<s>
In	O
model	B-Application
checking	I-Application
,	O
a	O
subfield	O
of	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
timed	B-Application
word	I-Application
is	O
an	O
extension	O
of	O
the	O
notion	O
of	O
words	O
,	O
in	O
a	O
formal	O
language	O
,	O
in	O
which	O
each	O
letter	O
is	O
associated	O
with	O
a	O
positive	O
time	O
tag	O
.	O
</s>
<s>
A	O
timed	O
language	O
is	O
a	O
set	O
of	O
timed	B-Application
words	I-Application
.	O
</s>
<s>
In	O
this	O
case	O
,	O
a	O
timed	B-Application
word	I-Application
is	O
a	O
sequence	O
of	O
actions	O
taken	O
by	O
the	O
elevators	O
and	O
its	O
users	O
,	O
with	O
time	O
stamps	O
to	O
recall	O
those	O
actions	O
.	O
</s>
<s>
The	O
timed	B-Application
word	I-Application
can	O
then	O
be	O
analyzed	O
by	O
formal	O
method	O
to	O
check	O
whether	O
a	O
property	O
such	O
that	O
"	O
each	O
time	O
the	O
elevator	O
is	O
called	O
,	O
it	O
arrives	O
in	O
less	O
than	O
three	O
minutes	O
assuming	O
that	O
no	O
one	O
held	O
the	O
door	O
for	O
more	O
than	O
fifteen	O
seconds	O
"	O
holds	O
.	O
</s>
<s>
A	O
statement	O
such	O
as	O
this	O
one	O
is	O
usually	O
expressed	O
in	O
metric	B-Application
temporal	I-Application
logic	I-Application
,	O
an	O
extension	O
of	O
linear	O
temporal	O
logic	O
which	O
allow	O
to	O
express	O
time	O
constraints	O
.	O
</s>
<s>
A	O
timed-word	B-Application
may	O
be	O
passed	O
to	O
a	O
model	O
,	O
such	O
as	O
a	O
timed	B-Application
automaton	I-Application
,	O
which	O
will	O
decide	O
,	O
given	O
the	O
letters	O
or	O
actions	O
which	O
already	O
occurred	O
,	O
what	O
is	O
the	O
next	O
action	O
which	O
should	O
be	O
done	O
.	O
</s>
<s>
Then	O
a	O
program	O
may	O
test	O
this	O
timed	B-Application
automaton	I-Application
and	O
check	O
the	O
above-mentioned	O
property	O
.	O
</s>
<s>
That	O
is	O
,	O
it	O
will	O
try	O
to	O
generate	O
a	O
timed-word	B-Application
in	O
which	O
the	O
door	O
is	O
never	O
held	O
open	O
for	O
more	O
than	O
fifteen	O
seconds	O
,	O
and	O
in	O
which	O
a	O
user	O
must	O
wait	O
more	O
than	O
three	O
minutes	O
after	O
calling	O
the	O
elevator	O
.	O
</s>
<s>
Given	O
an	O
alphabet	O
A	O
,	O
a	O
timed	B-Application
word	I-Application
is	O
a	O
sequence	O
,	O
finite	O
or	O
infinite	O
with	O
,	O
with	O
for	O
each	O
integer	O
.	O
</s>
<s>
If	O
the	O
sequence	O
is	O
infinite	O
but	O
the	O
sequence	O
of	O
is	O
bounded	O
,	O
then	O
this	O
word	O
is	O
said	O
to	O
be	O
a	O
Zeno	O
timed	B-Application
word	I-Application
,	O
in	O
reference	O
to	O
the	O
Zeno	O
's	O
paradoxes	O
where	O
an	O
infinite	O
number	O
of	O
action	O
occurs	O
in	O
a	O
finite	O
time	O
.	O
</s>
