
s
in
ter
m
s
o
f
p
er
f
o
r
m
an
ce
,
h
ig
h
lig
h
tin
g
tr
ad
e
-
o
f
f
s
in
f
lu
e
n
ce
d
b
y
e
x
ec
u
tio
n
s
ize
an
d
s
lice
co
m
p
lex
ity
.
C
o
m
p
ar
ativ
e
ev
alu
atio
n
s
wer
e
co
n
d
u
cte
d
ag
ain
s
t
to
o
ls
s
u
ch
as
J
av
aSlicer
an
d
Sli
ce
r
4
J
[
2
0
]
,
[
2
1
]
.
A
s
y
m
b
o
lic
a
b
s
tr
ac
tio
n
-
b
ased
d
y
n
am
ic
s
licin
g
m
o
d
el
f
o
r
lar
g
e
-
s
ca
le
ap
p
licatio
n
s
was
in
tr
o
d
u
ce
d
in
[
2
2
]
,
r
ep
lacin
g
t
r
ad
itio
n
al
m
em
o
r
y
r
ef
er
en
ce
tr
ac
k
in
g
with
an
ab
s
tr
ac
t m
em
o
r
y
m
o
d
el
o
p
er
atin
g
o
n
p
r
o
g
r
a
m
s
y
m
b
o
ls
.
Desp
ite
th
ese
ad
v
an
ce
m
en
ts
,
d
y
n
am
ic
s
licin
g
r
e
m
ain
s
u
n
s
u
itab
le
f
o
r
p
r
o
d
u
ctio
n
-
lev
el
d
ep
lo
y
m
en
t
d
u
e
to
th
e
h
ig
h
co
s
t o
f
r
u
n
tim
e
in
s
tr
u
m
en
tatio
n
[
1
]
.
T
o
m
itig
ate
th
is
,
a
h
y
b
r
id
s
tatic
-
d
y
n
a
m
ic
s
licin
g
ap
p
r
o
ac
h
was
in
tr
o
d
u
ce
d
,
wh
ic
h
d
em
o
n
s
tr
ates
th
e
r
ec
o
v
er
y
o
f
a
lar
g
e
p
r
o
p
o
r
tio
n
o
f
r
ele
v
an
t
s
tatem
en
ts
with
lim
ited
r
u
n
tim
e
o
v
er
h
ea
d
.
Sy
m
b
o
lic
s
licin
g
tech
n
iq
u
es
b
ased
o
n
s
y
m
b
o
lic
ex
ec
u
tio
n
h
a
v
e
also
b
ee
n
ex
p
lo
r
ed
[
1
4
]
,
b
u
t
th
ey
ar
e
c
o
m
p
u
tatio
n
ally
ex
p
en
s
iv
e
f
o
r
c
o
m
p
lex
J
av
a
p
r
o
g
r
am
s
with
n
u
m
er
o
u
s
ex
ec
u
ti
o
n
p
ath
s
,
lead
in
g
to
s
ca
lab
ilit
y
co
n
ce
r
n
s
.
Data
-
f
lo
w
-
g
u
id
e
d
s
tr
ateg
ies
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
im
p
r
o
v
e
s
licin
g
ac
cu
r
ac
y
[
1
5
]
,
y
et
th
e
y
s
tr
u
g
g
le
with
co
m
p
lex
c
o
n
tr
o
l
s
tr
u
ctu
r
e
s
co
m
m
o
n
i
n
o
b
ject
-
o
r
ien
ted
J
av
a
p
r
o
g
r
am
s
,
wh
ic
h
lim
its
th
eir
ef
f
ec
tiv
en
ess
f
o
r
d
esig
n
s
p
ec
if
icatio
n
ex
tr
ac
tio
n
.
Similar
ch
allen
g
es
r
elate
d
to
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
an
d
s
ca
lab
ilit
y
h
av
e
b
ee
n
r
ep
o
r
ted
in
la
r
g
e
-
s
ca
le
J
av
a
a
p
p
licatio
n
s
with
e
x
ten
s
iv
e
o
b
j
ec
t
-
o
r
ien
ted
f
ea
tu
r
es
[
2
3
]
,
[
2
4
]
.
So
m
e
ap
p
r
o
ac
h
es
p
r
im
ar
ily
f
o
cu
s
o
n
a
u
to
m
ated
p
r
o
g
r
a
m
r
ep
air
wh
ile
lar
g
ely
o
v
er
lo
o
k
i
n
g
th
e
r
o
le
o
f
f
u
n
ctio
n
al
d
ep
en
d
e
n
cies in
p
r
ec
is
e
s
lice
ex
tr
ac
tio
n
,
wh
ich
ca
n
r
estrict
ef
f
ec
tiv
e
p
r
o
g
r
am
ab
s
tr
ac
tio
n
[
2
3
]
.
E
x
ec
u
tio
n
-
g
u
id
e
d
an
d
p
r
ed
ict
iv
e
s
licin
g
ap
p
r
o
ac
h
es
r
ely
in
g
o
n
d
y
n
am
ic
d
e
p
en
d
e
n
ce
lear
n
in
g
h
a
v
e
also
b
ee
n
in
v
esti
g
ated
i
n
[
2
5
]
.
Ho
wev
e
r
,
th
ei
r
h
ea
v
y
r
elia
n
ce
o
n
ex
ec
u
tio
n
d
ata
r
estricts
ap
p
licab
ilit
y
in
s
ce
n
ar
io
s
wh
er
e
e
x
ec
u
tio
n
tr
a
ce
s
ar
e
in
co
m
p
lete,
u
n
av
ailab
le
,
o
r
co
s
tly
to
o
b
tain
.
Ma
ch
i
n
e
lear
n
in
g
(
ML
)
-
b
ased
s
licin
g
tech
n
iq
u
es
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
d
er
iv
e
f
o
r
m
al
d
esig
n
s
p
ec
if
icatio
n
s
f
r
o
m
J
av
a
p
r
o
g
r
am
s
[
1
9
]
,
[
2
6
]
,
[
2
7
]
,
b
u
t
th
ese
ap
p
r
o
ac
h
es
o
f
ten
in
tr
o
d
u
ce
a
d
d
itio
n
al
tr
ain
in
g
o
v
er
h
ea
d
an
d
d
ep
e
n
d
o
n
lar
g
e
lab
elled
d
atasets
.
Nev
er
th
eless
,
th
ese
s
tu
d
ies
co
llectiv
ely
h
ig
h
lig
h
t
th
e
im
p
o
r
tan
ce
o
f
s
tatic
s
li
cin
g
in
id
en
tify
in
g
im
p
licit a
n
d
n
o
n
-
tr
iv
ial
d
e
p
en
d
en
cies in
co
m
p
le
x
o
b
ject
-
o
r
i
en
ted
p
r
o
g
r
am
s
.
R
ec
en
t
ad
v
an
ce
m
en
ts
in
ar
ti
f
icial
in
tellig
en
ce
(
AI
)
-
ass
is
t
ed
p
r
o
g
r
am
a
n
aly
s
is
an
d
s
p
ec
if
icatio
n
tr
an
s
latio
n
f
u
r
t
h
er
d
e
m
o
n
s
tr
ate
a
g
r
o
win
g
co
n
v
er
g
en
ce
b
etwe
en
s
tatic
p
r
o
g
r
am
s
l
icin
g
an
d
m
ac
h
in
e
in
tellig
en
ce
[
2
8
]
,
[
2
9
]
.
T
h
ese
d
ev
elo
p
m
e
n
ts
r
ein
f
o
r
ce
th
e
n
e
ed
f
o
r
ef
f
icien
t,
d
ep
en
d
en
cy
-
a
war
e
s
tatic
s
licin
g
f
r
am
ewo
r
k
s
th
at
s
u
p
p
o
r
t
p
r
e
cise
p
r
o
g
r
a
m
a
b
s
tr
ac
tio
n
an
d
s
er
v
e
as
a
r
eliab
le
f
o
u
n
d
ati
o
n
f
o
r
d
o
wn
s
tr
ea
m
AI
-
d
r
iv
en
s
o
f
twar
e
en
g
in
ee
r
i
n
g
task
s
.
