<s>
A	O
tree-walking	B-Application
automaton	I-Application
(	O
TWA	O
)	O
is	O
a	O
type	O
of	O
finite	B-Architecture
automaton	I-Architecture
that	O
deals	O
with	O
tree	B-Data_Structure
structures	I-Data_Structure
rather	O
than	O
strings	O
.	O
</s>
<s>
For	O
a	O
different	O
notion	O
of	O
tree	B-Application
automaton	I-Application
,	O
closely	O
related	O
to	O
regular	O
tree	B-Application
languages	I-Application
,	O
see	O
branching	B-Application
automaton	I-Application
.	O
</s>
<s>
All	O
trees	B-Application
are	O
assumed	O
to	O
be	O
binary	O
,	O
with	O
labels	O
from	O
a	O
fixed	O
alphabet	O
Σ	O
.	O
</s>
<s>
Informally	O
,	O
a	O
tree-walking	B-Application
automaton	I-Application
(	O
TWA	O
)	O
A	O
is	O
a	O
finite	B-Architecture
state	I-Architecture
device	I-Architecture
that	O
walks	O
over	O
an	O
input	O
tree	O
in	O
a	O
sequential	O
manner	O
.	O
</s>
<s>
A	O
TWA	O
accepts	O
a	O
tree	O
if	O
it	O
enters	O
an	O
accepting	B-Architecture
state	I-Architecture
,	O
and	O
rejects	O
if	O
its	O
enters	O
a	O
rejecting	O
state	O
or	O
makes	O
an	O
infinite	O
loop	O
.	O
</s>
<s>
A	O
simple	O
example	O
of	O
a	O
tree-walking	B-Application
automaton	I-Application
is	O
a	O
TWA	O
that	O
performs	O
depth-first	B-Algorithm
search	I-Algorithm
(	O
DFS	O
)	O
on	O
the	O
input	O
tree	O
.	O
</s>
<s>
Unlike	O
branching	B-Application
automata	I-Application
,	O
tree-walking	O
automata	O
are	O
difficult	O
to	O
analyze	O
:	O
even	O
simple	O
properties	O
are	O
nontrivial	O
to	O
prove	O
.	O
</s>
<s>
the	O
set	O
of	O
languages	O
recognized	O
by	O
TWA	O
is	O
strictly	O
contained	O
in	O
regular	O
tree	B-Application
languages	I-Application
(	O
)	O
,	O
i.e.	O
</s>
<s>
there	O
exist	O
regular	O
languages	O
that	O
are	O
not	O
recognized	O
by	O
any	O
tree-walking	B-Application
automaton	I-Application
,	O
see	O
Bojańczyk	O
and	O
Colcombet	O
.	O
</s>
