<s>
An	O
embedded	B-Application
pushdown	I-Application
automaton	I-Application
or	O
EPDA	O
is	O
a	O
computational	B-Application
model	I-Application
for	O
parsing	O
languages	O
generated	O
by	O
tree-adjoining	O
grammars	O
(	O
TAGs	O
)	O
.	O
</s>
<s>
It	O
is	O
similar	O
to	O
the	O
context-free	O
grammar-parsing	O
pushdown	B-Application
automaton	I-Application
,	O
but	O
instead	O
of	O
using	O
a	O
plain	O
stack	B-Application
to	O
store	O
symbols	O
,	O
it	O
has	O
a	O
stack	B-Application
of	O
iterated	O
stacks	B-Application
that	O
store	O
symbols	O
,	O
giving	O
TAGs	O
a	O
generative	O
capacity	O
between	O
context-free	O
and	O
context-sensitive	O
grammars	O
,	O
or	O
a	O
subset	O
of	O
mildly	O
context-sensitive	O
grammars	O
.	O
</s>
<s>
Embedded	B-Application
pushdown	I-Application
automata	I-Application
should	O
not	O
be	O
confused	O
with	O
nested	B-Application
stack	I-Application
automata	I-Application
which	O
have	O
more	O
computational	O
power	O
.	O
</s>
<s>
An	O
EPDA	O
is	O
a	O
finite	O
state	O
machine	O
with	O
a	O
set	O
of	O
stacks	B-Application
that	O
can	O
be	O
themselves	O
accessed	O
through	O
the	O
embedded	O
stack	B-Application
.	O
</s>
<s>
Each	O
stack	B-Application
contains	O
elements	O
of	O
the	O
stack	B-Application
alphabet	O
,	O
and	O
so	O
we	O
define	O
an	O
element	O
of	O
a	O
stack	B-Application
by	O
,	O
where	O
the	O
star	O
is	O
the	O
Kleene	O
closure	O
of	O
the	O
alphabet	O
.	O
</s>
<s>
Each	O
stack	B-Application
can	O
then	O
be	O
defined	O
in	O
terms	O
of	O
its	O
elements	O
,	O
so	O
we	O
denote	O
the	O
th	O
stack	B-Application
in	O
the	O
automaton	O
using	O
a	O
double-dagger	O
symbol	O
:	O
,	O
where	O
would	O
be	O
the	O
next	O
accessible	O
symbol	O
in	O
the	O
stack	B-Application
.	O
</s>
<s>
The	O
embedded	O
stack	B-Application
of	O
stacks	B-Application
can	O
thus	O
be	O
denoted	O
by	O
.	O
</s>
<s>
is	O
the	O
finite	O
stack	B-Application
alphabet	O
;	O
</s>
<s>
Thus	O
the	O
transition	O
function	O
takes	O
a	O
state	O
,	O
the	O
next	O
symbol	O
of	O
the	O
input	O
string	O
,	O
and	O
the	O
top	O
symbol	O
of	O
the	O
current	O
stack	B-Application
and	O
generates	O
the	O
next	O
state	O
,	O
the	O
stacks	B-Application
to	O
be	O
pushed	O
and	O
popped	O
onto	O
the	O
embedded	O
stack	B-Application
,	O
the	O
pushing	B-Application
and	I-Application
popping	I-Application
of	O
the	O
current	O
stack	B-Application
,	O
and	O
the	O
stacks	B-Application
to	O
be	O
considered	O
the	O
current	O
stacks	B-Application
in	O
the	O
next	O
transition	O
.	O
</s>
<s>
More	O
conceptually	O
,	O
the	O
embedded	O
stack	B-Application
is	O
pushed	O
and	O
popped	O
,	O
the	O
current	O
stack	B-Application
is	O
optionally	O
pushed	O
back	O
onto	O
the	O
embedded	O
stack	B-Application
,	O
and	O
any	O
other	O
stacks	B-Application
one	O
would	O
like	O
are	O
pushed	O
on	O
top	O
of	O
that	O
,	O
with	O
the	O
last	O
stack	B-Application
being	O
the	O
one	O
read	O
from	O
in	O
the	O
next	O
iteration	O
.	O
</s>
<s>
Therefore	O
,	O
stacks	B-Application
can	O
be	O
pushed	O
both	O
above	O
and	O
below	O
the	O
current	O
stack	B-Application
.	O
</s>
<s>
where	O
is	O
the	O
current	O
state	O
,	O
the	O
s	O
are	O
the	O
stacks	B-Application
in	O
the	O
embedded	O
stack	B-Application
,	O
with	O
the	O
current	O
stack	B-Application
,	O
and	O
for	O
an	O
input	O
string	O
,	O
is	O
the	O
portion	O
of	O
the	O
string	O
already	O
processed	O
by	O
the	O
machine	O
and	O
is	O
the	O
portion	O
to	O
be	O
processed	O
,	O
with	O
its	O
head	O
being	O
the	O
current	O
symbol	O
read	O
.	O
</s>
