<s>
A	O
filtered-popping	B-General_Concept
recursive	I-General_Concept
transition	I-General_Concept
network	I-General_Concept
(	O
FPRTN	B-General_Concept
)	O
,	O
or	O
simply	O
filtered-popping	B-General_Concept
network	I-General_Concept
(	O
FPN	O
)	O
,	O
is	O
a	O
recursive	B-Application
transition	I-Application
network	I-Application
(	O
RTN	B-Application
)	O
extended	O
with	O
a	O
map	O
of	O
states	O
to	O
keys	O
where	O
returning	O
from	O
a	O
subroutine	O
jump	O
requires	O
the	O
acceptor	O
and	O
return	O
states	O
to	O
be	O
mapped	O
to	O
the	O
same	O
key	O
.	O
</s>
<s>
RTNs	B-Application
are	O
finite-state	B-Architecture
machines	I-Architecture
that	O
can	O
be	O
seen	O
as	O
finite-state	B-Architecture
automata	I-Architecture
extended	O
with	O
a	O
stack	B-Application
of	O
return	O
states	O
;	O
as	O
well	O
as	O
consuming	O
transitions	O
and	O
-transitions	O
,	O
RTNs	B-Application
may	O
define	O
call	O
transitions	O
.	O
</s>
<s>
These	O
transitions	O
perform	O
a	O
subroutine	O
jump	O
by	O
pushing	O
the	O
transition	O
's	O
target	O
state	O
onto	O
the	O
stack	B-Application
and	O
bringing	O
the	O
machine	O
to	O
the	O
called	O
state	O
.	O
</s>
<s>
Each	O
time	O
an	O
acceptor	O
state	O
is	O
reached	O
,	O
the	O
return	O
state	O
at	O
the	O
top	O
of	O
the	O
stack	B-Application
is	O
popped	O
out	O
,	O
provided	O
that	O
the	O
stack	B-Application
is	O
not	O
empty	O
,	O
and	O
the	O
machine	O
is	O
brought	O
to	O
this	O
state	O
.	O
</s>
<s>
Throughout	O
this	O
article	O
we	O
refer	O
to	O
filtered-popping	B-General_Concept
recursive	I-General_Concept
transition	I-General_Concept
networks	I-General_Concept
as	O
FPNs	O
,	O
though	O
this	O
acronym	O
is	O
ambiguous	O
(	O
e.g.	O
</s>
<s>
Filtered-popping	B-General_Concept
networks	I-General_Concept
and	O
FPRTNs	B-General_Concept
are	O
unambiguous	O
alternatives	O
.	O
</s>
<s>
for	O
each	O
pair	O
of	O
states	O
the	O
FPN	O
implicitly	O
defines	O
a	O
pop	O
transition	O
that	O
brings	O
the	O
machine	O
from	O
to	O
by	O
popping	O
from	O
the	O
stack	B-Application
iff	O
is	O
the	O
state	O
at	O
the	O
top	O
of	O
the	O
stack	B-Application
and	O
.	O
</s>
<s>
Push	O
transitions	O
initialize	O
subroutine	O
jumps	O
and	O
pop	O
transitions	O
are	O
equivalent	O
to	O
return	B-Language
statements	I-Language
.	O
</s>
<s>
A	O
(	O
natural	O
language	O
)	O
text	O
can	O
be	O
enriched	O
with	O
meta-information	O
by	O
the	O
application	O
of	O
a	O
RTN	B-Application
with	O
output	O
;	O
for	O
instance	O
,	O
a	O
RTN	B-Application
inserting	O
XML	B-Protocol
tags	O
can	O
be	O
used	O
for	O
transforming	O
a	O
plain	O
text	O
into	O
a	O
structured	O
XML	B-Protocol
document	I-Protocol
.	O
</s>
<s>
A	O
RTN	B-Application
with	O
output	O
representing	O
a	O
natural	O
language	O
grammar	O
would	O
delimit	O
and	O
add	O
the	O
syntactic	O
structure	O
of	O
each	O
text	O
sentence	O
(	O
see	O
parsing	B-Language
)	O
.	O
</s>
<s>
Other	O
RTNs	B-Application
with	O
output	O
could	O
simply	O
mark	O
text	O
segments	O
containing	O
relevant	O
information	O
(	O
see	O
information	B-General_Concept
extraction	I-General_Concept
)	O
.	O
</s>
<s>
The	O
application	O
of	O
a	O
RTN	B-Application
with	O
output	O
representing	O
an	O
ambiguous	O
grammar	O
results	O
in	O
a	O
set	O
of	O
possible	O
translations	O
or	O
interpretations	O
of	O
the	O
input	O
.	O
</s>
<s>
Computing	O
this	O
set	O
has	O
an	O
exponential	O
worst-case	B-General_Concept
cost	I-General_Concept
,	O
even	O
for	O
an	O
Earley	B-Algorithm
parser	I-Algorithm
for	O
RTNs	B-Application
with	O
output	O
,	O
due	O
to	O
cases	O
in	O
which	O
the	O
number	O
of	O
translations	O
increases	O
exponentially	O
w.r.t.	O
</s>
<s>
FPN	O
states	O
correspond	O
to	O
execution	O
states	O
(	O
see	O
instruction	B-General_Concept
steps	I-General_Concept
)	O
of	O
an	O
Earley-parser	O
for	O
RTNs	B-Application
without	O
output	O
,	O
and	O
FPN	O
transitions	O
correspond	O
to	O
possible	O
translations	O
of	O
input	O
symbols	O
.	O
</s>