T
h
er
eb
y
,
to
ad
d
r
e
s
s
th
ese
lim
itatio
n
s
,
th
er
e
is
a
n
ee
d
to
d
esig
n
an
d
tailo
r
a
s
im
p
lifie
d
an
d
c
o
m
p
u
tatio
n
ally
ef
f
icien
t
p
r
o
g
r
am
s
licin
g
m
eth
o
d
th
at
c
o
u
l
d
ac
cu
r
ately
ca
p
tu
r
e
im
p
licit
co
n
tr
o
l
an
d
f
u
n
ctio
n
al
d
ep
en
d
e
n
cies,
also
m
in
im
ize
r
ed
u
n
d
a
n
t
co
m
p
u
tatio
n
s
to
war
d
s
ex
tr
ac
tin
g
p
r
ec
is
e
f
o
r
m
al
s
o
f
twar
e
s
p
ec
if
icatio
n
s
f
r
o
m
J
av
a
p
r
o
g
r
am
s
,
w
h
ile
r
etain
in
g
a
b
ala
n
ce
b
et
wee
n
p
r
ec
is
io
n
v
s
p
er
f
o
r
m
an
ce
tr
a
d
e
-
o
f
f
s
.
I
n
r
ec
en
t
y
ea
r
s
,
AI
an
d
lar
g
e
lan
g
u
ag
e
m
o
d
els
(
L
L
Ms)
h
av
e
i
n
cr
ea
s
in
g
ly
s
u
p
p
o
r
ted
s
tatic
co
d
e
an
aly
s
is
,
p
r
o
g
r
am
co
m
p
r
e
h
e
n
s
io
n
,
an
d
au
t
o
m
ated
s
o
f
tw
ar
e
d
o
c
u
m
en
tatio
n
[
2
9
]
,
[
3
0
]
.
T
h
e
p
r
o
p
o
s
ed
s
tatic
-
b
ac
k
war
d
s
licin
g
f
r
am
e
wo
r
k
aim
s
to
co
m
p
lem
en
t
s
u
c
h
AI
-
d
r
iv
e
n
to
o
ls
b
y
p
r
o
d
u
cin
g
p
r
ec
is
e,
m
in
im
al
p
r
o
g
r
a
m
s
lices
an
d
o
b
ject
-
Z
s
p
ec
if
icatio
n
s
,
wh
ich
ca
n
b
e
au
to
m
atica
lly
tr
an
s
lated
in
to
h
u
m
a
n
-
r
ea
d
a
b
le
r
eq
u
ir
em
e
n
ts
,
en
ab
lin
g
d
o
wn
s
tr
ea
m
r
ea
s
o
n
in
g
f
o
r
r
eq
u
ir
e
m
en
t
ab
s
tr
ac
tio
n
,
test
g
en
er
a
tio
n
,
an
d
s
o
f
twar
e
m
o
d
er
n
izatio
n
.
T
h
er
ef
o
r
e,
an
e
f
f
icien
t
s
tatic
-
b
ac
k
war
d
s
licin
g
f
r
am
ewo
r
k
is
n
ee
d
ed
th
at
p
r
ec
is
ely
ca
p
tu
r
es
b
o
th
im
p
licit
co
n
tr
o
l
an
d
f
u
n
ctio
n
al
d
ep
en
d
e
n
cies
wh
ile
m
in
im
izin
g
r
ed
u
n
d
an
t
co
m
p
u
tatio
n
s
an
d
ac
h
iev
in
g
an
o
p
tim
al
b
alan
ce
b
etwe
en
s
licin
g
ac
cu
r
ac
y
an
d
co
m
p
u
tatio
n
a
l e
f
f
icien
cy
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
-
8
9
3
8
A
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u
ta
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l fra
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k
fo
r
a
b
s
tr
a
ctin
g
p
r
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a
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s
lices
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A
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4971
Mo
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y
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allen
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p
r
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p
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wo
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er
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y
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t
r
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s
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atica
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m
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al
y
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is
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t
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m
b
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es
co
m
p
u
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p
r
o
c
ess
es
o
f
r
estru
ctu
r
in
g
,
d
esig
n
in
f
o
r
m
atio
n
ex
tr
ac
tio
n
,
an
d
c
o
n
s
tr
u
ctio
n
o
f
a
d
ata
f
lo
w
tab
le
(
DFT)
to
co
m
p
u
te
th
e
f
u
n
ctio
n
al
d
ep
en
d
en
cies
with
r
ed
u
ce
d
a
n
d
o
p
tim
ized
co
s
t.
C
o
m
p
ar
ed
to
s
y
m
b
o
lic
an
d
g
r
ap
h
-
b
ased
s
lic
in
g
ap
p
r
o
ac
h
es,
th
e
p
r
o
p
o
s
ed
f
r
am
ewo
r
k
e
m
p
h
asizes
a
lig
h
t
weig
h
t,
DFT
-
d
r
iv
en
s
tatic
-
b
ac
k
war
d
s
licin
g
th
at
p
r
io
r
itizes
co
m
p
u
tatio
n
al
ef
f
icien
cy
an
d
p
r
ec
is
io
n
f
o
r
co
r
e
J
av
a
co
n
s
tr
u
cts.
W
h
ile
to
o
ls
lik
e
J
av
asli
ce
r
an
d
Sli
c
er
4
J
o
f
f
er
g
e
n
er
al
-
p
u
r
p
o
s
e
s
li
cin
g
,
th
ey
o
f
ten
in
cu
r
h
ig
h
e
r
o
v
er
h
ea
d
o
r
f
ail
t
o
ca
p
tu
r
e
n
o
n
-
tr
iv
ial
d
ep
en
d
en
ci
es in
leg
ac
y
J
av
a
p
r
o
g
r
a
m
s
.
T
h
e
p
r
o
p
o
s
ed
s
tatic
-
b
ac
k
war
d
s
licin
g
ap
p
r
o
ac
h
co
n
tr
ib
u
tes
to
war
d
s
en
h
a
n
cin
g
p
r
o
g
r
am
a
b
s
tr
ac
tio
n
an
d
f
o
r
m
al
s
p
ec
i
f
icatio
n
e
x
tr
ac
tio
n
b
y
ad
d
r
ess
in
g
th
e
lim
itatio
n
s
o
f
tr
a
d
itio
n
al
s
licin
g
m
eth
o
d
s
.
Un
lik
e
d
y
n
am
ic,
h
y
b
r
id
,
an
d
ML
-
b
a
s
ed
s
licin
g
,
wh
ich
s
u
f
f
e
r
f
r
o
m
h
ig
h
co
m
p
u
tatio
n
al
co
s
ts
a
n
d
c
o
m
p
lex
ity
,
th
is
m
eth
o
d
r
elies
o
n
s
tatic
J
av
a
p
r
o
g
r
am
an
aly
s
is
,
m
ak
in
g
it
c
o
s
t
-
ef
f
ec
tiv
e,
s
ca
lab
le,
an
d
ef
f
ici
en
t.
B
y
in
teg
r
atin
g
a
DFT,
it
s
y
s
tem
atica
lly
o
r
g
a
n
izes
v
ar
iab
le
in
ter
ac
tio
n
s
,
el
im
in
ates
f
alse
d
ep
en
d
en
cies,
r
em
o
v
e
s
r
ed
u
n
d
a
n
t
co
d
e,
a
n
d
im
p
r
o
v
es
s
licin
g
ac
cu
r
ac
y
.
T
h
e
co
m
b
in
atio
n
o
f
b
a
ck
war
d
s
licin
g
f
o
r
r
elev
an
ce
a
n
d
s
tatic
s
licin
g
f
o
r
r
ef
in
em
en
t
en
s
u
r
es
h
ig
h
p
r
ec
is
io
n
in
ex
tr
ac
tin
g
f
o
r
m
al
s
p
ec
if
icatio
n
s
.
