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115
91
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2
01
7
I
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s
t
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A
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.
1
.
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a
p
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e s
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o be
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eas
e t
he c
om
pl
ex
i
t
y
of
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he m
odel
[
1
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2]
.
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r
s
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[
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ar
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gat
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n
s
e
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p
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per
s
s
uc
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as
[1
-
13]
,
w
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h
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c
ont
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m
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at
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and m
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n t
hi
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aper
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w
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ont
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nue
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h
on m
ul
t
i
s
et
c
ont
r
ol
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e
d gr
am
m
ar
s
(
s
ee [
4]
)
;
w
e
i
n
v
es
t
i
gat
e
t
he
c
l
os
ur
e
pr
o
per
t
i
es
of
t
he f
am
i
l
y
of
l
an
guag
es
ge
ner
at
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y
m
ul
t
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s
et
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ont
r
ol
l
e
d
gr
am
m
a
r
s
.
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he
s
t
ud
y
of
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l
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t
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s
on
e
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or
m
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l
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t
heor
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i
t
pr
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des
a
m
eani
ngf
ul
m
er
i
t
i
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bot
h t
h
eor
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and
pr
ac
t
i
c
e of
gr
am
m
ar
s
.
T
hi
s
paper
i
s
s
t
r
uc
t
ur
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as
f
ol
l
o
w
s
.
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i
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s
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i
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al
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c
h
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gr
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m
ar
s
w
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h r
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gu
l
at
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d r
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w
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n
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t
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or
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c
oper
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l
a
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ages
t
h
at
w
i
l
l
be
us
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t
hr
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out
t
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s
t
ud
y
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hen,
w
e
r
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l
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t
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def
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i
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m
ul
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s
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c
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r
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d gr
am
m
ar
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def
i
ned i
n [
4
]
t
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h
er
w
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t
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r
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l
t
s
on t
h
ei
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ge
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r
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c
h t
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s
on t
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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IS
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N
:
2
502
-
4
752
Mul
t
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s
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C
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S
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)
37
2.
P
r
el
i
m
i
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ar
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es
I
n t
hi
s
s
ec
t
i
on,
w
e pr
es
ent
s
om
e bas
i
c
not
at
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on
s
,
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er
m
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d c
onc
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s
c
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o t
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or
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t
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and r
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e
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be us
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F
or
det
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l
s
,
t
h
e r
e
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s
r
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r
ed t
o [
1
,
2,
14
-
1
6]
.
T
hr
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out
t
he
pap
er
,
w
e
us
e t
he
f
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y
t
he c
ar
di
nal
i
t
y
of
a s
et
i
n w
hi
c
h i
s
t
he n
um
ber
of
el
e
m
ent
s
i
n t
h
e
s
et
as
w
el
l
as
n
ot
at
i
on
2
i
s
us
ed
t
o
de
pi
c
t
t
he
po
w
er
s
et
of
a
s
et
.
S
y
m
bol
∅
den
ot
es
t
h
e
em
pt
y
s
et
.
T
he
s
et
s
of
i
n
t
e
ger
,
na
t
ur
al
,
r
ea
l
an
d
r
at
i
on
al
n
um
ber
s
ar
e
denot
ed
b
y
ℤ
,
ℕ
,
ℝ
and
ℚ
,
r
es
pec
t
i
v
el
y
.
A
n
al
p
hab
et
i
s
a f
i
n
i
t
e
an
d
non
em
pt
y
s
et
of
s
y
m
bo
l
s
or
l
e
t
t
er
s
,
w
h
i
c
h
i
s
den
ot
e
d
b
y
Σ
and
a
s
t
r
i
ng
(
s
om
et
i
m
es
r
e
f
er
r
ed
as
w
or
d)
o
v
er
t
he
a
l
phab
et
Σ
i
s
a
f
i
ni
t
e
s
e
que
nc
e
of
s
y
m
bo
l
s
(
c
onc
at
enat
i
o
n
of
s
y
m
bol
s
)
f
r
o
m
Σ
.
T
he s
t
r
i
ng
w
i
t
hou
t
s
y
m
bol
s
i
s
c
al
l
ed
n
ul
l
or
em
pt
y
s
t
r
i
ng
an
d
deno
t
ed
b
y
.
T
he s
et
of
al
l
s
t
r
i
ng
s
(
i
nc
l
ud
i
ng
)
o
v
er
t
h
e a
l
ph
ab
et
,
Σ
i
s
de
not
ed
b
y
Σ
∗
a
nd
Σ
+
=
Σ
∗
−
{
}
.
A
s
t
r
i
ng
i
s
a s
ubs
t
r
i
n
g of
a s
t
r
i
ng
i
f
and onl
y
i
f
t
he
r
e ex
i
s
t
1
,
2
s
uc
h t
ha
t
=
1
2
w
her
e
1
,
2
,
,
∈
Σ
∗
.
S
t
r
in
g
i
s
a pr
ope
r
s
ubs
t
r
i
ng
of
if
≠
and
≠
.
T
he
l
en
gt
h of
s
t
r
i
ng
,
deno
t
ed b
y
|
|
,
i
s
t
he num
ber
of
s
y
m
bol
s
i
n t
he s
t
r
i
n
g.
O
b
v
i
ous
l
y
,
|
|
=
0
and
|
|
=
|
|
+
|
|
,
,
∈
Σ
∗
.
A
l
a
ng
uag
e
i
s
a s
ubs
et
of
Σ
∗
.
A
l
a
ngu
age
is
-
f
r
ee i
f
∉
.
F
or
a
s
et
,
a
m
ul
t
i
s
et
i
s
a
m
appi
n
g
:
→
ℕ
.
T
he
s
et
of
al
l
m
ul
t
i
s
et
s
ov
er
i
s
deno
t
ed
b
y
⊕
.
T
hen,
t
he s
e
t
i
s
a c
a
l
l
ed
t
he
b
as
i
c
s
et
of
⊕
.
F
or
a
m
ul
t
i
s
et
∈
⊕
an
d e
l
em
ent
∈
,
(
)
r
epr
es
ent
s
t
h
e n
um
ber
of
oc
c
ur
r
enc
es
of
in
.
A
C
hom
s
k
y
gr
am
m
ar
i
s
a
qua
dr
up
l
e
=
(
,
,
,
)
w
her
e
i
s
an al
p
ha
bet
of
nont
er
m
i
nal
s
,
i
s
an
al
p
ha
b
et
of
t
er
m
i
nal
s
and
∩
=
∅
,
∈
i
s
t
he
s
t
ar
t
s
y
m
bol
and
is
a
f
i
ni
t
e s
et
of
pr
oduc
t
i
ons
s
uc
h t
hat
⊆
(
∪
)
∗
(
∪
)
∗
×
(
∪
)
∗
.
W
e
s
i
m
pl
y
us
e
not
at
i
o
n
→
f
or
a pr
od
uc
t
i
o
n
(
,
)
∈
.
