<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
more	O
precisely	O
in	O
automata	B-Application
theory	I-Application
,	O
a	O
recognizable	B-Application
set	I-Application
of	O
a	O
monoid	O
is	O
a	O
subset	O
that	O
can	O
be	O
distinguished	O
by	O
some	O
morphism	O
to	O
a	O
finite	O
monoid	O
.	O
</s>
<s>
Recognizable	B-Application
sets	I-Application
are	O
useful	O
in	O
automata	B-Application
theory	I-Application
,	O
formal	O
languages	O
and	O
algebra	O
.	O
</s>
<s>
The	O
recognizable	O
subsets	O
of	O
are	O
precisely	O
the	O
regular	B-General_Concept
languages	I-General_Concept
.	O
</s>
<s>
Conversely	O
,	O
a	O
rational	B-Application
subset	I-Application
may	O
not	O
be	O
recognizable	O
,	O
even	O
if	O
is	O
finitely	O
generated	O
.	O
</s>
<s>
The	O
intersection	O
of	O
a	O
rational	B-Application
subset	I-Application
and	O
of	O
a	O
recognizable	O
subset	O
is	O
rational	O
.	O
</s>
<s>
Recognizable	B-Application
sets	I-Application
are	O
closed	O
under	O
inverse	O
of	O
morphisms	O
.	O
</s>
