<s>
In	O
automata	B-Application
theory	I-Application
,	O
a	O
generalized	B-Application
Büchi	I-Application
automaton	I-Application
is	O
a	O
variant	O
of	O
a	O
Büchi	B-General_Concept
automaton	I-General_Concept
.	O
</s>
<s>
The	O
difference	O
with	O
the	O
Büchi	B-General_Concept
automaton	I-General_Concept
is	O
the	O
accepting	O
condition	O
,	O
which	O
is	O
determined	O
by	O
a	O
set	O
of	O
sets	O
of	O
states	O
.	O
</s>
<s>
Generalized	O
Büchi	B-General_Concept
automata	I-General_Concept
are	O
equivalent	O
in	O
expressive	O
power	O
to	O
Büchi	B-General_Concept
automata	I-General_Concept
;	O
a	O
transformation	O
is	O
given	O
here	O
.	O
</s>
<s>
In	O
formal	O
verification	O
,	O
the	O
model	B-Application
checking	I-Application
method	O
needs	O
to	O
obtain	O
an	O
automaton	O
from	O
a	O
LTL	O
formula	O
that	O
specifies	O
the	O
desired	O
program	O
property	O
.	O
</s>
<s>
into	O
a	O
generalized	B-Application
Büchi	I-Application
automaton	I-Application
.	O
</s>
<s>
The	O
notion	O
of	O
generalized	B-Application
Büchi	I-Application
automaton	I-Application
was	O
introduced	O
specifically	O
for	O
this	O
translation	O
.	O
</s>
<s>
Formally	O
,	O
a	O
generalized	B-Application
Büchi	I-Application
automaton	I-Application
is	O
a	O
tuple	O
A	O
=(	O
Q	O
,	O
Σ	O
,	O
Δ	O
,	O
Q0	O
,	O
)	O
that	O
consists	O
of	O
the	O
following	O
components	O
:	O
</s>
<s>
For	O
more	O
comprehensive	O
formalism	O
see	O
also	O
ω-automaton	B-General_Concept
.	O
</s>
<s>
Labeled	B-Application
generalized	I-Application
Büchi	I-Application
automaton	I-Application
is	O
another	O
variation	O
in	O
which	O
input	O
is	O
matched	O
to	O
labels	O
on	O
the	O
states	O
rather	O
than	O
on	O
the	O
transitions	O
.	O
</s>
<s>
Formally	O
,	O
a	O
labeled	B-Application
generalized	I-Application
Büchi	I-Application
automaton	I-Application
is	O
a	O
tuple	O
A	O
=(	O
Q	O
,	O
Σ	O
,	O
L	O
,	O
Δ	O
,	O
Q0	O
,	O
)	O
that	O
consists	O
of	O
the	O
following	O
components	O
:	O
</s>