A
di
r
ec
t
der
i
v
at
i
o
n r
e
l
at
i
on
o
v
er
(
∪
)
∗
,
d
enot
ed
b
y
⇒
,
is
def
i
ned as
⇒
pr
ov
i
ded
i
f
an
d on
l
y
i
f
t
her
e i
s
a r
ul
e
→
∈
s
uc
h t
hat
=
1
2
and
=
1
2
f
or
s
o
m
e
1
,
2
∈
(
∪
)
∗
.
Si
nc
e
⇒
i
s
a r
el
at
i
on,
t
he
n i
t
s
th
,
≥
0
,
pow
er
i
s
de
not
e
d
b
y
⇒
,
i
t
s
t
r
a
ns
i
t
i
v
e c
l
os
ur
e
b
y
⇒
+
,
a
nd
i
t
s
r
ef
l
ex
i
v
e
and
t
r
ans
i
t
i
v
e
c
l
os
ur
e
b
y
⇒
∗
. A
s
tr
i
n
g
∈
(
∪
)
∗
i
s
a
s
e
nt
en
t
i
a
l
f
or
m
i
f
⇒
∗
.
If
∈
∗
,
t
hen
i
s
c
al
l
e
d
a
s
en
t
enc
e
or
a
t
er
m
i
na
l
s
t
r
i
ng an
d
⇒
∗
i
s
s
ai
d t
o b
e a s
uc
c
es
s
f
ul
der
i
v
at
i
o
n.
W
e al
s
o us
e t
he n
ot
at
i
o
ns
⇒
or
0
1
…
.
t
o
deno
t
e
t
h
e
d
er
i
v
at
i
on
t
hat
us
es
t
he
s
eq
ue
nc
e
of
r
ul
es
=
0
1
…
,
∈
,
1
≤
≤
.
T
he
l
an
gua
ge
ge
ner
at
ed
b
y
,
de
not
ed
b
y
(
)
,
i
s
d
ef
i
ned
as
(
)
=
{
∈
∗
|
⇒
∗
}
.
T
w
o
gr
am
m
a
r
s
1
an
d
2
ar
e c
al
l
e
d
t
o be
eq
ui
v
a
l
e
nt
i
f
a
nd o
nl
y
i
f
t
he
y
g
ener
a
t
e t
he s
am
e l
angu
age
,
i
.e
.,
(
1
)
=
(
2
)
.
T
her
e ar
e
f
i
v
e m
ai
n t
y
pes
of
gr
am
m
ar
s
de
pend
i
n
g on
t
h
ei
r
pr
od
uc
t
i
o
ns
f
or
m
s
→
:
a)
a r
egu
l
ar
i
f
∈
∗
∪
∗
and
∈
,
b)
a l
i
ne
ar
i
f
∈
∗
∪
∗
∗
an
d
∈
,
c)
a c
ont
ex
t
-
f
r
ee i
f
∈
(
∪
)
∗
and
∈
,
d)
a c
ont
ex
t
-
s
ens
i
t
i
v
e i
f
∈
(
∪
)
∗
+
(
∪
)
∗
and
∈
(
∪
)
+
w
her
e
|
|
≤
|
|
and
e)
a
r
ec
ur
s
i
v
el
y
en
um
er
abl
e
or
unr
es
t
r
i
c
t
e
d i
f
∈
(
∪
)
+
a
nd
∈
(
∪
)
∗
w
her
e
c
ont
ai
ns
at
l
eas
t
one
no
nt
e
r
m
i
nal
s
y
m
b
ol
.
T
he f
a
m
i
l
i
es
of
l
ang
uag
es
gener
at
ed
b
y
ar
bi
t
r
ar
y
,
c
o
nt
ex
t
s
ens
i
t
i
v
e,
c
o
nt
ex
t
f
r
ee,
r
egu
l
ar
,
l
i
n
ear
an
d
f
i
n
i
t
e
gr
am
m
ar
s
ar
e
den
ot
ed
b
y
,
,
,
,
,
and
,
r
es
pec
t
i
v
el
y
.
F
or
t
hes
e
l
an
gua
ge f
am
i
l
i
es
,
C
h
om
s
k
y
h
i
er
ar
c
h
y
ho
l
ds
:
⊂
⊂
⊂
⊂
⊂
.
B
ef
or
e m
ov
i
ng t
o
t
he o
per
at
i
o
ns
on l
ang
uag
es
,
w
e
r
ec
al
l
s
om
e def
i
ni
t
i
o
n of
r
egul
at
ed
gr
am
m
a
r
s
m
ent
i
oned
i
n t
h
i
s
s
t
ud
y
.
A
m
at
r
i
x
gr
am
m
ar
i
s
a qua
dr
up
l
e
=
(
,
,
,
)
w
her
e
,
and
ar
e d
ef
i
ned
as
f
or
c
ont
ex
t
-
f
r
ee gr
am
m
ar
and
i
s
a s
et
of
m
at
r
i
c
es
,
t
hat
ar
e f
i
ni
t
e
s
equenc
es
of
c
ont
ex
t
-
f
r
ee r
ul
es
f
r
om
×
(
∪
)
∗
. It
s
l
ang
uag
e
i
s
def
i
ned
b
y
(
)
=
{
∈
∗
|
⇒
a
nd
∈
∗
}
.
A
n ad
di
t
i
v
e v
al
enc
e gr
am
m
ar
i
s
a 5
-
t
up
l
es
=
(
,
,
,
,
)
w
her
e
,
,
,
ar
e def
i
ned
as
f
or
a c
ont
ex
t
-
f
r
ee gr
am
m
ar
and
i
s
a m
appi
n
g f
r
om
i
nt
o s
et
ℤ
(
s
et
ℚ
)
.
T
he l
ang
u
age
gener
at
ed
b
y
t
h
e gr
am
m
ar
c
ons
i
s
t
s
of
al
l
s
t
r
i
ng
∈
∗
s
uc
h t
hat
t
her
e
i
s
a
der
i
v
at
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
25
02
-
4
752
I
J
E
EC
S
V
o
l.
8
,
N
o.
1,
O
c
t
o
ber
20
17
:
36
–
42
38
1
2
…
w
her
e
∑
(
)
=
0
=
1
.
T
h
e f
am
i
l
i
es
of
l
a
ngua
ges
gen
er
at
e
d
b
y
m
a
t
r
i
x
an
d
add
i
t
i
v
e
v
a
l
enc
e
gr
am
m
ar
s
(
w
i
t
h
er
as
i
ng
r
u
es
)
a
r
e
de
not
e
d
b
y
,
,
(
,
)
,
r
es
pec
t
i
v
e
l
y
.
N
o
w
,
w
e r
ec
a
l
l
s
om
e s
et
-
t
heor
et
i
c
o
per
at
i
ons
t
hat
w
i
l
l
b
e
us
ed
t
o
i
n
v
es
t
i
gat
e
t
h
e
c
l
os
ur
e
pr
oper
t
i
es
of
a gr
am
m
ar
.
