<s>
In	O
automata	B-Application
theory	I-Application
,	O
a	O
tree	O
is	O
a	O
particular	O
way	O
of	O
representing	O
a	O
tree	O
structure	O
as	O
sequences	O
of	O
natural	O
numbers	O
.	O
</s>
<s>
For	O
example	O
,	O
each	O
node	O
of	O
the	O
tree	O
is	O
a	O
word	O
over	O
set	O
of	O
natural	O
numbers	O
(	O
)	O
,	O
which	O
helps	O
this	O
definition	O
to	O
be	O
used	O
in	O
automata	B-Application
theory	I-Application
.	O
</s>
<s>
In	O
the	O
case	O
of	O
ranked	B-Application
alphabets	I-Application
,	O
an	O
extra	O
function	O
Ar	O
:	O
Σ	O
→	O
is	O
defined	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
above	O
definition	O
is	O
used	O
in	O
the	O
definition	O
of	O
an	O
infinite	B-Application
tree	I-Application
automaton	I-Application
.	O
</s>
