<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
deterministic	B-General_Concept
acyclic	I-General_Concept
finite	I-General_Concept
state	I-General_Concept
automaton	I-General_Concept
(	O
DAFSA	B-General_Concept
)	O
,	O
</s>
<s>
is	O
a	O
data	B-General_Concept
structure	I-General_Concept
that	O
represents	O
a	O
set	O
of	O
strings	O
,	O
and	O
allows	O
for	O
a	O
query	O
operation	O
that	O
tests	O
whether	O
a	O
given	O
string	O
belongs	O
to	O
the	O
set	O
in	O
time	O
proportional	O
to	O
its	O
length	O
.	O
</s>
<s>
Algorithms	O
exist	O
to	O
construct	O
and	O
maintain	O
such	O
automata	B-Application
,	O
while	O
keeping	O
them	O
minimal	B-General_Concept
.	O
</s>
<s>
A	O
DAFSA	B-General_Concept
is	O
a	O
special	O
case	O
of	O
a	O
finite	O
state	O
recognizer	O
that	O
takes	O
the	O
form	O
of	O
a	O
directed	O
acyclic	O
graph	O
with	O
a	O
single	O
source	O
vertex	O
(	O
a	O
vertex	O
with	O
no	O
incoming	O
edges	O
)	O
,	O
in	O
which	O
each	O
edge	O
of	O
the	O
graph	O
is	O
labeled	O
by	O
a	O
letter	O
or	O
symbol	O
,	O
and	O
in	O
which	O
each	O
vertex	O
has	O
at	O
most	O
one	O
outgoing	O
edge	O
for	O
each	O
possible	O
letter	O
or	O
symbol	O
.	O
</s>
<s>
The	O
strings	O
represented	O
by	O
the	O
DAFSA	B-General_Concept
are	O
formed	O
by	O
the	O
symbols	O
on	O
paths	O
in	O
the	O
graph	O
from	O
the	O
source	O
vertex	O
to	O
any	O
sink	O
vertex	O
(	O
a	O
vertex	O
with	O
no	O
outgoing	O
edges	O
)	O
.	O
</s>
<s>
In	O
fact	O
,	O
a	O
deterministic	B-General_Concept
finite	I-General_Concept
state	I-General_Concept
automaton	I-General_Concept
is	O
acyclic	O
if	O
and	O
only	O
if	O
it	O
recognizes	O
a	O
finite	O
set	O
of	O
strings	O
.	O
</s>
<s>
By	O
allowing	O
the	O
same	O
vertices	O
to	O
be	O
reached	O
by	O
multiple	O
paths	O
,	O
a	O
DAFSA	B-General_Concept
may	O
use	O
significantly	O
fewer	O
vertices	O
than	O
the	O
strongly	O
related	O
trie	B-General_Concept
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
A	O
trie	B-General_Concept
for	O
those	O
four	O
words	O
would	O
have	O
12	O
vertices	O
,	O
one	O
for	O
each	O
of	O
the	O
strings	O
formed	O
as	O
a	O
prefix	O
of	O
one	O
of	O
these	O
words	O
,	O
or	O
for	O
one	O
of	O
the	O
words	O
followed	O
by	O
the	O
end-of-string	O
marker	O
.	O
</s>
<s>
However	O
,	O
a	O
DAFSA	B-General_Concept
can	O
represent	O
these	O
same	O
four	O
words	O
using	O
only	O
six	O
vertices	O
vi	O
for	O
0≤i≤5	O
,	O
and	O
the	O
following	O
edges	O
:	O
an	O
edge	O
from	O
v0	O
to	O
v1	O
labeled	O
"	O
t	O
"	O
,	O
two	O
edges	O
from	O
v1	O
to	O
v2	O
labeled	O
"	O
a	O
"	O
and	O
"	O
o	O
"	O
,	O
an	O
edge	O
from	O
v2	O
to	O
v3	O
labeled	O
"	O
p	O
"	O
,	O
an	O
edge	O
v3	O
to	O
v4	O
labeled	O
"	O
s	O
"	O
,	O
and	O
edges	O
from	O
v3	O
and	O
v4	O
to	O
v5	O
labeled	O
with	O
the	O
end-of-string	O
marker	O
.	O
</s>
<s>
There	O
is	O
a	O
tradeoff	O
between	O
memory	O
and	O
functionality	O
,	O
because	O
a	O
standard	O
DAFSA	B-General_Concept
can	O
tell	O
you	O
if	O
a	O
word	O
exists	O
within	O
it	O
,	O
but	O
it	O
cannot	O
point	O
you	O
to	O
auxiliary	O
information	O
about	O
that	O
word	O
,	O
whereas	O
a	O
trie	B-General_Concept
can	O
.	O
</s>
<s>
The	O
primary	O
difference	O
between	O
DAFSA	B-General_Concept
and	O
trie	B-General_Concept
is	O
the	O
elimination	O
of	O
suffix	O
and	O
infix	O
redundancy	O
in	O
storing	O
strings	O
.	O
</s>
<s>
The	O
trie	B-General_Concept
eliminates	O
prefix	O
redundancy	O
since	O
all	O
common	O
prefixes	O
are	O
shared	O
between	O
strings	O
,	O
such	O
as	O
between	O
doctors	O
and	O
doctorate	O
the	O
doctor	O
prefix	O
is	O
shared	O
.	O
</s>
<s>
In	O
a	O
DAFSA	B-General_Concept
common	O
suffixes	O
are	O
also	O
shared	O
,	O
for	O
words	O
that	O
have	O
the	O
same	O
set	O
of	O
possible	O
suffixes	O
as	O
each	O
other	O
.	O
</s>
<s>
Because	O
the	O
terminal	O
nodes	O
of	O
a	O
DAFSA	B-General_Concept
can	O
be	O
reached	O
by	O
multiple	O
paths	O
,	O
a	O
DAFSA	B-General_Concept
cannot	O
directly	O
store	O
auxiliary	O
information	O
relating	O
to	O
each	O
path	O
,	O
e.g.	O
</s>