L
et
1
and
2
be t
w
o l
a
ngu
ag
es
.
T
hen,
t
he un
i
on
(
∪
)
,
in
t
e
r
se
ct
i
o
n
(
∩
)
,
di
f
f
er
enc
e
(
−
)
and c
o
nc
at
e
nat
i
on
(
⋅
)
of
1
and
2
ar
e def
i
ned
as
:
1
∪
2
=
{
∶
∈
1
∈
2
}
1
∩
2
=
{
∶
∈
1
∈
2
}
1
−
2
=
{
∶
∈
1
∉
2
}
1
⋅
2
=
{
1
2
∶
1
∈
1
2
∈
2
}
T
he c
o
m
pl
em
ent
of
⊆
Σ
∗
w
i
t
h
r
es
pec
t
t
o
Σ
∗
i
s
d
ef
i
ned
as
=
Σ
∗
−
.
F
or
a l
ang
uag
e
, th
e
i
t
er
at
i
ons
of
i
s
def
i
n
ed as
:
0
=
{
}
,
1
=
,
2
=
,
⋯
∗
=
⋃
≥
0
(
it
e
r
a
ti
on
c
lo
s
u
r
e
:
K
lee
n
e
s
t
ar
)
.
+
=
⋃
≥
1
(
pos
i
t
i
v
e
i
t
er
at
i
on c
l
os
ur
e
:
K
l
e
en
e p
l
us
)
.
G
i
v
e
n
t
w
o
a
l
ph
ab
et
s
Σ
1
,
Σ
2
,
a
m
appi
ng
ℎ
:
Σ
1
∗
→
Σ
2
∗
i
s
c
al
l
ed
a
m
or
phi
s
m
or
s
y
non
y
m
ous
l
y
a hom
om
or
p
hi
s
m
i
f
and onl
y
i
f
:
(
i)
f
or
ev
er
y
∈
Σ
1
∗
,
t
her
e
e
xi
st
s
∈
Σ
2
∗
s
uc
h t
hat
=
ℎ
(
)
an
d
i
s d
i
st
i
n
ct
,
(
ii)
f
or
ev
er
y
,
∈
Σ
1
∗
∶
ℎ
(
)
=
ℎ
(
)
ℎ
(
)
.
A
m
or
phi
s
m
i
s
-
f
r
ee
i
f
f
or
e
v
er
y
∈
Σ
1
∗
,
ℎ
(
)
≠
.
T
hen,
a
m
or
phi
s
m
i
s
k
now
n
as
a
n
i
s
om
or
phi
s
m
w
he
n f
or
ev
er
y
,
∈
Σ
1
∗
,
if
ℎ
(
)
=
ℎ
(
)
t
hen
=
.
F
or
a
w
or
d
=
1
2
…
,
∈
Σ
,
1
≤
≤
,
t
he
m
i
r
r
or
i
m
age
of
(
a.
k
.
a.
r
ev
er
s
al
)
i
s
obt
a
i
n
i
ng
b
y
w
r
i
t
i
n
g
t
h
e
w
o
r
d
i
n
t
h
e
r
e
v
er
s
e
or
d
er
s
u
c
h
…
1
2
and
i
t
i
s
den
ot
e
d
b
y
.
T
her
ef
or
e,
f
or
a l
angu
ag
e
⊆
Σ
∗
,
w
e def
i
n
ed
i
t
s
m
i
r
r
or
i
m
age as
=
{
:
∈
}
.
3
.
M
u
l
ti
s
e
t C
o
n
tr
o
l
l
e
d
G
r
a
m
m
a
r
s
:
D
e
fi
n
i
ti
o
n
s
a
n
d
G
e
n
e
r
a
ti
v
e
P
o
w
e
r
I
nf
or
m
al
l
y
,
a
m
ul
t
i
s
et
c
ont
r
ol
l
e
d
gr
am
m
ar
i
s
a c
o
nt
ex
t
-
f
r
ee gr
am
m
ar
=
(
,
,
,
)
equ
i
pp
ed
w
i
t
h
an
ar
i
t
hm
e
t
i
c
ex
pr
es
s
i
on
o
v
er
m
ul
t
i
s
et
s
on
t
er
m
i
nal
s
.
F
or
ea
c
h
pr
od
uc
t
i
o
n
:
→
∈
, th
e
m
u
l
ti
s
e
t
[
]
∈
⨁
,
c
al
l
ed “
c
ount
er
”
,
i
s
def
i
n
ed r
e
pr
es
ent
i
ng t
he t
er
m
i
nal
oc
c
ur
r
enc
es
i
n
.
F
or
ex
am
pl
e,
i
f
=
{
,
}
and
:
→
∈
i
s
a pr
oduc
t
i
o
n,
t
hen
[
]
=
(
2
,
1
)
.
A
d
er
i
v
at
i
on
i
n
t
he
gr
am
m
ar
i
s
s
uc
c
es
s
f
ul
i
f
onl
y
i
f
t
he
v
a
l
ue
of
t
he ex
pr
es
s
i
on
of
m
ul
t
i
s
et
s
r
es
ul
t
ed
f
r
o
m
t
he der
i
v
at
i
on
i
n
a t
r
ue
r
el
a
t
i
o
n
w
i
t
h
a c
er
t
ai
n
t
hr
es
h
ol
d
[
4]
.
T
he f
or
m
al
d
ef
i
ni
t
i
o
n
of
m
ul
t
i
s
et
c
ont
r
ol
l
ed
gr
am
m
ar
s
i
s
por
t
r
a
y
e
d i
n t
h
e f
ol
l
o
w
in
g
d
e
f
in
it
io
n
.
D
e
fi
n
i
ti
o
n
1
[
4]
A
m
ul
t
i
s
et
c
ont
r
ol
l
ed
gr
am
m
ar
i
s
a
6
-
t
upl
es
=
(
,
,
,
,
⊕
,
)
w
h
er
e
,
and
ar
e
def
i
n
ed
as
f
or
a
c
ont
ex
t
-
f
r
ee
gr
am
m
a
r
,
i
s
a
f
i
ni
t
e
s
ubs
et
of
×
(
∪
)
∗
×
⨁
and
:
⨁
→
ℤ
i
s
a
l
i
ne
ar
or
non
l
i
ne
a
r
f
unc
t
i
on
.
A
t
r
i
pl
e
(
,
,
)
∈
i
s
w
r
i
t
t
en as
→
[
]
.
If
(
1
,
2
,
…
,
)
,
∈
,
1
≤
≤
i
s
a l
i
n
ear
,
t
h
en i
t
i
s
i
n t
he f
or
m
o
f
(
1
,
2
,
…
,
)
=
∑
(
)
+
=
1
0
w
h
er
e
∈
ℤ
,
0
≤
≤
.
T
hen,
as
a no
n
l
i
n
ear
f
unc
t
i
on
,
w
e c
an
c
ons
i
de
r
l
og
ar
i
t
hm
s
,
pol
y
n
om
i
al
s
,
r
at
i
on
al
,
ex
p
one
nt
i
al
,
p
o
w
er
and
s
o
on.
