<s>
Syntactic	B-General_Concept
parsing	I-General_Concept
is	O
the	O
automatic	O
analysis	O
of	O
syntactic	B-Application
structure	I-Application
of	O
natural	O
language	O
,	O
especially	O
syntactic	O
relations	O
(	O
in	O
dependency	O
grammar	O
)	O
and	O
labelling	O
spans	O
of	O
constituents	O
(	O
in	O
constituency	O
grammar	O
)	O
.	O
</s>
<s>
Syntactic	B-General_Concept
parsing	I-General_Concept
is	O
one	O
of	O
the	O
important	O
tasks	O
in	O
computational	O
linguistics	O
and	O
natural	B-Language
language	I-Language
processing	I-Language
,	O
and	O
has	O
been	O
a	O
subject	O
of	O
research	O
since	O
the	O
mid-20th	O
century	O
with	O
the	O
advent	O
of	O
computers	O
.	O
</s>
<s>
Different	O
theories	O
of	O
grammar	O
propose	O
different	O
formalisms	O
for	O
describing	O
the	O
syntactic	B-Application
structure	I-Application
of	O
sentences	O
.	O
</s>
<s>
Part-of-speech	O
tagging	O
(	O
which	O
resolves	O
some	O
semantic	O
ambiguity	O
)	O
is	O
a	O
related	O
problem	O
,	O
and	O
often	O
a	O
prerequisite	O
for	O
or	O
a	O
subproblem	O
of	O
syntactic	B-General_Concept
parsing	I-General_Concept
.	O
</s>
<s>
Syntactic	O
parses	O
can	O
be	O
used	O
for	O
information	B-General_Concept
extraction	I-General_Concept
(	O
e.g.	O
</s>
<s>
event	O
parsing	O
,	O
semantic	O
role	O
labelling	O
,	O
entity	O
labelling	O
)	O
and	O
may	O
be	O
further	O
used	O
to	O
extract	O
formal	B-Application
semantic	I-Application
representations	I-Application
.	O
</s>
<s>
The	O
most	O
popular	O
algorithm	O
for	O
constituency	O
parsing	O
is	O
the	O
Cocke	B-Application
–	I-Application
Kasami	I-Application
–	I-Application
Younger	I-Application
algorithm	I-Application
(	O
CKY	O
)	O
,	O
which	O
is	O
a	O
dynamic	O
programming	O
algorithm	O
which	O
constructs	O
a	O
parse	O
in	O
worst-case	O
time	O
,	O
on	O
a	O
sentence	O
of	O
words	O
and	O
is	O
the	O
size	O
of	O
a	O
CFG	O
given	O
in	O
Chomsky	O
Normal	O
Form	O
.	O
</s>
<s>
One	O
way	O
to	O
do	O
this	O
is	O
by	O
using	O
a	O
probabilistic	B-General_Concept
context-free	I-General_Concept
grammar	I-General_Concept
(	O
PCFG	B-General_Concept
)	O
which	O
has	O
a	O
probability	O
of	O
each	O
constituency	O
rule	O
,	O
and	O
modifying	O
CKY	O
to	O
maximise	O
probabilities	O
when	O
parsing	O
bottom-up	O
.	O
</s>
<s>
A	O
further	O
modification	O
is	O
the	O
lexicalized	O
PCFG	B-General_Concept
,	O
which	O
assigns	O
a	O
head	O
to	O
each	O
constituent	O
and	O
encodes	O
rule	O
for	O
each	O
lexeme	O
in	O
that	O
head	O
slot	O
.	O
</s>
<s>
Thus	O
,	O
where	O
a	O
PCFG	B-General_Concept
may	O
have	O
a	O
rule	O
"	O
NP	O
→	O
DT	O
NN	O
"	O
(	O
a	O
noun	O
phrase	O
is	O
a	O
determiner	O
and	O
a	O
noun	O
)	O
while	O
a	O
lexicalized	O
PCFG	B-General_Concept
will	O
specifically	O
have	O
rules	O
like	O
"	O
NP(dog )	O
→	O
DT	O
NN(dog )	O
"	O
or	O
"	O
NP(person )	O
"	O
etc	O
.	O
</s>
<s>
More	O
recent	O
work	O
does	O
neural	O
scoring	O
of	O
span	O
probabilities	O
(	O
which	O
can	O
take	O
into	O
account	O
context	O
unlike	O
(	O
P	O
)	O
CFGs	O
)	O
to	O
feed	O
to	O
CKY	O
,	O
such	O
as	O
by	O
using	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
or	O
transformer	B-Algorithm
on	O
top	O
of	O
word	B-General_Concept
embeddings	I-General_Concept
.	O
</s>
<s>
This	O
was	O
followed	O
by	O
the	O
work	O
of	O
Yue	O
Zhang	O
and	O
Stephen	O
Clark	O
in	O
2009	O
,	O
which	O
added	O
beam	B-Algorithm
search	I-Algorithm
to	O
the	O
decoder	O
to	O
make	O
more	O
globally-optimal	O
parses	O
.	O
</s>
<s>
picking	O
the	O