Ad
d
itio
n
ally
,
its
r
u
n
tim
e
-
in
d
ep
e
n
d
en
t
ex
ec
u
tio
n
m
ak
es
it
id
ea
l
f
o
r
lar
g
e
-
s
ca
le
J
av
a
p
r
o
g
r
am
s
,
s
o
f
t
war
e
r
e
-
en
g
in
ee
r
i
n
g
,
an
d
f
o
r
m
al
v
er
if
icatio
n
.
Her
e,
th
e
s
licin
g
f
r
am
ewo
r
k
s
er
v
es
a
s
a
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
th
at
g
e
n
er
ates
p
r
ec
is
e
an
d
m
in
im
al
c
o
d
e
r
e
p
r
esen
tatio
n
s
,
wh
er
ea
s
th
e
p
r
o
p
o
s
ed
s
tu
d
y
a
ls
o
en
v
is
io
n
s
an
e
x
ten
s
io
n
wh
er
e
AI
/
L
L
M
co
m
p
o
n
en
ts
tr
a
n
s
late
th
ese
f
o
r
m
a
l
r
ep
r
esen
tatio
n
s
in
to
s
tr
u
ctu
r
ed
h
u
m
an
-
r
ea
d
ab
le
r
e
q
u
ir
em
e
n
ts
,
m
ak
in
g
th
e
s
y
s
tem
u
s
ef
u
l
f
o
r
m
o
d
er
n
s
o
f
twar
e
en
g
in
ee
r
in
g
task
s
.
T
h
er
e
f
o
r
e,
th
e
p
r
o
p
o
s
ed
s
licin
g
f
r
am
ewo
r
k
ca
n
f
u
r
t
h
er
in
teg
r
ate
with
L
L
Ms
to
tr
an
s
late
f
o
r
m
al
o
b
ject
-
Z
s
p
ec
if
icatio
n
s
in
to
s
tr
u
ctu
r
e
d
n
at
u
r
al
-
lan
g
u
ag
e
r
e
q
u
ir
em
e
n
ts
.
Her
e
,
th
e
alig
n
m
en
t
b
etwe
en
s
tatic
s
licin
g
an
d
AI
-
b
ased
s
p
ec
if
icatio
n
tr
a
n
s
latio
n
b
r
i
d
g
es
f
o
r
m
al
p
r
o
g
r
a
m
an
al
y
s
is
with
in
tellig
en
t
r
eq
u
ir
em
e
n
t g
en
er
ati
o
n
.
2.
M
E
T
H
O
D
T
h
e
wo
r
k
p
r
o
p
o
s
es
a
s
im
p
lifie
d
an
d
co
m
p
u
tatio
n
ally
ef
f
ici
en
t
s
tatic
-
b
ac
k
war
d
s
licin
g
ap
p
r
o
ac
h
th
at
is
an
aly
tically
tailo
r
ed
with
a
s
er
ies
o
f
ef
f
ec
tiv
e
co
m
p
u
tin
g
s
tep
s
to
ex
t
r
ac
t
p
r
ec
is
e
f
o
r
m
al
s
o
f
twar
e
s
p
ec
if
icatio
n
s
f
r
o
m
J
av
a
p
r
o
g
r
am
s
.
T
h
e
p
r
o
p
o
s
ed
co
m
p
u
tatio
n
al
f
r
am
ewo
r
k
,
r
ea
lized
as
a
to
o
l
,
in
v
o
lv
es
a
s
et
o
f
co
r
e
co
m
p
u
tin
g
p
r
o
ce
s
s
es
v
iz.
r
estru
ctu
r
in
g
th
e
in
p
u
t
p
r
o
g
r
am
with
a
p
r
e
-
p
r
o
ce
s
s
in
g
s
tag
e,
ab
s
tr
ac
tio
n
o
f
co
n
tr
o
l
f
l
o
w
in
f
o
r
m
atio
n
,
ab
s
tr
ac
tio
n
o
f
DFT,
ab
s
tr
ac
tio
n
o
f
f
u
n
ctio
n
al
d
ep
en
d
en
cies
f
r
o
m
DFT,
o
b
tain
i
n
g
m
in
im
al
co
v
er
o
f
th
e
f
u
n
ctio
n
al
d
ep
en
d
en
cies
,
an
d
ex
tr
ac
tio
n
o
f
th
e
b
ac
k
war
d
s
lice
f
r
o
m
th
e
m
in
im
al
co
v
er
attr
ib
u
tes.
T
h
ese
s
tep
s
ar
e
in
te
n
d
ed
to
o
p
tim
ize
th
e
p
er
f
o
r
m
a
n
ce
o
f
s
tatic
-
b
ac
k
war
d
s
licin
g
f
o
r
d
er
iv
i
n
g
p
r
ec
is
e
f
o
r
m
al
s
o
f
twar
e
d
esig
n
s
p
ec
if
icatio
n
s
with
r
ed
u
ce
d
co
s
t
an
d
ef
f
o
r
t.
T
h
e
f
o
llo
win
g
Fig
u
r
e
1
s
h
o
ws
th
e
b
lo
ck
-
b
ased
ar
ch
itectu
r
e
o
f
th
e
p
r
o
p
o
s
ed
s
licin
g
ap
p
r
o
ac
h
.
Fig
u
r
e
1
.
C
o
r
e
c
o
m
p
u
tin
g
s
tep
s
in
v
o
lv
ed
in
p
r
o
p
o
s
ed
s
tatic
-
b
ac
k
war
d
s
licin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
9
6
9
-
4
9
7
9
4972
2
.
1
.
P
re
-
pro
ce
s
s
ing
s
t
a
g
e
f
o
r
J
a
v
a
pro
g
ra
m
re
s
t
ruct
urin
g
T
h
e
p
r
o
p
o
s
ed
co
m
p
u
tatio
n
a
l
f
r
am
ewo
r
k
in
teg
r
ates
a
p
r
e
-
p
r
o
ce
s
s
in
g
s
tag
e
in
J
av
a
p
r
o
g
r
am
r
estru
ctu
r
in
g
.
T
h
e
p
r
im
e
m
o
ti
v
e
o
f
th
is
co
m
p
u
tin
g
s
tep
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to
en
s
u
r
e
th
at
t
h
e
in
p
u
t
p
r
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g
r
am
is
in
s
tr
u
ctu
r
ed
an
d
well
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d
ef
in
ed
f
o
r
m
at
to
p
o
s
itiv
ely
in
f
lu
en
ce
th
e
p
er
f
o
r
m
an
ce
o
f
p
r
o
g
r
am
s
licin
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as
with
o
u
t
p
r
o
p
er
re
-
s
tr
u
ctu
r
in
g
t
h
e
p
r
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g
r
am
s
licin
g
b
ec
o
m
e
er
r
o
r
-
p
r
o
n
e,
in
ef
f
icien
t
an
d
co
m
p
u
tatio
n
ally
m
o
r
e
ex
p
e
n
s
iv
e.
T
h
is
s
tag
e
n
o
t
o
n
ly
h
el
p
s
elim
in
ate
th
e
ir
r
elev
an
t
an
d
u
n
s
tr
u
ctu
r
e
d
co
d
e
b
u
t
also
m
ak
es
th
e
J
av
a
p
r
o
g
r
a
m
s
u
itab
le
to
im
p
r
o
v
e
th
e
co
n
tr
o
l
f
lo
w
r
ep
r
esen
tatio
n
an
d
d
ata
f
lo
w
an
aly
s
is
.
L
et
b
e
th
e
in
p
u
t
J
av
a
p
r
o
g
r
am
wh
ich
is
r
ep
r
esen
ted
as
a
s
eq
u
e
n
ce
o
f
li
n
es
u
s
in
g
(
1
)
,
an
d
tr
an
s
f
o
r
m
atio
n
p
r
o
ce
s
s
is
also
d
ef
in
ed
as
a
f
u
n
ctio
n
u
s
in
g
(
2
)
.
