<s>
Grammar	B-Algorithm
induction	I-Algorithm
(	O
or	O
grammatical	B-Algorithm
inference	I-Algorithm
)	O
is	O
the	O
process	O
in	O
machine	O
learning	O
of	O
learning	O
a	O
formal	O
grammar	O
(	O
usually	O
as	O
a	O
collection	O
of	O
re-write	O
rules	O
or	O
productions	O
or	O
alternatively	O
as	O
a	O
finite	B-Architecture
state	I-Architecture
machine	I-Architecture
or	O
automaton	O
of	O
some	O
kind	O
)	O
from	O
a	O
set	O
of	O
observations	O
,	O
thus	O
constructing	O
a	O
model	O
which	O
accounts	O
for	O
the	O
characteristics	O
of	O
the	O
observed	O
objects	O
.	O
</s>
<s>
More	O
generally	O
,	O
grammatical	B-Algorithm
inference	I-Algorithm
is	O
that	O
branch	O
of	O
machine	O
learning	O
where	O
the	O
instance	O
space	O
consists	O
of	O
discrete	O
combinatorial	O
objects	O
such	O
as	O
strings	O
,	O
trees	O
and	O
graphs	O
.	O
</s>
<s>
Grammatical	B-Algorithm
inference	I-Algorithm
has	O
often	O
been	O
very	O
focused	O
on	O
the	O
problem	O
of	O
learning	O
finite	B-Architecture
state	I-Architecture
machines	I-Architecture
of	O
various	O
types	O
(	O
see	O
the	O
article	O
Induction	O
of	O
regular	B-General_Concept
languages	I-General_Concept
for	O
details	O
on	O
these	O
approaches	O
)	O
,	O
since	O
there	O
have	O
been	O
efficient	O
algorithms	O
for	O
this	O
problem	O
since	O
the	O
1980s	O
.	O
</s>
<s>
Other	O
classes	O
of	O
grammars	O
for	O
which	O
grammatical	B-Algorithm
inference	I-Algorithm
has	O
been	O
studied	O
are	O
combinatory	O
categorial	O
grammars	O
,	O
stochastic	B-General_Concept
context-free	I-General_Concept
grammars	I-General_Concept
,	O
contextual	O
grammars	O
and	O
pattern	O
languages	O
.	O
</s>
<s>
There	O
is	O
a	O
wide	O
variety	O
of	O
methods	O
for	O
grammatical	B-Algorithm
inference	I-Algorithm
.	O
</s>
<s>
For	O
approaches	O
to	O
infer	O
subclasses	O
of	O
regular	B-General_Concept
languages	I-General_Concept
in	O
particular	O
,	O
see	O
Induction	O
of	O
regular	B-General_Concept
languages	I-General_Concept
.	O
</s>
<s>
A	O
more	O
recent	O
textbook	O
is	O
de	O
la	O
Higuera	O
(	O
2010	O
)	O
,	O
which	O
covers	O
the	O
theory	O
of	O
grammatical	B-Algorithm
inference	I-Algorithm
of	O
regular	B-General_Concept
languages	I-General_Concept
and	O
finite	B-Architecture
state	I-Architecture
automata	I-Architecture
.	O
</s>
<s>
D'Ulizia	O
,	O
Ferri	O
and	O
Grifoni	O
provide	O
a	O
survey	O
that	O
explores	O
grammatical	B-Algorithm
inference	I-Algorithm
methods	O
for	O
natural	O
languages	O
.	O
</s>
<s>
This	O
particular	O
approach	O
can	O
be	O
characterized	O
as	O
"	O
hypothesis	O
testing	O
"	O
and	O
bears	O
some	O
similarity	O
to	O
Mitchel	O
's	O
version	B-General_Concept
space	I-General_Concept
algorithm	O
.	O
</s>
<s>
Grammatical	B-Algorithm
induction	I-Algorithm
using	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
is	O
the	O
process	O
of	O
evolving	O
a	O
representation	O
of	O
the	O
grammar	O
of	O
a	O
target	O
language	O
through	O
some	O
evolutionary	O
process	O
.	O
</s>
<s>
Formal	O
grammars	O
can	O
easily	O
be	O
represented	O
as	O
tree	B-Application
structures	I-Application
of	O
production	O
rules	O
that	O
can	O
be	O
subjected	O
to	O
evolutionary	O
operators	O
.	O
</s>
<s>
Algorithms	O
of	O
this	O
sort	O
stem	O
from	O
the	O
genetic	B-Algorithm
programming	I-Algorithm
paradigm	O
pioneered	O
by	O
John	O
Koza	O
.	O
</s>
<s>
