<s>
In	O
automata	B-Application
theory	I-Application
,	O
a	O
semi-deterministic	B-Application
Büchi	I-Application
automaton	I-Application
(	O
also	O
known	O
as	O
Büchi	B-General_Concept
automaton	I-General_Concept
deterministic	O
in	O
the	O
limit	O
,	O
or	O
limit-deterministic	O
Büchi	B-General_Concept
automaton	I-General_Concept
)	O
is	O
a	O
special	O
type	O
of	O
Büchi	B-General_Concept
automaton	I-General_Concept
.	O
</s>
<s>
For	O
every	O
Büchi	B-General_Concept
automaton	I-General_Concept
,	O
a	O
semi-deterministic	B-Application
Büchi	I-Application
automaton	I-Application
can	O
be	O
constructed	O
such	O
that	O
both	O
recognize	O
the	O
same	O
ω-language	O
.	O
</s>
<s>
But	O
,	O
a	O
deterministic	O
Büchi	B-General_Concept
automaton	I-General_Concept
may	O
not	O
exist	O
for	O
the	O
same	O
ω-language	O
.	O
</s>
<s>
In	O
standard	O
model	B-Application
checking	I-Application
against	O
linear	O
temporal	O
logic	O
(	O
LTL	O
)	O
properties	O
,	O
it	O
is	O
sufficient	O
to	O
translate	O
an	O
LTL	O
formula	O
into	O
a	O
non-deterministic	O
Büchi	B-General_Concept
automaton	I-General_Concept
.	O
</s>
<s>
But	O
,	O
in	O
probabilistic	O
model	B-Application
checking	I-Application
,	O
LTL	O
formulae	O
are	O
typically	O
translated	O
into	O
deterministic	O
Rabin	O
automata	O
(	O
DRA	O
)	O
,	O
as	O
for	O
instance	O
in	O
the	O
PRISM	B-Application
tool	O
.	O
</s>
<s>
Indeed	O
,	O
semi-deterministic	O
Büchi	B-General_Concept
automata	I-General_Concept
are	O
sufficient	O
in	O
probabilistic	O
model	B-Application
checking	I-Application
.	O
</s>
<s>
A	O
Büchi	B-General_Concept
automaton	I-General_Concept
(	O
Q	O
,	O
Σ	O
,	O
∆	O
,	O
Q0	O
,	O
F	O
)	O
is	O
called	O
semi-deterministic	O
if	O
Q	O
is	O
the	O
union	O
of	O
two	O
disjoint	O
subsets	O
N	O
and	O
D	O
such	O
that	O
F⊆D	O
and	O
,	O
for	O
every	O
d∈D	O
,	O
automaton	O
(	O
D	O
,	O
Σ	O
,	O
∆	O
,	O
{	O
d}	O
,	O
F	O
)	O
is	O
deterministic	O
.	O
</s>
<s>
Any	O
given	O
Büchi	B-General_Concept
automaton	I-General_Concept
can	O
be	O
transformed	O
into	O
a	O
semi-deterministic	B-Application
Büchi	I-Application
automaton	I-Application
that	O
recognizes	O
the	O
same	O
language	O
,	O
using	O
following	O
construction	O
.	O
</s>
<s>
Suppose	O
A	O
=(	O
Q	O
,	O
Σ	O
,	O
∆	O
,	O
Q0	O
,	O
F	O
)	O
is	O
a	O
Büchi	B-General_Concept
automaton	I-General_Concept
.	O
</s>
<s>
By	O
construction	O
,	O
A	O
 '	O
is	O
a	O
semi-deterministic	B-Application
Büchi	I-Application
automaton	I-Application
.	O
</s>