=
{
}
=
1
(
1
)
F
:
P
jav
a
→
P′
jav
a
(
2
)
W
h
er
e
r
ep
r
esen
ts
th
e
i
-
th
li
n
e
in
th
e
s
o
u
r
ce
co
d
e
a
n
d
′
r
ef
er
s
to
th
e
r
estru
ctu
r
ed
J
av
a
p
r
o
g
r
am
.
T
h
e
p
r
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r
am
r
estru
ctu
r
in
g
ap
p
r
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ac
h
in
th
e
p
r
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p
o
s
ed
wo
r
k
in
itially
p
er
f
o
r
m
s
th
e
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p
en
d
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g
o
f
u
s
er
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class
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an
d
in
ter
f
ac
es
to
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in
p
u
t
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av
a
p
r
o
g
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am
P
jav
a
∪
S
(
P
U
,
C
U
,
I
U
)
an
d
it
is
p
er
f
o
r
m
ed
with
th
e
f
u
n
ctio
n
o
f
A
(
P
jav
a
)
.
T
h
e
m
ath
em
atica
l e
x
p
r
ess
io
n
u
s
in
g
(
3
)
to
(
5
)
r
e
p
r
esen
ts
th
is
f
lo
w.
L
e
t
(
′
)
b
e
th
e
s
et
o
f
all
co
m
m
en
t
lin
es
in
′
.
Fu
r
th
er
,
th
e
co
m
p
u
tin
g
p
r
o
ce
s
s
P
′
′
jav
a
elim
in
ates
th
e
co
m
m
en
t
lin
es
wh
ile
o
n
l
y
c
o
n
s
id
er
in
g
th
e
e
x
ec
u
tab
le
s
tatem
en
ts
a
n
d
ig
n
o
r
i
n
g
th
e
c
o
m
m
en
t
lin
es
in
′
.
Her
e,
ε
(
P
′
jav
a
)
=
{
L
i
∈
P
′
jav
a
|
∀
L
i
∈
sL
C
,
mL
C
}
.
T
h
e
co
m
p
u
tin
g
is
f
u
r
th
er
p
er
f
o
r
m
ed
u
s
in
g
(
6
)
.
P′
ja
v
a
=
A
(
P
jav
a
)
(
3
)
P′
ja
v
a
=
P
jav
a
∪
S
(
P
U
,
C
U
,
I
U
)
(
4
)
P′
ja
v
a
=
P
jav
a
⨁
S
(
P
U
,
C
U
,
I
U
)
(
5
)
P
′
′
jav
a
=
P
′
jav
a
\
ε
(
P
′
jav
a
)
(
6
)
W
h
er
e
′
′
r
ef
er
s
to
th
e
tr
an
s
f
o
r
m
ed
J
av
a
p
r
o
g
r
am
wh
ich
is
o
b
ta
in
ed
wh
ile
elim
in
atin
g
th
e
co
m
m
en
t lin
es.
I
n
co
n
tin
u
atio
n
,
th
e
c
o
m
p
u
tin
g
p
r
o
ce
s
s
f
u
r
th
er
also
en
a
b
les
elim
in
atio
n
o
f
th
e
b
lan
k
lin
es
in
th
e
p
r
e
-
p
r
o
ce
s
s
in
g
s
tag
e
f
r
o
m
th
e
t
r
an
s
f
o
r
m
e
d
co
d
e
o
f
P
′
′
jav
a
co
n
s
id
er
in
g
as in
(
7
)
.
P
′
′
jav
a
=
P
′
′
jav
a
\
{
{
L
i
}
i
=
1
n
∈
P
′
′
jav
a
|
L
i
=
""
}
(
7
)
W
h
er
e
P
′
′
jav
a
r
ef
er
s
to
a
s
et
o
r
o
r
d
er
ed
lis
t
o
f
all
lin
es
f
r
o
m
th
e
J
a
v
a
p
r
o
g
r
am
af
ter
p
r
e
v
io
u
s
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
s
.
L
i
r
ep
r
esen
ts
a
lin
e
o
f
co
d
e
f
r
o
m
P
′
′
jav
a
in
d
ex
ed
by
f
r
o
m
1
t
o
.
T
h
e
co
n
d
itio
n
L
i
=
""
id
en
tifie
s
lin
es
th
at
ar
e
em
p
ty
o
r
b
lan
k
lin
es
,
wh
er
ea
s
\
r
ep
r
esen
ts
a
s
et
d
if
f
er
en
ce
o
p
er
ato
r
.
T
h
e
co
n
d
itio
n
L
i
=
""
also
im
p
lies
th
at
r
em
o
v
e
all
lin
es
L
i
th
at
ar
e
em
p
ty
s
tr
in
g
s
.
I
t a
ls
o
tr
an
s
f
o
r
m
s
m
u
ltip
le
d
ec
lar
atio
n
s
tatem
en
ts
in
to
a
s
in
g
l
e
d
ec
lar
atio
n
s
tatem
en
t u
s
in
g
a
f
u
n
ctio
n
o
f
tr
an
s
f
o
r
m
atio
n
ƒ
t
r
an
s
(
′
′
)
.
I
f
=
{
}
=
1
r
ep
r
esen
ts
s
et
o
f
in
d
iv
id
u
al
d
ec
lar
ati
o
n
s
in
′
′
.
T
h
en
t
h
e
f
u
n
ctio
n
ƒ
t
r
an
s
(
s
∈
P
′
′
jav
a
)
p
r
o
ce
s
s
=
{
}
=
1
an
d
m
er
g
e
m
u
ltip
le
d
ec
lar
atio
n
s
in
to
a
s
in
g
le
s
tatem
en
t
,
co
n
s
id
er
in
g
as in
(
8
)
.
=
Type
⊕
〈
{
}
=
1
〉
(8
)
Her
e
r
ef
er
s
to
th
e
co
n
s
o
lid
ated
s
tatem
en
t
,
i.e
.
th
e
c
o
m
p
u
ted
f
in
al
s
in
g
le
-
lin
e
d
ec
lar
atio
n
.
Her
e
th
e
Type
r
ef
er
s
to
t
h
e
d
ata
ty
p
es th
at
co
u
ld
b
e
eith
er
i
n
t,
f
l
o
at
an
d
ch
a
r
.
I
t c
o
n
s
id
er
s
th
e
d
ata
ty
p
e
s
h
a
r
ed
b
y
all
v
ar
iab
les
b
ein
g
d
ec
lar
ed
.
T
h
e
co
n
ca
ten
atio
n
o
p
e
r
atio
n
s
y
m
b
o
lically
j
o
in
s
item
s
to
g
eth
er
in
to
o
n
e
s
y
n
tactic
u
n
it.
Als
o
,
th
e
ter
m
{
}
=
1
is
a
tu
p
le
o
f
v
a
r
iab
le
id
en
tifie
r
s
wh
er
e
r
ep
r
esen
ts
th
e
to
tal
n
u
m
b
er
o
f
v
a
r
iab
les
b
ein
g
d
ec
lar
ed
.
Fo
r
m
u
ltip
le
d
ata
ty
p
es
,
th
e
tr
a
n
s
f
o
r
m
atio
n
is
ap
p
lied
in
d
e
p
e
n
d
en
tly
f
o
r
ea
c
h
ty
p
e
,
co
n
s
id
e
r
in
g
th
e
(
9
)
.
ƒ
t
r
an
s
(
s
)
=
⋃
(
Type
i
⊕
∑
v
i
,
j
ξ
i
j
−
1
)
T
y
p
e
i
(
9
)
Her
e
⋃
(
∗
)
en
s
u
r
es e
ac
h
ty
p
e’
s
v
ar
i
ab
les ar
e
clu
s
ter
ed
s
ep
ar
ately
an
d
ξ
i
is
th
e
n
u
m
b
er
o
f
v
ar
iab
le
s
o
f
Type
i
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
n
e
fficien
t c
o
mp
u
ta
tio
n
a
l fra
mewo
r
k
fo
r
a
b
s
tr
a
ctin
g
p
r
o
g
r
a
m
s
lices
…
(
A
p
a
r
n
a
K
u
d
lo
o
r
S
id
d
a
lin
g
a
ia
h
)
4973
T
h
e
ap
p
r
o
ac
h
f
u
r
th
er
also
tr
an
s
f
o
r
m
s
th
e
m
u
lti
-
lin
e
s
tatem
en
ts
in
to
a
s
in
g
le
s
tatem
en
t
lin
e
an
d
allo
t
lin
e
n
u
m
b
er
s
to
ex
ec
u
tab
le
s
ta
tem
en
ts
.