Koza	O
represented	O
Lisp	B-Language
programs	O
as	O
trees	O
.	O
</s>
<s>
Fitness	O
is	O
measured	O
by	O
scoring	O
the	O
output	O
from	O
the	O
functions	O
of	O
the	O
Lisp	B-Language
code	O
.	O
</s>
<s>
Similar	O
analogues	O
between	O
the	O
tree	O
structured	O
lisp	B-Language
representation	O
and	O
the	O
representation	O
of	O
grammars	O
as	O
trees	O
,	O
made	O
the	O
application	O
of	O
genetic	B-Algorithm
programming	I-Algorithm
techniques	O
possible	O
for	O
grammar	B-Algorithm
induction	I-Algorithm
.	O
</s>
<s>
In	O
the	O
case	O
of	O
grammar	B-Algorithm
induction	I-Algorithm
,	O
the	O
transplantation	O
of	O
sub-trees	O
corresponds	O
to	O
the	O
swapping	O
of	O
production	O
rules	O
that	O
enable	O
the	O
parsing	O
of	O
phrases	O
from	O
some	O
language	O
.	O
</s>
<s>
Its	O
parent	B-Application
nodes	I-Application
corresponds	O
to	O
a	O
non-terminal	O
symbol	O
(	O
e.g.	O
</s>
<s>
Ultimately	O
,	O
the	O
root	B-Application
node	I-Application
might	O
correspond	O
to	O
a	O
sentence	O
non-terminal	O
.	O
</s>
<s>
Like	O
all	O
greedy	B-Algorithm
algorithms	I-Algorithm
,	O
greedy	O
grammar	B-Algorithm
inference	I-Algorithm
algorithms	O
make	O
,	O
in	O
iterative	O
manner	O
,	O
decisions	O
that	O
seem	O
to	O
be	O
the	O
best	O
at	O
that	O
stage	O
.	O
</s>
<s>
Because	O
there	O
are	O
several	O
ways	O
to	O
define	O
'	O
the	O
stage	O
 '	O
and	O
'	O
the	O
best	O
 '	O
,	O
there	O
are	O
also	O
several	O
greedy	O
grammar	B-Algorithm
inference	I-Algorithm
algorithms	O
.	O
</s>
<s>
Lempel-Ziv-Welch	B-Algorithm
algorithm	I-Algorithm
creates	O
a	O
context-free	O
grammar	O
in	O
a	O
deterministic	O
way	O
such	O
that	O
it	O
is	O
necessary	O
to	O
store	O
only	O
the	O
start	O
rule	O
of	O
the	O
generated	O
grammar	O
.	O
</s>
<s>
Sequitur	B-Algorithm
and	O
its	O
modifications	O
.	O
</s>
<s>
Byte	B-Algorithm
pair	I-Algorithm
encoding	I-Algorithm
and	O
its	O
optimizations	O
.	O
</s>
<s>
Pattern	B-General_Concept
theory	I-General_Concept
,	O
formulated	O
by	O
Ulf	O
Grenander	O
,	O
is	O
a	O
mathematical	O
formalism	O
to	O
describe	O
knowledge	O
of	O
the	O
world	O
as	O
patterns	O
.	O
</s>
<s>
It	O
differs	O
from	O
other	O
approaches	O
to	O
artificial	B-Application
intelligence	I-Application
in	O
that	O
it	O
does	O
not	O
begin	O
by	O
prescribing	O
algorithms	O
and	O
machinery	O
to	O
recognize	O
and	O
classify	O
patterns	O
;	O
rather	O
,	O
it	O
prescribes	O
a	O
vocabulary	O
to	O
articulate	O
and	O
recast	O
the	O
pattern	O
concepts	O
in	O
precise	O
language	O
.	O
</s>
<s>
Broad	O
in	O
its	O
mathematical	O
coverage	O
,	O
pattern	B-General_Concept
theory	I-General_Concept
spans	O
algebra	O
and	O
statistics	O
,	O
as	O
well	O
as	O
local	O
topological	O
and	O
global	O
entropic	O
properties	O
.	O
</s>
<s>
The	O
principle	O
of	O
grammar	B-Algorithm
induction	I-Algorithm
has	O
been	O
applied	O
to	O
other	O
aspects	O
of	O
natural	B-Language
language	I-Language
processing	I-Language
,	O
and	O
has	O
been	O
applied	O
(	O
among	O
many	O
other	O
problems	O
)	O
to	O
semantic	B-Application
parsing	I-Application
,	O
natural	B-General_Concept
language	I-General_Concept
understanding	I-General_Concept
,	O
example-based	B-General_Concept
translation	I-General_Concept
,	O
language	O
acquisition	O
,	O
grammar-based	O
compression	O
,	O
and	O
anomaly	B-Algorithm
detection	I-Algorithm
.	O
</s>
