<s>
finite	O
state	O
model	B-Application
checking	I-Application
needs	O
to	O
find	O
a	O
Büchi	B-General_Concept
automaton	I-General_Concept
(	O
BA	O
)	O
equivalent	O
to	O
a	O
given	O
linear	O
temporal	O
logic	O
(	O
LTL	O
)	O
formula	O
,	O
i.e.	O
,	O
such	O
that	O
the	O
LTL	O
formula	O
and	O
the	O
BA	O
recognize	O
the	O
same	O
ω-language	O
.	O
</s>
<s>
The	O
first	O
step	O
produces	O
a	O
generalized	B-Application
Büchi	I-Application
automaton	I-Application
(	O
GBA	B-Application
)	O
from	O
a	O
LTL	O
formula	O
.	O
</s>
<s>
The	O
second	O
step	O
translates	O
this	O
GBA	B-Application
into	O
a	O
BA	O
,	O
which	O
involves	O
a	O
relatively	O
easy	O
construction	O
.	O
</s>
<s>
The	O
algorithms	O
for	O
transforming	O
LTL	O
to	O
GBA	B-Application
differ	O
in	O
their	O
construction	O
strategies	O
but	O
they	O
all	O
have	O
a	O
common	O
underlying	O
principle	O
,	O
i.e.	O
,	O
each	O
state	O
in	O
the	O
constructed	O
automaton	O
represents	O
a	O
set	O
of	O
LTL	O
formulas	O
that	O
are	O
expected	O
to	O
be	O
satisfied	O
by	O
the	O
remaining	O
input	O
word	O
after	O
occurrence	O
of	O
the	O
state	O
during	O
a	O
run	O
.	O
</s>
<s>
The	O
subsets	O
of	O
cl( f )	O
are	O
going	O
to	O
serve	O
as	O
states	O
of	O
the	O
equivalent	O
GBA	B-Application
.	O
</s>
<s>
We	O
aim	O
to	O
construct	O
the	O
GBA	B-Application
such	O
that	O
if	O
a	O
state	O
corresponds	O
to	O
a	O
subset	O
M	O
⊆	O
cl( f )	O
then	O
the	O
GBA	B-Application
has	O
an	O
accepting	O
run	O
starting	O
from	O
the	O
state	O
for	O
a	O
word	O
if	O
and	O
only	O
if	O
the	O
word	O
satisfies	O
every	O
formula	O
in	O
M	O
and	O
violates	O
every	O
formula	O
in	O
cl( f )	O
\	O
M	O
.	O
</s>
<s>
We	O
are	O
going	O
to	O
use	O
only	O
cs( f )	O
as	O
the	O
states	O
of	O
GBA	B-Application
.	O
</s>
<s>
In	O
the	O
second	O
step	O
,	O
it	O
builds	O
a	O
labeled	B-Application
generalized	I-Application
Büchi	I-Application
automaton	I-Application
(	O
LGBA	O
)	O
by	O
defining	O
nodes	O
of	O
the	O
graph	O
as	O
states	O
and	O
directed	O
edges	O
as	O
transitions	O
.	O
</s>
<s>
-	O
LTL2TGBA	O
translator	O
included	O
in	O
Object-oriented	O
model	B-Application
checking	I-Application
library	O
SPOT	O
.	O
</s>