I
f
e
(
P
′
′
jav
a
)
is
a
s
et
o
f
ex
ec
u
tab
le
s
tatem
en
ts
in
a
p
r
o
g
r
am
P
′
′
jav
a
s
u
ch
as
e
(
P
′
′
jav
a
)
=
{
∈
P
′
′
jav
a
|
→
e
xe
c
s
t
at
em
en
t
}
.
T
h
en
it
ass
ig
n
s
a
u
n
iq
u
e
lin
e
n
u
m
b
er
to
th
e
ex
ec
u
ta
b
le
s
tatem
en
t u
s
in
g
(
1
0
)
.
′
=
(
.
(
)
→
)
,
wh
er
e
∀
∈
e
(
P
′
′
jav
a
(
1
0
)
W
h
er
e
r
ef
er
s
to
th
e
ex
ec
u
tab
le
s
tatem
en
ts
f
r
o
m
th
e
p
r
e
-
p
r
o
ce
s
s
ed
J
av
a
p
r
o
g
r
a
m
.
Als
o
.
(
)
en
s
u
r
es
th
at
a
lin
e
n
u
m
b
e
r
is
ass
ig
n
ed
to
th
e
-
th
ex
ec
u
tab
le
lin
e.
→
r
e
p
r
esen
ts
a
m
ap
p
in
g
f
u
n
ctio
n
t
h
at
p
air
s
a
lin
e
n
u
m
b
er
with
its
co
r
r
esp
o
n
d
in
g
lin
e.
Fin
ally
,
′
f
o
r
m
s
th
e
n
ew
r
ep
r
esen
tatio
n
o
f
th
e
lin
e
n
o
w
tag
g
ed
with
th
e
lin
e
n
u
m
b
e
r
.
Fu
r
th
er
,
th
e
co
m
p
u
tin
g
p
r
o
c
ess
id
en
tifie
s
an
d
r
em
o
v
es
th
e
u
n
u
s
ed
v
a
r
iab
les
an
d
m
ak
es
th
e
tr
an
s
f
o
r
m
ed
J
av
a
p
r
o
g
r
am
P
′
′
jav
a
m
o
r
e
s
u
itab
le
f
o
r
f
u
r
th
er
an
aly
s
is
.
T
h
e
p
r
o
g
r
am
r
estru
ctu
r
in
g
is
m
o
d
eled
h
er
e
with
an
o
p
tim
ized
f
lo
w
o
f
ex
ec
u
tio
n
,
wh
ich
is
an
ess
en
tial
s
tep
to
en
s
u
r
e
ac
c
u
r
ate,
e
f
f
i
cien
t
,
an
d
s
ca
lab
le
p
r
o
g
r
a
m
s
licin
g
.
I
t
h
as
to
b
e
n
o
ted
th
at
th
e
r
elate
d
u
s
er
-
d
e
f
i
n
ed
p
ac
k
a
g
es
ar
e
p
r
o
ce
s
s
ed
a
n
d
in
co
r
p
o
r
ated
i
n
to
th
e
cu
r
r
e
n
t p
r
o
g
r
am
if
th
e
J
av
a
p
r
o
g
r
am
co
n
tain
s
ex
ter
n
al
li
n
k
ed
class
es im
p
o
r
ted
f
r
o
m
o
t
h
er
p
ac
k
a
g
es.
2
.
2
.
Abs
t
ra
ct
io
n
o
f
co
ntr
o
l f
lo
w
info
rm
a
t
i
o
n f
ro
m
re
-
s
t
r
uct
ured
J
a
v
a
pro
g
r
a
m
T
h
e
p
r
o
p
o
s
ed
wo
r
k
also
co
n
s
id
er
s
ab
s
tr
ac
tio
n
o
f
co
n
tr
o
l
f
lo
w
in
f
o
r
m
atio
n
f
r
o
m
th
e
r
e
-
s
tr
u
ctu
r
ed
J
av
a
p
r
o
g
r
a
m
.
Af
ter
an
aly
zi
n
g
th
e
b
aselin
e
s
tu
d
ies,
it
h
as
b
ee
n
o
b
s
er
v
ed
t
h
at
co
n
t
r
o
l
f
l
o
w
ab
s
tr
ac
tio
n
p
lay
s
a
cr
u
cial
r
o
le
in
p
r
o
g
r
am
s
licin
g
.
T
h
er
e
b
y
,
in
th
e
p
r
o
p
o
s
ed
wo
r
k
th
e
c
o
n
tr
o
l f
l
o
w
in
f
o
r
m
atio
n
lo
g
ic
i
s
f
u
r
th
er
d
er
iv
ed
in
th
e
f
o
r
m
o
f
4
-
co
l
s
tr
u
ctu
r
ed
tab
u
lar
f
o
r
m
wh
ich
is
d
e
f
in
e
d
u
s
in
g
(
1
1
)
.
Her
e
co
lu
m
n
r
ep
r
esen
ts
th
e
in
itiatio
n
o
f
th
e
J
av
a
p
r
o
g
r
a
m
,
wh
er
ea
s
th
e
s
ec
o
n
d
co
lu
m
n
r
ep
r
esen
ts
th
e
o
cc
u
r
r
en
ce
o
f
th
e
f
ir
s
t
en
co
u
n
ter
e
d
c
o
n
tr
o
l
o
r
co
n
d
it
io
n
al
s
tatem
en
t.
T
h
ir
d
co
lu
m
n
1
r
ep
r
esen
ts
th
e
s
tatem
en
t
w
h
er
e
th
e
co
n
tr
o
l
ju
m
p
s
if
th
e
co
n
tr
o
l
s
tatem
en
t
is
tr
u
e
f
o
r
p
ar
ticu
lar
in
p
u
ts
an
d
th
e
f
o
u
r
t
h
co
lu
m
n
2
r
ep
r
esen
t
s
th
e
s
tatem
en
t
wh
er
e
th
e
f
alse statem
en
t g
ets ex
ec
u
ted
.
(
P
′
′
jav
a
)
=
{
〈
,
,
1
,
2
〉
|
∈
,
1
,
2
∈
P
′
′
jav
a
}
(
1
1
)
T
h
is
tab
u
lar
r
ep
r
esen
tatio
n
in
t
h
e
p
r
o
p
o
s
ed
wo
r
k
ca
p
tu
r
es
th
e
co
n
tr
o
l
f
l
o
w
tr
an
s
itio
n
s
in
th
e
f
o
r
m
o
f
with
in
P
′
′
jav
a
an
d
f
u
r
th
er
h
elp
s
f
o
r
m
u
latin
g
DFT
in
th
e
co
n
tr
o
l f
lo
w
o
r
d
er
.
2
.
3
.
Abs
t
ra
ct
io
n
o
f
da
t
a
f
lo
w
t
a
ble in c
o
ntr
o
l f
lo
w
o
rder
T
h
e
s
tu
d
y
r
ea
lizes
th
at
th
e
d
ata
v
ar
iab
les
in
th
e
p
r
o
g
r
am
is
b
ased
o
n
th
e
co
n
tr
o
l
f
lo
w
o
r
d
er
a
n
d
f
u
r
t
h
er
,
th
e
p
r
o
p
o
s
ed
wo
r
k
co
n
s
id
er
s
(
P
′
′
jav
a
)
o
f
P
′
′
jav
a
an
d
aim
s
to
f
o
r
m
u
late
th
e
DFT
in
th
e
o
r
d
er
o
f
co
n
tr
o
l
f
lo
w.