T
hus
,
t
he
l
an
gu
age
ge
ner
at
ed
b
y
m
ul
t
i
s
et
c
o
nt
r
ol
l
e
d gr
a
m
m
ar
i
s
def
i
ned b
y
(
,
,
∗
)
=
{
∣
[
]
∈
(
)
,
(
)
∗
}
w
h
er
e
t
he r
e
l
at
i
o
n
∗
∈
{
=
,
<
,
>
,
≤
,
≥
}
,
∈
,
⊆
ℤ
i
s
a
c
ut
poi
n
t
s
et
a
nd
(
)
=
{
[
]
∈
∗
×
⨁
∣
⇒
[
]
w
her
e
=
1
2
⋯
}
.
D
e
fi
n
i
ti
o
n
2
A
m
ul
t
i
s
et
c
ont
r
ol
l
e
d gr
am
m
ar
=
(
,
,
,
,
⊕
,
)
is
c
a
lle
d
a)
r
egul
ar
i
f
e
ac
h
pr
oduc
t
i
o
n
i
n
t
h
e
gr
am
m
ar
has
t
h
e
f
or
m
s
uc
h
→
[
]
or
→
[
]
w
her
e
∈
∗
and
,
∈
.
b)
l
i
n
ear
i
f
eac
h pr
o
duc
t
i
on i
n t
he gr
am
m
ar
has
t
he f
or
m
s
uc
h
→
1
2
[
]
or
→
[
]
w
her
e
,
1
,
2
∈
∗
and
,
∈
.
c)
c
ont
ex
t
-
f
r
ee
i
f
eac
h pr
odu
c
t
i
on i
n t
he gr
am
m
ar
has
t
he f
or
m
s
uc
h
→
[
]
w
h
er
e
∈
(
∪
)
∗
and
∈
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
EC
S
IS
S
N
:
2
502
-
4
752
Mul
t
i
s
et
C
ont
r
o
l
l
ed G
r
a
mm
ar
s
:
N
or
ma
l
F
or
m
and
C
l
os
ur
e P
r
o
per
t
i
es
(
S
al
bi
a
h A
s
ha
a
r
i
)
39
T
he
f
a
m
i
l
i
es
of
l
ang
uag
es
gener
at
ed
b
y
m
ul
t
i
s
e
t
c
ont
r
ol
l
e
d
r
eg
ul
ar
,
l
i
near
and
c
ont
ex
t
-
f
r
ee gr
a
m
m
ar
s
w
i
t
h
and
w
i
t
ho
ut
er
as
i
ng r
u
l
es
ar
e
deno
t
ed b
y
,
,
(
,
,
)
r
es
pec
t
i
v
el
y
.
W
e
al
s
o
us
e
br
ac
k
et
not
at
i
on
[
]
,
∈
{
,
,
}
t
o s
h
o
w
t
hat
a
s
t
at
em
ent
h
ol
ds
bot
h c
as
es
of
w
i
t
h
a
nd
w
i
t
hou
t
er
as
i
ng
r
ul
es
.
T
he
f
ol
l
o
w
i
ng
t
he
or
em
s
how
s
t
h
e c
om
put
at
i
on
al
po
w
er
s
po
s
s
es
s
ed b
y
m
ul
t
i
s
et
c
o
nt
r
ol
l
ed gr
am
m
ar
s
.
C
om
bi
ni
ng
t
he
r
es
ul
t
s
abo
v
e,
w
e f
or
m
t
he f
ol
l
o
w
i
ng
r
el
at
i
o
ns
as
i
n F
i
gur
e 1
.
T
h
eo
r
em
1 [
4]
⊂
.
⊂
.
−
≠
∅
.
⊂
.
−
≠
∅
.
[
]
⊆
[
]
.
F
i
gur
e
1.
T
he h
i
er
ar
c
h
y
of
f
am
i
l
i
es
of
l
an
gua
ge
gen
er
a
t
ed b
y
m
ul
t
i
s
et
c
o
nt
r
o
l
l
e
d gr
am
m
a
r
.
4
.
A
M
u
l
ti
s
e
t C
h
o
m
s
k
y
N
o
r
m
a
l
F
o
r
m
A
nor
m
al
f
or
m
i
s
i
nt
r
oduc
e
d
w
i
t
h t
h
e i
nt
en
t
t
o
t
r
ans
f
or
m
a gr
a
m
m
a
r
i
nt
o a s
t
and
a
r
d f
o
r
m
b
y
i
m
pos
i
ng
i
t
w
i
t
h
r
es
t
r
i
c
t
i
ons
.
I
n
f
or
m
al
l
an
gu
age
t
h
eor
y
,
a
v
a
r
i
et
y
of
nor
m
al
f
or
m
s
w
er
e
f
i
r
s
t
i
n
v
es
t
i
gat
e
d
and
de
v
e
l
o
ped
t
o s
o
l
v
e t
he r
udi
m
ent
ar
y
p
r
obl
em
s
i
nv
ol
v
i
ng c
o
nt
ex
t
-
f
r
ee
l
an
gua
ges
s
uc
h
f
or
m
a
k
i
ng
i
t
eas
y
t
o
ana
l
y
z
e
a
nd
t
o
c
ons
t
r
uc
t
pr
oof
s
r
egar
di
ng
par
t
i
c
ul
ar
pr
oper
t
i
es
of
t
he
gr
am
m
a
r
s
,
i
.
e.
,
f
or
t
es
t
i
ng
e
m
p
t
i
nes
s
and d
ec
i
d
i
ng
m
e
m
ber
s
hi
p
m
at
t
er
s
w
i
t
h m
or
e eas
i
l
y
.
O
n
e of
t
he m
os
t
us
ef
ul
,
w
e
l
l
-
c
ons
t
r
uc
t
ed an
d po
pu
l
ar
nor
m
al
f
or
m
s
t
o deal
w
i
t
h c
on
t
ex
t
-
f
r
ee gr
am
m
ar
i
s
C
hom
s
k
y
n
or
m
al
f
or
m
(
C
N
F
)
due t
o i
t
s
s
i
m
pl
e s
t
r
uc
t
ur
e (
bi
n
ar
y
t
r
ee)
.
T
he us
e
of
C
N
F
al
l
o
w
s
eas
i
l
y
t
o d
et
er
m
i
ne
w
het
h
er
a s
t
r
i
ng i
s
gen
er
at
e
d b
y
t
he c
ont
ex
t
-
f
r
ee gr
am
m
a
r
or
not
us
i
ng
pol
y
n
om
i
al
t
i
m
e al
g
or
i
t
hm
s
(
f
or
i
ns
t
anc
e,
C
Y
K
al
gor
i
t
h
m
)
.
