<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
clock	O
is	O
a	O
mathematical	O
object	O
used	O
to	O
model	O
time	O
.	O
</s>
<s>
Those	O
clocks	O
are	O
used	O
in	O
the	O
definition	O
of	O
timed	B-Application
automaton	I-Application
,	O
signal	B-Application
automaton	I-Application
,	O
timed	B-Application
propositional	I-Application
temporal	I-Application
logic	I-Application
and	O
clock	O
temporal	O
logic	O
.	O
</s>
<s>
They	O
are	O
also	O
used	O
in	O
programs	O
such	O
as	O
UPPAAL	B-Application
which	O
implement	O
timed	B-Application
automata	I-Application
.	O
</s>
<s>
The	O
program	O
UPPAAL	B-Application
introduce	O
the	O
notion	O
of	O
inactive	O
clocks	O
.	O
</s>
<s>
For	O
example	O
,	O
UPPAAL	B-Application
supports	O
Boolean	O
variables	O
directly	O
.	O
</s>
<s>
Timed	B-Application
automata	I-Application
and	O
signal	B-Application
automata	I-Application
can	O
encode	O
a	O
Boolean	O
value	O
in	O
their	O
locations	O
.	O
</s>
<s>
In	O
timed	B-Application
propositional	I-Application
temporal	I-Application
logic	I-Application
,	O
the	O
formula	O
,	O
which	O
restart	O
and	O
then	O
evaluates	O
,	O
can	O
be	O
replaced	O
by	O
the	O
formula	O
,	O
where	O
and	O
are	O
copies	O
of	O
the	O
formulas	O
,	O
where	O
are	O
replaced	O
by	O
the	O
true	O
and	O
false	O
constant	O
respectively	O
.	O
</s>
<s>
A	O
region'''	O
is	O
a	O
non-empty	O
zone	O
in	O
which	O
no	O
constraint	O
greater	O
than	O
are	O
used	O
,	O
and	O
furthermore	O
,	O
such	O
that	O
it	O
is	O
minimal	O
for	O
the	O
inclusion	O
.	O
</s>
