<s>
In	O
computer	B-General_Concept
science	I-General_Concept
and	O
automata	B-Application
theory	I-Application
,	O
a	O
Weak	B-Application
Büchi	I-Application
automaton	I-Application
is	O
a	O
formalism	O
which	O
represents	O
a	O
set	O
of	O
infinite	O
words	O
.	O
</s>
<s>
A	O
Weak	B-Application
Büchi	I-Application
automaton	I-Application
is	O
a	O
modification	O
of	O
Büchi	B-General_Concept
automaton	I-General_Concept
such	O
that	O
for	O
all	O
pair	O
of	O
states	O
and	O
belonging	O
to	O
the	O
same	O
strongly	O
connected	O
component	O
,	O
is	O
accepting	O
if	O
and	O
only	O
if	O
is	O
accepting	O
.	O
</s>
<s>
A	O
Büchi	B-General_Concept
automaton	I-General_Concept
accepts	O
a	O
word	O
if	O
there	O
exists	O
a	O
run	O
,	O
such	O
that	O
at	O
least	O
one	O
state	O
occurring	O
infinitely	O
often	O
in	O
the	O
final	O
state	O
set	O
.	O
</s>
<s>
For	O
Weak	O
Büchi	B-General_Concept
automata	I-General_Concept
,	O
this	O
condition	O
is	O
equivalent	O
to	O
the	O
existence	O
of	O
a	O
run	O
which	O
ultimately	O
stays	O
in	O
the	O
set	O
of	O
accepting	O
states	O
.	O
</s>
<s>
Weak	O
Büchi	B-General_Concept
automata	I-General_Concept
are	O
strictly	O
less-expressive	O
than	O
Büchi	B-General_Concept
automata	I-General_Concept
and	O
than	O
Co-Büchi	O
automata	O
.	O
</s>
<s>
The	O
deterministic	O
Weak	O
Büchi	B-General_Concept
automata	I-General_Concept
can	O
be	O
minimized	O
in	O
time	O
.	O
</s>
<s>
The	O
languages	O
accepted	O
by	O
Weak	O
Büchi	B-General_Concept
automata	I-General_Concept
are	O
closed	O
under	O
union	O
and	O
intersection	O
but	O
not	O
under	O
complementation	O
.	O
</s>
<s>
For	O
example	O
,	O
can	O
be	O
recognised	O
by	O
a	O
Weak	B-Application
Büchi	I-Application
automaton	I-Application
but	O
its	O
complement	O
cannot	O
.	O
</s>
<s>
Non-deterministic	O
Weak	O
Büchi	B-General_Concept
automata	I-General_Concept
are	O
more	O
expressive	O
than	O
Weak	O
Büchi	B-General_Concept
automata	I-General_Concept
.	O
</s>
<s>
As	O
an	O
example	O
,	O
the	O
language	O
can	O
be	O
decided	O
by	O
a	O
Weak	B-Application
Büchi	I-Application
automaton	I-Application
but	O
by	O
no	O
deterministic	O
Büchi	B-General_Concept
automaton	I-General_Concept
.	O
</s>