A
c
ont
ex
t
-
f
r
ee
gr
am
m
ar
i
s
s
ai
d
t
o
be
i
n
C
N
F
i
f
and
on
l
y
i
f
al
l
i
t
s
pr
oduc
t
i
ons
ar
e
i
n
f
o
r
m
of
→
and
→
w
h
er
e
,
,
ar
e v
ar
i
a
bl
e
s
and
i
s
ex
ac
t
l
y
a t
er
m
i
nal
.
H
er
e,
w
e
pr
o
v
e t
hat
our
m
ul
t
i
s
et
c
ont
r
ol
l
ed c
o
nt
ex
t
-
f
r
ee gr
am
m
ar
s
c
an al
s
o be t
r
a
ns
f
or
m
ed i
n t
o
eq
ui
v
al
e
nt
C
N
F
s
.
T
h
eo
r
em
1
F
or
an
y
m
ul
t
i
s
et
c
ont
r
o
l
l
ed
c
on
t
ex
t
-
f
r
ee
gr
am
m
ar
,
t
her
e
ex
i
s
t
s
an
equ
i
v
al
e
nt
m
ul
t
i
s
et
c
o
nt
r
ol
l
ed
c
o
nt
ex
t
-
f
r
ee
gr
am
m
ar
′
i
n
m
ul
t
i
s
et
C
hom
s
k
y
n
or
m
al
f
o
r
m
(
m
CNF
)
.
P
r
oof
:
Let
be
a
m
ul
t
i
s
et
c
ont
r
ol
l
e
d
c
ont
ex
t
-
f
r
ee
gr
am
m
ar
.
T
hen,
an
y
s
uc
h
gr
am
m
ar
c
an be
c
on
v
er
t
e
d i
nt
o
an
equ
i
v
al
ent
gr
am
m
ar
′
w
h
er
e a
l
l
i
t
s
pr
o
duc
t
i
ons
ar
e
i
n f
or
m
of
→
or
/
and
→
w
it
h
>
0
,
w
her
e
i
s
t
he
z
er
o v
ec
t
or
,
,
,
ar
e v
ar
i
a
bl
es
an
d
is
a
t
er
m
i
nal
.
I
t
i
s
do
ne
i
n t
hr
ee
phas
es
.
P
has
e
1
.
W
e c
ons
t
r
uc
t
a
gr
am
m
a
r
1
t
hat
i
s
e
qu
i
v
al
e
n
t
t
o
gr
am
m
ar
an
d
d
oes
n
ot
hav
e an
y
pr
o
duc
t
i
on i
n t
he
f
or
m
of
→
w
her
e
,
∈
.
S
up
pos
e
t
hat
w
e h
av
e pr
od
uc
t
i
o
ns
⟶
in
t
hat
l
e
ad t
o a s
er
i
es
of
f
or
m
o
f
der
i
v
at
i
o
n s
uc
h
1
1
2
2
3
⋯
+
1
⎯
⎯
+
2
⎯
⎯
w
it
h
∉
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
25
02
-
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I
J
E
EC
S
V
o
l.
8
,
N
o.
1,
O
c
t
o
ber
20
17
:
36
–
42
40
A
c
c
or
di
n
gl
y
,
w
e s
u
bs
t
i
t
ut
e
al
l
s
uc
h “
s
eq
uenc
e”
pr
odu
c
t
i
ons
1
1
,
1
2
2
,
…
,
+
1
⎯
⎯
in
b
y
a s
i
ng
l
e
pr
od
uc
t
i
o
n
→
,
w
her
e
=
1
+
2
+
⋯
+
+
1
.
T
hus
,
t
he
g
r
amma
r
1
is
equ
i
v
al
e
nt
t
o t
h
e gr
am
m
ar
.
P
has
e 2
.
W
e c
ons
t
r
uc
t
a
gr
am
m
a
r
2
t
hat
i
s
eq
ui
v
a
l
en
t
t
o gr
am
m
ar
1
w
i
t
h c
on
di
t
i
o
n
s
uc
h al
l
pr
o
duc
t
i
ons
i
n
2
ar
e
not
i
n t
he f
or
m
o
f
→
1
2
⋯
,
>
0
,
>
2
w
her
e
s
ar
e
t
er
m
i
nal
s
.
F
or
ev
er
y
r
ul
e
of
t
he
f
or
m
abo
v
e,
w
e
i
nt
r
o
duc
e
a
ne
w
r
ul
e
→
1
2
⋯
w
h
er
e
al
l
w
h
er
e
t
er
m
i
nal
s
ar
e
r
epl
ac
ed
w
i
t
h
n
e
w
v
ar
i
ab
l
es
s
,
and
r
ul
es
of
t
he
f
o
rm
→
f
or
eac
h
w
h
er
e
i
s
t
he
v
ec
t
or
c
ont
ai
ni
n
g a s
i
g
nl
e
one
w
hi
c
h
i
s
at
p
os
i
t
i
o
n
.
T
her
ef
or
e,
w
e
get
2
w
i
t
h
al
l
i
t
s
pr
oduc
t
i
o
ns
ar
e
onl
y
i
n
t
he
f
or
m
s
→
,
∈
or
/
and
→
1
⋯
,
≥
2
,
1
,
2
,
…
,
∈
.
H
er
e,
i
t
i
s
o
bv
i
ous
t
h
at
gr
am
m
ar
2
i
s
e
qu
i
v
al
e
nt
t
o
gr
am
m
a
r
1
.
P
has
e
3
.
W
e c
ons
t
r
uc
t
a
gr
am
m
a
r
′
t
hat
i
s
eq
ui
v
a
l
e
n
t
t
o
gr
am
m
ar
2
w
her
e al
l
i
t
s
pr
oduc
t
i
ons
ar
e
o
nl
y
i
n
t
he
f
or
m
o
f
→
or
→
wi
t
h
>
0
,
,
,
∈
and
∈
.
C
o
ns
i
de
r
a pr
oduc
t
i
on
i
n
fo
r
m
o
f
0
→
1
⋯
w
it
h
>
2
in
2
.
T
hen,
w
e s
ubs
t
i
t
ut
e t
hi
s
pr
od
uc
t
i
o
n
w
i
t
h t
h
e
pr
oduc
t
i
ons
0
→
1
1
1
0
→
2
2
⋮
−
2
0
→
−
1
w
her
e
’
ar
e ne
w
no
nt
er
m
i
na
l
s
.
T
hus
,
t
he o
bt
a
i
ne
d gr
am
m
ar
′
i
s
equ
i
v
al
e
nt
t
o gr
am
m
ar
,
w
hi
c
h
i
s
m
ul
t
i
s
et
C
h
om
s
k
y
nor
m
al
f
or
m
.
E
xam
p
l
e
1
L
et
1
=
(
{
,
,
}
,
{
,
,
}
,
,
,
⊕
,
)
be
a
m
ul
t
i
s
et
c
ont
ex
t
-
f
r
ee
gr
a
m
m
ar
w
her
e
c
ons
i
s
t
s
of
t
he f
ol
l
o
w
i
ng
pr
od
uc
t
i
o
ns
:
0
∶
→
[
(
0
,
0
,
0
)
]
,
1
∶
→
[
(
1
,
1
,
0
)
]
,
2
∶
→
[
(
0
,
0
,
1
)
]
,
3
∶
→
[
(
1
,
1
,
0
)
]
,
4
∶
→
[
(
0
,
0
,
1
)
]
,
and
(
,
,
)
=
(
)
+
(
)
+
(
−
1
)
(
)
+
(
−
1
)
(
)
.
