<s>
In	O
model	B-Application
checking	I-Application
,	O
the	O
Metric	B-Application
Interval	I-Application
Temporal	I-Application
Logic	I-Application
(	O
MITL	B-Application
)	O
is	O
a	O
fragment	O
of	O
Metric	B-Application
Temporal	I-Application
Logic	I-Application
(	O
MTL	O
)	O
.	O
</s>
<s>
This	O
fragment	O
is	O
often	O
preferred	O
to	O
MTL	O
because	O
some	O
problems	O
that	O
are	O
undecidable	O
for	O
MTL	O
become	O
decidable	O
for	O
MITL	B-Application
.	O
</s>
<s>
A	O
MITL	B-Application
formula	O
is	O
an	O
MTL	O
formula	O
,	O
such	O
that	O
each	O
set	O
of	O
reals	O
used	O
in	O
subscript	O
are	O
intervals	O
,	O
which	O
are	O
not	O
singletons	O
,	O
and	O
whose	O
bounds	O
are	O
either	O
a	O
natural	O
number	O
or	O
are	O
infinite	O
.	O
</s>
<s>
This	O
is	O
impossible	O
in	O
MITL	B-Application
.	O
</s>
<s>
Instead	O
,	O
MITL	B-Application
can	O
say	O
T	O
:	O
"	O
P	O
held	O
between	O
9	O
and	O
10	O
time	O
units	O
ago	O
"	O
.	O
</s>
<s>
Since	O
MITL	B-Application
can	O
express	O
T	O
but	O
not	O
S	O
,	O
in	O
a	O
sense	O
,	O
MITL	B-Application
is	O
a	O
restriction	O
of	O
MTL	O
which	O
allows	O
only	O
less	O
precise	O
statements	O
.	O
</s>
<s>
Let	O
us	O
now	O
consider	O
a	O
system	O
,	O
such	O
as	O
a	O
timed	B-Application
automaton	I-Application
or	O
a	O
signal	B-Application
automaton	I-Application
,	O
which	O
want	O
to	O
know	O
at	O
each	O
instant	O
whether	O
S	O
holds	O
or	O
not	O
.	O
</s>
<s>
One	O
of	O
the	O
main	O
advantage	O
of	O
MITL	B-Application
is	O
that	O
each	O
operator	O
has	O
the	O
bounded	O
variability	O
property	O
.	O
</s>
<s>
Thus	O
this	O
system	O
must	O
recall	O
at	O
most	O
21	O
events	O
,	O
and	O
hence	O
can	O
be	O
implemented	O
as	O
a	O
timed	B-Application
automaton	I-Application
or	O
a	O
signal	B-Application
automaton	I-Application
.	O
</s>
<s>
Examples	O
of	O
MITL	B-Application
formulas	O
:	O
</s>
<s>
The	O
fragment	O
Closed-MITL	O
contains	O
the	O
negation	O
of	O
formulas	O
of	O
Open-MITL	O
.	O
</s>
<s>
The	O
fragment	O
Coflat-MITL	O
contains	O
the	O
negation	O
of	O
formulas	O
of	O
Flat-MITL	O
.	O
</s>
<s>
Over	O
signals	B-Application
,	O
MITL0	O
is	O
as	O
expressive	O
as	O
MITL	B-Application
.	O
</s>
<s>
This	O
can	O
be	O
proven	O
by	O
applying	O
the	O
following	O
rewriting	O
rules	O
to	O
a	O
MITL	B-Application
formula	O
.	O
</s>
<s>
Contrary	O
to	O
the	O
case	O
of	O
signals	B-Application
,	O
MITL	B-Application
is	O
strictly	O
more	O
expressive	O
than	O
MITL0	O
,	O
∞	O
.	O
</s>
<s>
The	O
problem	O
of	O
deciding	O
whether	O
a	O
MITL	B-Application
formula	O
is	O
satisfiable	O
over	O
a	O
signal	O
is	O
in	O
PSPACE-complete	O
.	O
</s>