T
h
e
p
r
o
p
o
s
ed
wo
r
k
c
o
n
s
id
er
s
DFT
as
a
s
tr
u
ctu
r
ed
tab
u
lar
r
ep
r
esen
tatio
n
in
th
e
f
o
r
m
o
f
in
wh
ich
ea
ch
r
o
w
co
r
r
esp
o
n
d
s
to
a
p
r
o
g
r
am
s
tatem
en
t a
n
d
also
co
n
s
i
s
ts
o
f
th
r
ee
attr
ib
u
tes
u
s
in
g
(
1
2
)
.
(
)
=
{
〈
′
,
,
〉
|
∈
[
1
,
]
}
(
1
2
)
W
h
er
e
′
r
ef
er
s
to
th
e
-
th
p
r
o
g
r
am
s
tatem
en
t
with
lin
e
n
u
m
b
er
f
o
r
n
u
m
b
er
o
f
p
r
o
g
r
am
s
ta
tem
en
ts
.
Als
o
,
h
er
e
b
o
th
,
co
lu
m
n
s
r
ep
r
esen
t
s
et
o
f
v
ar
ia
b
les
d
ef
in
e
d
at
s
tate
m
en
t
n
u
m
b
er
o
f
lin
es
an
d
s
et
o
f
v
ar
iab
les
r
ef
er
r
ed
at
s
tatem
en
t n
u
m
b
er
o
f
lin
es
.
I
n
th
e
p
r
o
p
o
s
ed
s
licin
g
ap
p
r
o
ac
h
,
th
e
i
n
clu
s
io
n
o
f
DFT
o
f
f
er
s
ef
f
icien
t
tr
ac
k
in
g
o
f
v
ar
iab
le
d
ep
e
n
d
en
cies
,
wh
ich
also
p
r
eser
v
es
th
e
co
n
tr
o
l
f
lo
w
o
r
d
er
.
I
t
s
ig
n
if
ican
tly
o
p
tim
izes
a
n
d
en
h
an
ce
s
th
e
p
er
f
o
r
m
an
ce
o
f
f
u
r
th
er
task
s
s
u
ch
as
ab
s
tr
ac
tio
n
o
f
f
u
n
ctio
n
al
d
ep
en
d
e
n
cies
an
d
also
in
th
e
lo
n
g
er
r
u
n
in
f
l
u
en
ce
s
th
e
s
licin
g
ap
p
r
o
ac
h
as we
ll.
2
.
4
.
Abs
t
ra
ct
io
n
o
f
f
un
ct
io
n
a
l dependenc
ies f
ro
m
da
t
a
f
lo
w
t
a
ble
T
h
e
p
r
o
p
o
s
ed
wo
r
k
also
ass
u
m
es
th
at
f
u
n
ctio
n
al
d
ep
en
d
en
cy
ex
is
ts
wh
en
a
v
ar
iab
le
d
e
f
in
ed
at
a
ce
r
tain
s
tatem
en
t
d
ep
en
d
s
o
n
v
ar
ia
b
les
r
ef
er
r
e
d
to
in
t
h
e
p
r
ev
i
o
u
s
co
m
p
u
tin
g
s
tep
s
o
r
s
tatem
en
ts
.
T
h
e
f
u
n
ctio
n
ality
ca
n
b
e
ab
s
tr
ac
ted
b
y
f
in
d
in
g
th
e
f
u
n
ctio
n
al
d
ep
en
d
en
cies
e
x
is
tin
g
b
etwe
en
th
e
d
e
f
in
ed
a
n
d
r
ef
er
r
ed
v
ar
iab
les
.
I
n
th
e
p
r
o
p
o
s
ed
wo
r
k
,
th
e
f
u
n
ctio
n
al
d
e
p
en
d
en
c
y
in
a
p
r
o
g
r
a
m
P
′
′
jav
a
is
m
ath
em
atica
lly
r
ep
r
esen
ted
u
s
in
g
(
1
3
)
as a
r
el
atio
n
o
f
ƒ
wh
ich
is
ex
tr
ac
ted
f
r
o
m
th
e
(
)
.
ƒ
(
,
)
=
{
〈
′
,
′
,
〉
|
∈
⋂
,
>
}
(
1
3
)
Her
e
′
r
ef
er
s
to
th
e
d
e
f
in
in
g
p
r
o
g
r
a
m
s
tatem
en
t
wh
er
e
t
h
e
is
th
e
s
et
o
f
v
a
r
iab
les
d
ef
i
n
ed
.
′
r
ef
er
s
to
th
e
d
ep
e
n
d
en
t
p
r
o
g
r
am
s
tatem
en
t
lin
e
wh
er
e
th
e
was
p
r
e
v
io
u
s
ly
r
ef
er
r
ed
.
Als
o
r
ef
er
s
to
th
e
d
ep
e
n
d
en
t
co
m
m
o
n
v
ar
iab
les
estab
lis
h
in
g
th
e
f
u
n
ctio
n
al
d
ep
e
n
d
en
cy
.
T
h
e
c
o
n
d
itio
n
o
f
>
im
p
lies
th
at
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
9
6
9
-
4
9
7
9
4974
d
ep
en
d
e
n
cy
f
o
llo
ws
th
e
J
av
a
p
r
o
g
r
am
ex
ec
u
tio
n
o
r
d
e
r
wi
th
in
cr
ea
s
in
g
p
r
o
g
r
am
s
tatem
en
ts
.
Her
e
,
in
th
e
p
r
o
p
o
s
ed
wo
r
k
t
h
is
ab
s
tr
ac
tio
n
h
elp
s
id
en
tify
th
e
f
u
n
ctio
n
al
d
ep
en
d
e
n
cies a
cr
o
s
s
th
e
p
r
o
g
r
am
,
an
d
it is
cr
u
cial
f
o
r
s
licin
g
an
d
o
p
tim
izatio
n
.
I
n
co
n
tin
u
atio
n
,
th
e
n
ex
t
s
tag
e
f
u
r
th
er
ex
tr
ac
ts
th
e
m
in
im
al
co
v
er
attr
ib
u
tes
o
f
th
e
f
u
n
ctio
n
al
d
ep
en
d
en
cies.
2
.
5
.
F
ind
ing
m
ini
m
a
l c
o
v
er
o
f
t
he
f
un
ct
io
na
l dependenc
i
es
I
n
th
is
co
m
p
u
tin
g
s
tep
,
th
e
p
r
o
p
o
s
ed
wo
r
k
aim
s
to
m
in
im
ize
ƒ
(
,
)
s
u
ch
as
ƒ
→
ƒ
wh
ile
elim
in
atin
g
th
e
r
ed
u
n
d
an
t
d
ep
e
n
d
en
cies.
T
h
is
ap
p
r
o
ac
h
en
s
u
r
es
th
at
o
n
ly
a
m
in
im
al
s
et
o
f
f
u
n
ctio
n
al
attr
ib
u
tes
s
h
o
u
ld
b
e
ex
tr
ac
ted
f
r
o
m
ƒ
(
,
)
wh
ich
a
r
e
e
s
s
en
tial
f
o
r
p
r
o
g
r
am
s
licin
g
.
T
h
e
s
tu
d
y
ass
u
m
es
th
at
if
〈
′
,
′
,
〉
i
s
co
n
s
id
er
ed
a
r
e
d
u
n
d
an
t
f
u
n
ctio
n
al
d
e
p
en
d
e
n
cy
,
th
at
m
ea
n
s
t
h
at
ap
p
ea
r
s
in
m
u
ltip
le
f
u
n
cti
o
n
al
d
e
p
en
d
e
n
cies
with
d
if
f
er
en
t
p
r
o
g
r
am
s
tatem
en
t
n
u
m
b
er
s
.
Ho
wev
er
,
f
o
r
p
r
o
g
r
am
s
licin
g
,
o
n
ly
a
f
ew
s
ig
n
if
ican
t
d
ep
en
d
en
cies
ar
e
r
eq
u
ir
ed
to
ex
tr
ac
t
m
in
im
al
co
v
e
r
attr
ib
u
tes.