T
hen,
t
o c
on
v
er
t
t
he
gr
am
m
ar
1
i
nt
o
C
hom
s
k
y
n
or
m
al
f
or
m
,
w
e pr
oc
ee
d as
b
el
o
w
:
F
i
rs
t
,
re
p
l
ac
e
→
[
(
1
,
1
,
0
)
]
w
it
h
→
[
(
0
,
0
,
0
)
]
,
→
[
(
1
,
0
,
0
)
]
,
→
[
(
0
,
1
,
0
)
]
.
T
hen,
→
[
(
0
,
0
,
1
)
]
b
y
→
[
(
0
,
0
,
0
)
]
,
→
[
(
0
,
0
,
1
)
]
.
N
e
x
t,
→
[
(
1
,
1
,
0
)
]
b
y
→
[
(
0
,
1
,
0
)
]
.
Las
t
,
r
ep
l
ac
e
→
[
(
0
,
0
,
0
)
]
b
y
→
[
(
0
,
0
,
0
)
]
and
→
[
(
0
,
0
,
0
)
]
.
H
enc
e,
w
e c
an ha
v
e a m
ul
t
i
s
et
c
ont
r
ol
l
e
d c
ont
ex
t
f
r
ee gr
am
m
ar
i
n C
hom
s
k
y
no
r
m
a
l
f
or
m
w
i
t
h
pr
oduc
t
i
ons
s
uc
h:
0
∶
→
[
(
0
,
0
,
0
)
]
,
1
∶
→
[
(
0
,
0
,
0
)
]
,
2
∶
→
[
(
0
,
0
,
0
)
]
,
3
∶
→
[
(
0
,
0
,
0
)
]
,
4
∶
→
[
(
0
,
0
,
0
)
]
,
5
∶
→
[
(
0
,
0
,
1
)
]
,
6
∶
→
[
(
1
,
0
,
0
)
]
,
7
∶
→
[
(
0
,
1
,
0
)
]
,
8
∶
→
[
(
0
,
0
,
1
)
]
,
and
(
,
,
)
=
(
)
+
(
)
+
(
−
1
)
(
)
+
(
−
1
)
(
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
EC
S
IS
S
N
:
2
502
-
4
752
Mul
t
i
s
et
C
ont
r
o
l
l
ed G
r
a
mm
ar
s
:
N
or
ma
l
F
or
m
and
C
l
os
ur
e P
r
o
per
t
i
es
(
S
al
bi
a
h A
s
ha
a
r
i
)
41
5
.
C
l
o
s
u
re
Pr
o
p
e
r
ti
e
s
C
l
os
ur
e
pr
op
er
t
i
es
ar
e of
t
e
n ha
nd
y
i
n pr
o
v
i
ng
t
he
or
et
i
c
al
pr
oper
t
i
es
of
gr
am
m
ar
s
and
l
an
gua
ges
as
w
e
l
l
as
i
n c
ons
t
r
uc
t
i
n
g n
e
w
a
nd c
om
pl
ex
l
an
gua
ges
f
r
o
m
ex
i
s
t
i
ng l
ang
uag
es
.
T
her
ef
or
e,
her
e
b
y
us
i
n
g
t
he
s
t
a
ndar
d
pr
o
of
,
w
e
i
n
v
e
s
t
i
gat
e
t
h
e
c
l
os
ur
e
pr
o
p
er
t
i
es
t
hat
c
an
be
o
w
ne
d b
y
m
ul
t
i
s
et
c
o
nt
r
ol
l
e
d gr
am
m
ar
s
.
T
he
f
a
m
i
l
i
es
of
l
ang
uag
es
gener
at
ed
b
y
m
ul
t
i
s
e
t
c
ont
r
ol
l
e
d
r
eg
ul
ar
,
l
i
near
and
c
ont
ex
t
-
f
r
ee gr
am
m
ar
s
w
i
t
h
l
i
near
c
ount
er
(
)
f
unc
t
i
o
ns
ar
e d
enot
ed b
y
,
,
.
L
em
m
a
1
(
u
ni
o
n)
T
h
e
f
a
m
ilie
s
,
an
d
ar
e
c
l
os
e
d
u
nder
un
i
on
oper
at
i
o
n.
P
r
oof
:
Let
1
and
2
be
t
w
o
l
a
n
guag
es
i
n
w
it
h
∈
{
,
,
}
gener
a
t
ed
b
y
m
ul
t
i
s
et
c
ont
r
o
l
l
ed
gr
a
m
m
ar
s
1
=
(
1
,
,
1
,
1
,
⊕
1
,
1
)
an
d
2
=
(
2
,
,
2
,
2
,
⊕
2
,
2
)
,
r
es
pec
t
i
v
el
y
,
w
h
er
e
1
an
d
2
ar
e
l
i
n
ear
f
unc
t
i
ons
.
W
i
t
hout
l
os
s
of
g
ener
a
l
i
t
y
,
w
e
a
s
s
u
m
e
t
hat
1
∩
2
=
∅
,
an
d
s
et
=
1
∪
2
∪
{
}
w
her
e
i
s
a
ne
w
no
nt
er
m
i
nal
s
y
m
bol
.
T
hen
,
w
e
def
i
n
e
t
he gr
am
m
ar
s
=
(
,
,
,
,
⊕
,
)
w
h
er
e
=
1
∪
2
∪
{
→
1
,
→
2
}
an
d
=
1
+
2
.
T
hus
,
i
t
i
s
not
di
f
f
i
c
ul
t
t
o
not
i
c
e t
hat
∶
(
,
,
∗
)
=
(
1
,
,
∗
)
∪
(
2
,
,
∗
)
.
L
em
m
a 2
(
K
l
ee
ne
-
s
t
ar
)
T
he f
am
i
l
y
of
and
ar
e c
l
o
s
ed und
er
K
l
ee
ne
-
s
t
ar
oper
at
i
o
n.
P
r
oof
(
)
:
F
or
a
g
i
v
en m
ul
t
i
s
et
c
ont
r
ol
l
e
d r
eg
ul
ar
l
ang
uag
e
, l
e
t
=
(
,
,
,
,
⊕
,
)
be
a
m
ul
t
i
s
e
t
c
ont
r
o
l
l
ed
r
e
gul
ar
gr
am
m
ar
w
i
t
h
=
(
)
.