best	O
option	O
at	O
each	O
time-step	O
of	O
building	O
the	O
tree	O
,	O
leading	O
to	O
potentially	O
non-optimal	O
or	O
ill-formed	O
trees	O
)	O
or	O
use	O
beam	B-Algorithm
search	I-Algorithm
to	O
increase	O
performance	O
while	O
not	O
sacrificing	O
efficiency	O
.	O
</s>
<s>
In	O
this	O
approach	O
,	O
constituent	O
parsing	O
is	O
modelled	O
like	O
machine	B-Application
translation	I-Application
:	O
the	O
task	O
is	O
sequence-to-sequence	B-Algorithm
conversion	O
from	O
the	O
sentence	O
to	O
a	O
constituency	O
parse	O
,	O
in	O
the	O
original	O
paper	O
using	O
a	O
deep	O
LSTM	B-Algorithm
with	O
an	O
attention	B-General_Concept
mechanism	I-General_Concept
.	O
</s>
<s>
This	O
runs	O
in	O
with	O
a	O
beam	B-Algorithm
search	I-Algorithm
decoder	O
of	O
width	O
10	O
(	O
but	O
they	O
found	O
little	O
benefit	O
from	O
greater	O
beam	O
size	O
and	O
even	O
limiting	O
it	O
to	O
greedy	O
decoding	O
performs	O
well	O
)	O
,	O
and	O
achieves	O
competitive	O
performance	O
with	O
traditional	O
algorithms	O
for	O
context-free	O
parsing	O
like	O
CKY	O
.	O
</s>
<s>
Many	O
modern	O
approaches	O
to	O
dependency	O
tree	O
parsing	O
use	O
transition-based	O
parsing	O
(	O
the	O
base	O
form	O
of	O
this	O
is	O
sometimes	O
called	O
arc-standard	O
)	O
as	O
formulated	O
by	O
Joakim	O
Nivre	O
in	O
2003	O
,	O
which	O
extends	O
on	O
shift-reduce	B-Application
parsing	I-Application
by	O
keeping	O
a	O
running	O
stack	O
of	O
tokens	O
,	O
and	O
deciding	O
from	O
three	O
operations	O
for	O
the	O
next	O
token	O
encountered	O
:	O
</s>
<s>
Modern	O
methods	O
use	O
a	O
neural	O
classifier	O
which	O
is	O
trained	O
on	O
word	B-General_Concept
embeddings	I-General_Concept
,	O
beginning	O
with	O
work	O
by	O
Danqi	O
Chen	O
and	O
Christopher	O
Manning	O
in	O
2014	O
.	O
</s>
<s>
These	O
all	O
only	O
support	O
projective	B-Algorithm
trees	O
so	O
far	O
,	O
wherein	O
edges	O
do	O
not	O
cross	O
given	O
the	O
token	O
ordering	O
from	O
the	O
sentence	O
.	O
</s>
<s>
For	O
non-projective	O
trees	O
,	O
Nivre	O
in	O
2009	O
modified	O
arc-standard	O
transition-based	O
parsing	O
to	O
add	O
the	O
operation	O
(	O
swap	O
the	O
top	O
two	O
tokens	O
on	O
the	O
stack	O
,	O
assuming	O
the	O
formulation	O
where	O
the	O
next	O
token	O
is	O
always	O
added	O
to	O
the	O
stack	O
first	O
)	O
.	O
</s>
<s>
A	O
chart-based	O
dynamic	O
programming	O
approach	O
to	O
projective	B-Algorithm
dependency	O
parsing	O
was	O
proposed	O
by	O
Michael	O
Collins	O
in	O
1996	O
and	O
further	O
optimised	O
by	O
Jason	O
Eisner	O
in	O
the	O
same	O
year	O
.	O
</s>
<s>
Given	O
this	O
,	O
we	O
can	O
use	O
an	O
extension	O
of	O
the	O
Chu	B-Algorithm
–	I-Algorithm
Liu/Edmonds	I-Algorithm
algorithm	I-Algorithm
with	O
an	O
edge	O
scorer	O
and	O
a	O
label	O
scorer	O
.	O
</s>
<s>
It	O
can	O
handle	O
non-projective	O
trees	O
unlike	O
the	O
arc-standard	O
transition-based	O
parser	O
and	O
CKY	O
.	O
</s>
<s>
As	O
before	O
,	O
the	O
scorers	O
can	O
be	O
neural	O
(	O
trained	O
on	O
word	B-General_Concept
embeddings	I-General_Concept
)	O
or	O
feature-based	O
.	O
</s>
<s>
Given	O
that	O
much	O
work	O
on	O
English	O
syntactic	B-General_Concept
parsing	I-General_Concept
depended	O
on	O
the	O
Penn	O
Treebank	O
,	O
which	O
used	O
a	O
constituency	O
formalism	O
,	O
many	O
works	O
on	O
dependency	O
parsing	O
developed	O
ways	O
to	O
deterministically	O
convert	O
the	O
Penn	O
formalism	O
to	O
a	O
dependency	O
syntax	B-Application
,	O
in	O
order	O
to	O
use	O
it	O
as	O
training	O
data	O
.	O
</s>