T
h
is
ap
p
r
o
ac
h
also
h
elp
s
r
ed
u
ce
t
h
e
c
o
m
p
u
t
atio
n
al
co
m
p
lex
ity
an
d
co
s
t
in
th
e
p
r
o
p
o
s
ed
s
tatic
-
b
ac
k
war
d
s
licin
g
ap
p
r
o
ac
h
.
I
t
also
im
p
r
o
v
es
th
e
clar
ity
an
d
m
ain
tain
ab
ilit
y
o
f
lar
g
er
J
av
a
p
r
o
g
r
a
m
s
.
2
.
6
.
E
x
t
r
a
ct
ing
t
he
ba
c
k
wa
r
d sl
ice
f
ro
m
m
ini
m
a
l c
o
v
er
a
t
t
ribute
s
T
h
e
p
r
o
p
o
s
ed
wo
r
k
cu
s
to
m
iz
es
an
im
p
r
o
v
e
d
s
tatic
-
b
ac
k
war
d
s
licin
g
ap
p
r
o
ac
h
b
ased
o
n
W
eiser
’
s
alg
o
r
ith
m
.
Similar
ly
,
th
e
s
tu
d
y
co
n
s
id
er
s
p
r
o
g
r
am
s
licin
g
a
s
co
m
p
u
tin
g
a
s
u
b
s
et
o
f
p
r
o
g
r
am
s
tatem
en
ts
th
at
co
n
tr
ib
u
tes
to
war
d
s
th
e
v
alu
e
o
f
a
v
ar
ia
b
le
at
s
p
ec
if
ic
p
r
o
g
r
am
p
o
in
ts
.
T
h
e
p
r
o
p
o
s
ed
s
licin
g
,
ca
lled
b
ac
k
war
d
s
licin
g
,
s
ea
r
ch
es
an
d
ex
tr
ac
ts
o
n
ly
th
o
s
e
p
r
o
g
r
a
m
s
tatem
en
t
s
wh
ich
ar
e
co
n
tr
i
b
u
tin
g
to
t
h
e
ca
lcu
latio
n
o
f
t
h
e
s
licin
g
v
ar
iab
le
,
an
d
it c
an
b
e
r
ep
r
esen
ted
at
(
1
4
)
.
=
{
}
∪
{
|
〈
′
,
′
,
〉
∈
ƒ
,
′
∈
}
(
1
4
)
T
h
e
ab
o
v
e
p
r
o
ce
s
s
co
m
p
u
tes
th
e
last
o
cc
u
r
r
en
ce
o
f
o
f
th
e
s
licin
g
v
ar
ia
b
le
an
d
f
u
r
th
er
co
m
p
u
tes
th
e
s
tatem
en
ts
th
at
d
ef
in
e
in
th
e
p
r
ev
io
u
s
d
ep
en
d
en
cies.
I
n
(
1
4
)
r
ep
r
esen
ts
th
e
s
et
o
f
all
lin
e
s
in
clu
d
ed
i
n
th
e
p
r
o
g
r
a
m
s
lice.
r
ef
e
r
s
to
th
e
s
licin
g
cr
iter
io
n
lin
e
an
d
ƒ
h
elp
s
d
er
iv
in
g
th
e
m
in
im
al
s
et
o
f
d
ep
en
d
en
cies
r
elev
an
t to
.
Fu
r
th
er
,
t
h
e
alg
o
r
ith
m
also
en
ab
les o
p
tim
ized
tr
a
v
er
s
al
co
n
s
id
er
in
g
th
e
m
ath
em
atica
l (
1
5
)
.
=
∪
{
|
∃
〈
′
,
′
,
〉
∈
ƒ
,
′
∈
}
(
1
5
)
Her
e
r
ep
r
esen
ts
th
e
cu
r
r
en
t
s
lice
i.e
.
th
e
s
et
o
f
lin
es
in
f
lu
e
n
cin
g
th
e
v
alu
e
o
f
th
e
tar
g
et
a
ttrib
u
te
,
th
e
m
in
im
al
s
et
o
f
r
elev
an
t
d
ata
d
ep
en
d
en
cies
also
e
x
p
lo
r
e
d
v
ia
ƒ
.
Her
e
∃
im
p
lies
ex
is
ten
ce
,
an
d
f
u
r
th
er
th
e
p
r
o
ce
s
s
k
ee
p
s
ex
p
a
n
d
in
g
th
e
s
lice
b
y
in
clu
d
in
g
an
y
th
at
d
ef
in
es
th
e
s
licin
g
v
ar
iab
le
.
I
t
co
n
tin
u
es
ad
d
in
g
th
e
co
n
tr
ib
u
tin
g
s
tatem
en
ts
iter
ativ
ely
.
Fin
ally
,
th
ese
lin
e
n
u
m
b
er
s
ar
e
e
x
tr
ac
ted
f
r
o
m
th
e
DFT
an
d
th
e
co
r
r
esp
o
n
d
in
g
s
tatem
en
ts
f
r
o
m
th
e
r
estru
ctu
r
ed
in
p
u
t
p
r
o
g
r
am
ar
e
s
liced
,
ig
n
o
r
i
n
g
th
e
ir
r
elev
an
t
s
tatem
en
ts
.
Fu
r
th
er
,
th
ese
s
lices
ar
e
u
s
ed
to
ab
s
tr
ac
t
th
e
s
o
f
twar
e
f
o
r
m
al
s
p
ec
if
icatio
n
o
f
th
e
g
iv
e
n
p
r
o
g
r
a
m
.
T
h
e
s
am
e
p
r
o
ce
d
u
r
e
is
f
o
llo
wed
f
o
r
all
m
in
im
al
co
v
er
attr
ib
u
tes
,
o
b
ta
in
in
g
m
u
ltip
le
s
lices
f
o
r
a
n
y
g
iv
en
p
r
o
g
r
am
.
Her
e
th
e
o
u
tp
u
t
(
)
∈
r
ep
r
esen
ts
th
e
s
et
o
f
b
ac
k
war
d
s
lices
f
o
r
th
e
s
licin
g
v
ar
iab
le
.
Fu
r
th
e
r
,
th
e
ex
tr
ac
ted
b
ac
k
war
d
p
r
o
g
r
a
m
s
lices
(
)
∈
ar
e
r
ep
r
esen
ted
u
s
in
g
o
b
ject
-
Z
n
o
tatio
n
,
en
s
u
r
in
g
m
ath
em
atica
l
p
r
ec
is
io
n
an
d
s
t
r
u
ctu
r
ed
r
ep
r
esen
tatio
n
.
I
t
h
as
to
b
e
n
o
ted
th
at
th
e
p
r
o
p
o
s
ed
s
licin
g
f
r
am
ewo
r
k
o
p
er
ates
with
lin
ea
r
c
o
m
p
lex
it
y
r
elativ
e
to
t
h
e
n
u
m
b
e
r
o
f
e
x
e
cu
tab
le
s
tatem
en
ts
in
t
h
e
a
n
aly
ze
d
J
av
a
p
r
o
g
r
am
s
.
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h
ile
n
o
p
s
eu
d
o
co
d
e
is
in
clu
d
ed
,
th
e
co
m
p
lete
s
licin
g
wo
r
k
f
lo
w
is
s
y
s
tem
atica
lly
r
ep
r
es
en
ted
th
r
o
u
g
h
f
o
r
m
al
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er
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s
an
d
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r
r
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d
i
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g
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ch
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atic
f
ig
u
r
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n
s
u
r
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n
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eth
o
d
o
lo
g
ical
clar
ity
an
d
r
ep
r
o
d
u
cib
ilit
y
.
2
.
7
.