T
hen,
i
t
i
s
n
ot
d
i
f
f
i
c
ul
t
t
o
not
i
c
e
t
h
at
t
he l
an
gua
ge
∗
i
s
ge
ner
at
ed
b
y
m
ul
t
i
s
et
c
o
nt
r
o
l
l
e
d r
eg
ul
ar
gr
am
m
ar
′
=
{
∪
{
′
}
,
,
∪
{
′
→
,
′
→
}
∪
{
→
:
→
∈
,
∈
∗
}
,
′
,
⊕
,
}
w
her
e
′
i
s
a n
e
w
nont
er
m
i
nal
s
y
m
bo
l
.
P
r
oof
(
)
:
Le
t
a
l
a
ngu
age
i
s
gen
er
at
e
d b
y
m
ul
t
i
s
et
c
ont
r
ol
l
e
d c
on
t
ex
t
-
f
r
ee gr
a
m
m
ar
=
(
,
,
,
,
⊕
,
)
.
T
hen,
i
t
i
s
eas
y
t
o
s
ee
t
h
a
t
t
he
l
a
ngu
age
∗
i
s
gener
at
e
d
b
y
g
r
am
m
ar
s
uc
h
′
=
{
∪
{
′
}
,
,
∪
{
′
→
′
|
}
,
′
,
⊕
,
}
w
her
e
′
i
s
a
ne
w
no
nt
er
m
i
nal
s
y
m
bol
.
L
em
m
a 3
(
h
om
o
m
or
phi
s
m
)
T
h
e
f
a
m
ilie
s
,
an
d
ar
e c
l
os
e
d
und
er
hom
o
m
or
phi
s
m
.
P
r
oof
:
Let
∈
,
∈
{
,
,
}
be a
l
a
n
gu
age
g
ener
a
t
ed
b
y
a
m
ul
t
i
s
et
c
ont
r
ol
l
ed
gr
am
m
ar
=
(
,
,
,
,
⊕
,
)
an
d
l
e
t
ℎ
:
∗
→
1
∗
be
a
hom
o
m
or
phi
s
m
.
T
h
en,
t
her
e
i
s
a m
ul
t
i
s
et
c
ont
r
o
l
l
ed
gr
am
m
ar
′
=
(
,
1
,
1
,
1
,
⊕
,
′
)
s
uc
h t
hat
(
′
)
=
ℎ
(
)
.
1.
re
g
u
l
a
r
:
f
or
ev
er
y
pr
od
uc
t
i
on
i
n
t
h
e
f
or
m
of
:
→
[
]
in
,
w
e
c
ons
t
r
uc
t
t
he
pr
oduc
t
i
on
ℎ
(
)
:
→
ℎ
(
)
[
′
]
in
1
w
her
e
∈
∗
,
∈
∪
{
}
and
∈
⨁
,
′
∈
1
⨁
;
2.
l
i
n
ear
:
f
or
e
v
er
y
pr
o
duc
t
i
on
i
n
t
h
e f
or
m
of
:
→
1
2
[
]
in
,
w
e c
ons
t
r
uc
t
t
he
pr
oduc
t
i
on
ℎ
(
)
:
→
ℎ
(
1
)
ℎ
(
2
)
[
′
]
,
w
her
e
1
,
2
∈
∗
,
∈
∪
{
}
and
∈
⨁
,
′
∈
1
⨁
;
3.
co
n
t
ext
-
f
r
ee:
f
or
ev
er
y
p
r
oduc
t
i
o
n
i
n
t
he
f
or
m
of
:
→
1
1
2
2
…
+
1
[
]
,
≥
0
,
w
e c
o
ns
t
r
uc
t
t
he
pr
od
uc
t
i
on
ℎ
(
)
:
→
ℎ
(
1
)
1
ℎ
(
2
)
2
…
ℎ
(
)
ℎ
(
+
1
)
[
]
,
≥
0
w
her
e
,
∈
∗
,
1
≤
≤
+
1
,
∈
∪
{
}
,
1
≤
≤
and
∈
⨁
,
′
∈
1
⨁
.
W
e
def
i
ne
′
i
n t
h
e a
bo
v
e
pr
oduc
t
i
ons
as
′
=
0
if
|
ℎ
(
)
|
=
0
,
′
=
if
|
ℎ
(
)
|
=
1
,
an
d
′
=
/
|
ℎ
(
)
|
if
|
ℎ
(
)
|
>
1
.
T
hen
′
has
t
h
e s
am
e c
oof
i
c
i
ent
f
or
eac
h s
y
m
bol
′
=
ℎ
(
)
∈
1
as
∈
.
I
n ev
er
y
s
uc
c
es
s
f
ul
der
i
v
at
i
o
n i
n
gener
at
i
n
g t
he s
t
r
i
ng
∈
∗
,
w
e r
ep
l
ac
e
∈
wi
t
h
ℎ
(
)
∈
1
i
n t
he c
or
r
es
po
nd
i
n
g
der
i
v
at
i
o
n a
nd o
bt
a
i
n
ℎ
(
)
∈
1
∗
.
T
hus
ℎ
(
)
=
(
′
)
.
L
em
m
a 4
(
m
i
r
r
or
i
m
age)
T
he
f
a
m
ilie
s
,
an
d
ar
e
c
l
o
s
ed
u
nder
m
i
r
r
or
i
m
age oper
at
i
o
n.
P
r
oof
:
Let
be a
l
an
gua
ge
g
ener
at
ed
b
y
a m
ul
t
i
s
et
c
o
nt
r
ol
l
e
d r
eg
ul
ar
gr
am
m
ar
(
l
i
ne
ar
gr
am
m
ar
,
c
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
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02
-
4
752
I
J
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EC
S
V
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8
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c
t
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20
17
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42
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f
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s
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and m
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ons
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6
.
C
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s
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l
,
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e
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d
bac
k
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he
def
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n
i
t
i
on
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d
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om
put
at
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l
po
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er
s
of
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ul
t
i
s
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ont
r
ol
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ed
gr
am
m
a
r
s
def
i
ned
i
n
[
4]
w
her
e
i
n
a
ddi
t
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o
n
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e
h
av
e
i
nv
es
t
i
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t
he
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l
os
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e
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t
i
es
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ul
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ont
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ar
s
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as
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dec
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da
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l
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o b
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ed
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c
k
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o
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e
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e
m
e
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ts
T
hi
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h
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en
s
u
ppor
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d
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y
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ant
s
R
I
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S
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-
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532
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d
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R
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S
1
3
-
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-
0315
of
Mi
n
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M
al
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oug
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U
ni
v
er
s
i
t
y
M
al
a
y
s
i
a
.
R
ef
er
en
ces
[1
]
D
as
s
ow
J
,
P
aun G
.
R
eg
ul
at
e
d R
ew
r
i
t
i
ng i
n F
or
m
a
l
Lan
gu
age T
heor
y
.
S
pr
i
n
ger
B
er
l
i
n
H
ei
del
ber
g:
N
ew
Y
or
k
,
1
989
.
[2
]
M
eduna
A
,
Z
e
m
ek
P
.
R
eg
ul
a
t
ed
G
r
am
m
ar
s
a
nd
A
u
t
om
at
a.
S
pr
i
ng
er
B
er
l
i
n
H
ei
d
el
ber
g:
N
ew
Y
or
k
,
2014.
[3
]
A
br
aha
m
A
.
S
om
e Q
ues
t
i
o
ns
of
P
hr
as
e S
t
r
u
c
t
ur
e G
r
am
m
ar
s
.
C
om
put
at
i
o
nal
Li
ngu
i
s
t
i
c
s
.
19
65;
4:
61
-
70.
[4
]
A
s
haar
i
S
,
T
ur
aev
S
,
M
T
am
r
i
n M
I
,
O
k
hunov
A
,
Z
huk
aba
y
ev
a
T
.
M
ul
t
i
s
et
C
o
nt
r
ol
l
ed G
r
am
m
ar
s
.
J
our
n
al
o
f
T
h
eor
et
i
c
a
l
an
d A
pp
l
i
ed
I
nf
or
m
at
i
on
T
ec
hno
l
og
y
.
2
017.
[5
]
A
s
haar
i
S
,
T
ur
aev
S
,
O
k
huno
v
A
.
S
t
r
uc
t
ur
al
l
y
an
d A
r
i
t
hm
et
i
c
al
l
y
C
o
nt
r
o
l
l
ed
G
r
am
m
ar
s
.
I
n
t
er
nat
i
ona
l
J
our
n
al
o
n P
er
c
ept
i
v
e an
d C
o
gni
t
i
v
e C
om
p
ut
i
n
g
.
2
016;
2(
2)
:
25
-
35.
[6
]
Lobo
D
,
V
i
c
o
F
J
,
D
a
s
s
ow
J
.
G
r
ap
h G
r
a
m
m
ar
s
w
i
t
h
S
t
r
i
ng
-
R
e
gul
a
t
ed
R
ew
r
i
t
i
ng.
T
heor
et
i
c
a
l
C
om
put
er
S
c
i
en
c
e
.
2011
;
41
2(
43)
:
61
01
-
6
111.
[7
]
S
t
i
ebe
R
.
O
n
G
r
am
m
ar
s
C
on
t
r
ol
l
e
d
by
P
ar
i
k
h
V
ec
t
or
s
.
I
n:
Langu
age
A
l
i
v
e,
LN
C
S
7300
.
S
pr
i
n
ger
B
er
l
i
n H
ei
de
l
ber
g:
N
ew
Y
o
rk
.
2012:
246
-
264.
[8
]
D
as
s
ow
J
,
T
ur
aev
S
.
P
et
r
i
N
et
C
ont
r
ol
l
ed G
r
am
m
ar
s
w
i
t
h a B
ounded N
u
m
ber
o
f
A
ddi
t
i
on
al
P
l
ac
es
.
J
our
n
al
o
f
A
c
t
a C
y
b
er
net
i
c
a
.
2
010;
1
9:
6
09
-
6
34.
[9
]
D
as
s
ow
J
,
T
ur
aev
S
.
k
-
P
et
r
i
N
et
C
ont
r
ol
l
ed G
r
a
m
m
ar
s
.
I
n
:
Langu
age a
nd A
ut
o
m
at
a T
heor
y
and
A
ppl
i
c
at
i
on
s
,
LA
T
A
200
8,
LN
C
S
5196,
S
pr
i
n
ger
B
er
l
i
n
H
ei
d
el
ber
g:
N
ew
Y
or
k
.
200
8:
20
9
-
22
0.
[1
0
]
D
as
s
ow
J
,
T
ur
aev
S
.
A
r
b
i
t
r
ar
y
P
et
r
i
N
et
C
ont
r
o
l
l
e
d
G
r
am
m
ar
s
.
P
r
o
c
eed
i
ng
s
o
f
2
nd
I
nt
er
nat
i
ona
l
W
o
r
k
s
hop
on N
o
n
-
C
l
a
s
s
i
c
a
l
F
or
m
al
Lan
gua
ges
i
n
Li
n
gui
s
t
i
c
s
.
T
ar
r
agon
a,
S
p
ai
n.
2
0
08
:
27
-
40.
[1
1
]
S
t
i
ebe R
,
T
ur
aev
S
.
C
apa
c
i
t
y
B
ound
ed G
r
am
m
ar
s
an
d P
et
r
i
N
et
s
.
In
:
J
. D
a
s
s
o
w
, G
. P
i
g
h
i
z
z
i
n
i
, B
.
T
r
ut
he (
E
ds
.
)
,
11t
h I
nt
er
n
at
i
o
nal
W
o
r
k
s
h
op on D
es
c
r
i
p
t
i
on
al
C
om
pl
ex
i
t
y
of
F
or
m
al
S
y
s
t
em
s
(
D
C
F
S
2009)
E
P
T
C
S
3.
2
009:
193
-
20
3.
[1
2
]
C
as
t
an
o J
.
M
.
G
l
obal
I
nde
x
G
r
am
m
ar
s
and D
es
c
r
i
p
t
i
v
e P
ow
er
.
J
our
nal
of
Lo
gi
c
,
L
ang
uage an
d
I
nf
or
m
at
i
on
.
2
004;
13(
4)
:
40
3
-
419.
[1
3
]
K
udl
e
k
M
,
M
ar
t
i
n C
,
P
aun G
.
T
o
w
ar
d a F
or
m
al
M
ac
r
o
s
et
T
heor
y
.
I
n:
C
al
u
de,
C
.
S
P
aun,
G
,
R
oz
enber
g,
G
.
,
S
a
l
om
aa,
A
.
(
E
ds
.
)
,
M
ul
t
i
s
e
t
P
r
oc
es
s
i
ng
,
W
M
C
200
0,
LN
C
S
223
5,
S
pr
i
nger
B
er
l
i
n
H
ei
del
ber
g:
N
ew
Y
or
k
.
2001:
1
23
-
133
.
[1
4
]
S
al
om
aa A
.
F
or
m
al
l
ang
uag
es
.
A
c
ad
em
i
c
P
r
e
s
s
:
N
ew
Y
or
k
.
1973.
[1
5
]
S
i
ps
er
M
.
I
nt
r
oduc
t
i
on
t
o
t
h
e
T
heor
y
of
C
om
put
at
i
on.
3
rd
e
dn.
C
enga
ge
Lear
ni
n
g:
U
ni
t
e
d
S
t
at
es
o
f
A
m
er
i
c
a.
2013
.
[1
6
]
Ma
r
t
i
n
-
V
i
de C
.
F
or
m
a
l
L
an
guage
s
f
or
L
i
ng
ui
s
t
s
:
C
l
as
s
i
c
al
and
N
on
c
l
a
s
s
i
c
a
l
M
odel
s
.
O
x
f
or
d
H
andbo
ok
o
f
C
om
put
a
t
i
o
nal
Li
ngui
s
t
i
c
s
.
O
x
f
or
d U
ni
v
er
s
i
t
y
P
r
es
s
:
O
x
f
or
d.
2001.
Evaluation Warning : The document was created with Spire.PDF for Python.