P
o
t
ent
ia
l
a
r
t
if
icia
l int
ellig
ence
/
la
rg
e
la
ng
ua
g
e
m
o
de
l
inte
g
ra
t
io
n
W
h
ile
th
e
cu
r
r
en
t
s
tu
d
y
f
o
cu
s
es
o
n
s
tatic
-
b
ac
k
war
d
s
licin
g
an
d
o
b
ject
-
Z
s
p
ec
if
icatio
n
e
x
t
r
ac
tio
n
,
th
e
r
esu
ltin
g
f
o
r
m
al
r
e
p
r
esen
tatio
n
s
ca
n
s
er
v
e
as
in
p
u
t
to
AI
-
d
r
iv
en
to
o
ls
f
o
r
m
o
d
er
n
s
o
f
twar
e
en
g
in
ee
r
in
g
task
s
.
I
n
p
ar
ticu
lar
,
ex
tr
ac
ted
o
b
ject
-
Z
s
p
ec
if
icatio
n
s
ca
n
b
e
n
o
r
m
a
lized
in
to
s
im
p
ler
to
k
en
s
a
n
d
p
r
o
ce
s
s
ed
b
y
L
L
Ms
to
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er
ate
s
tr
u
ctu
r
ed
,
h
u
m
an
-
r
ea
d
ab
le
r
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q
u
ir
em
e
n
ts
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e.
g
.
ac
to
r
s
,
ac
tio
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s
,
p
r
e
-
co
n
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itio
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p
o
s
t
-
co
n
d
itio
n
s
,
a
n
d
in
v
ar
ian
ts
)
in
J
SON
f
o
r
m
at,
en
ab
lin
g
au
t
o
m
ated
d
o
c
u
m
en
tatio
n
,
r
eq
u
ir
em
e
n
t
e
x
tr
ac
tio
n
,
a
n
d
s
o
f
twar
e
m
o
d
er
n
izatio
n
.
Po
s
t
-
p
r
o
ce
s
s
in
g
with
r
u
le
-
b
ased
ch
ec
k
s
ca
n
also
en
s
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r
e
co
r
r
ec
tn
ess
,
an
d
o
p
tio
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al
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in
e
-
t
u
n
in
g
o
n
p
air
e
d
o
b
ject
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Z
a
n
d
r
eq
u
ir
em
en
t
d
atasets
ca
n
f
u
r
th
er
im
p
r
o
v
e
ac
cu
r
ac
y
.
T
h
is
in
t
eg
r
atio
n
r
em
ain
s
a
p
r
o
s
p
ec
tiv
e
ex
ten
s
io
n
o
f
th
e
f
r
am
ewo
r
k
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d
d
o
es n
o
t a
f
f
ec
t th
e
cu
r
r
en
t e
x
p
er
im
e
n
tal
ev
alu
atio
n
.
L
L
Ms w
o
u
ld
au
to
m
atica
lly
tr
an
s
late
f
o
r
m
al
p
r
o
g
r
a
m
s
lices
in
to
h
u
m
an
-
r
e
ad
ab
le
r
eq
u
ir
e
m
en
ts
.
T
h
is
p
r
o
s
p
ec
tiv
e
in
teg
r
atio
n
r
em
ain
s
f
u
tu
r
e
wo
r
k
an
d
is
n
o
t
ex
p
er
im
e
n
tally
v
alid
ated
h
er
e.
A
lg
o
r
ith
m
1
s
u
m
m
a
r
izes
th
e
k
ey
s
tep
s
o
f
th
e
p
r
o
p
o
s
ed
s
tatic
-
b
ac
k
war
d
s
licin
g
f
r
am
ewo
r
k
.
I
t
also
p
r
o
v
i
d
es
a
c
o
m
p
ac
t
p
r
o
ce
d
u
r
al
v
ie
w
o
f
th
e
p
r
o
p
o
s
ed
s
tatic
-
b
ac
k
war
d
s
licin
g
f
r
am
e
wo
r
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
n
e
fficien
t c
o
mp
u
ta
tio
n
a
l fra
mewo
r
k
fo
r
a
b
s
tr
a
ctin
g
p
r
o
g
r
a
m
s
lices
…
(
A
p
a
r
n
a
K
u
d
lo
o
r
S
id
d
a
lin
g
a
ia
h
)
4975
Alg
o
r
ith
m
1
.
DFT
-
d
r
iv
en
s
tatic
-
b
ac
k
war
d
s
licin
g
Input: Java source code, slicing criterion
〈
,
〉
Output: Minimal backward slice,
ob
ject
-
Z
specification
Begin
1. Pre
-
process and restructure core Java program
to obtain structured program
P
′
′
j
a
v
a
2. Abstract
control flow information
(
P
′
′
j
a
v
a
)
3. Construct
data flow table
(
)
in control
-
flow order
4. Compute functional dependencies
ƒ
(
,
)
from
5. Compute the minimal cover
ƒ
by eliminate false and redundant dependencies
6. Apply backward slicing w.r.t
〈
,
〉
7. Generate minimal slice
(
)
and generate the corresponding
ob
ject
-
Z
specification
End
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
ex
p
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im
en
tal
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th
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o
r
m
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lated
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o
l
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er
f
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ed
f
o
r
v
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io
u
s
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av
a
p
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g
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a
m
s
s
u
ch
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to
m
ated
teller
m
ac
h
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e
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AT
M
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,
s
tu
d
en
t g
r
ad
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g
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an
d
Kar
n
atak
a
co
m
m
o
n
en
t
r
an
ce
test
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KC
E
T
)
,
co
n
s
id
er
in
g
th
e
in
teg
r
ate
d
d
ev
elo
p
m
en
t
e
n
v
ir
o
n
m
en
t
(
I
DE
)
o
f
Py
C
h
ar
m
.
Her
e
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
s
ar
e
s
cr
ip
te
d
in
a
s
in
g
le
f
ile
im
p
lem
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tatio
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n
s
id
er
in
g
Py
th
o
n
.
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h
e
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al
u
atio
n
f
r
am
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ter
n
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l
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em
o
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o
f
1
2
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d
a
6
4
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it
W
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e
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atio
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y
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s
u
p
p
o
r
ted
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th
e
x
6
4
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ased
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r
o
ce
s
s
o
r
.
Fo
r
ex
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e
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im
en
tal
ev
alu
atio
n
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e
s
tu
d
y
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o
n
s
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er
s
a
J
av
a
p
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g
r
am
f
o
r
f
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n
d
in
g
q
u
a
d
r
atic
r
o
o
ts
wh
ich
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
f
r
am
ew
o
r
k
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alu
ated
o
n
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e
J
av
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a
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s
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ll
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ties
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ed
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E
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ted
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n
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e
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tatic
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ata
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n
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u
r
e
2
.
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n
p
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t
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ad
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ati
c
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r
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ad
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atic
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ts
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illu
s
tr
ated
in
Fig
u
r
e
3
.
Fig
u
r
e
3
(
a)
clea
r
l
y
s
h
o
ws
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e
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n
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o
l f
lo
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(
C
FT)
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e
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e
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r
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in
Fig
u
r
e
3
(
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)
f
o
r
th
e
s
am
e
J
av
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p
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g
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m
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
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15
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5
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20
26
:
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9
6
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7
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4976
(
a)
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Fig
u
r
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3
.
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atic
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av
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h
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d
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les
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o
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o
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m
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h
e
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ject
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s
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e
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r
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er
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o
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er
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h
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e
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o
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r
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ize
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e
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h
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ich
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n
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f
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w
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le
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g
e
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ap
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s
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ch
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M
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ca
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KC
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T
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lib
r
ar
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em
p
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s
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e
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ig
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al
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es 2
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ile
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ately
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t
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ee
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R
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OV)
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h
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tr
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ted
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n
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o
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ig
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ican
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e
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e
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tr
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ig
n
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Fig
u
r
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4
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u
r
e
4
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ates
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ates
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1
4
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27
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r
r
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t
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r
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o
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th
e
Fig
u
r
e
5
.
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I
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A
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4977
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4
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,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
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t J Ar
tif
I
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tell
,
Vo
l.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
9
6
9
-
4
9
7
9
4978
au
to
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[
1
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