<s>
In	O
computer	O
science	O
theory	O
–	O
particularly	O
formal	O
language	O
theory	O
–	O
Glushkov	B-General_Concept
's	I-General_Concept
construction	I-General_Concept
algorithm	I-General_Concept
,	O
invented	O
by	O
Victor	O
Mikhailovich	O
Glushkov	O
,	O
transforms	O
a	O
given	O
regular	B-Language
expression	I-Language
into	O
an	O
equivalent	O
nondeterministic	B-General_Concept
finite	I-General_Concept
automaton	I-General_Concept
(	O
NFA	O
)	O
.	O
</s>
<s>
Thus	O
,	O
it	O
forms	O
a	O
bridge	O
between	O
regular	B-Language
expressions	I-Language
and	O
nondeterministic	B-General_Concept
finite	I-General_Concept
automata	I-General_Concept
:	O
two	O
abstract	O
representations	O
of	O
the	O
same	O
class	O
of	O
formal	O
languages	O
.	O
</s>
<s>
A	O
regular	B-Language
expression	I-Language
may	O
be	O
used	O
to	O
conveniently	O
describe	O
an	O
advanced	O
search	O
pattern	O
in	O
a	O
"	O
find	O
and	O
replace	O
"	O
–	O
like	O
operation	O
of	O
a	O
text	B-Device
processing	I-Device
utility	O
.	O
</s>
<s>
Glushkov	B-General_Concept
's	I-General_Concept
algorithm	I-General_Concept
can	O
be	O
used	O
to	O
transform	B-Language
it	O
into	O
an	O
NFA	O
,	O
which	O
furthermore	O
is	O
small	O
by	O
nature	O
,	O
as	O
the	O
number	O
of	O
its	O
states	O
equals	O
the	O
number	O
of	O
symbols	O
of	O
the	O
regular	B-Language
expression	I-Language
,	O
plus	O
one	O
.	O
</s>
<s>
Subsequently	O
,	O
the	O
NFA	O
can	O
be	O
made	O
deterministic	O
by	O
the	O
powerset	B-General_Concept
construction	I-General_Concept
and	O
then	O
be	O
minimized	B-General_Concept
to	O
get	O
an	O
optimal	O
automaton	O
corresponding	O
to	O
the	O
given	O
regular	B-Language
expression	I-Language
.	O
</s>
<s>
From	O
another	O
,	O
more	O
theoretical	O
point	O
of	O
view	O
,	O
Glushkov	B-General_Concept
's	I-General_Concept
algorithm	I-General_Concept
is	O
a	O
part	O
of	O
the	O
proof	O
that	O
NFA	O
and	O
regular	B-Language
expressions	I-Language
both	O
accept	O
exactly	O
the	O
same	O
languages	O
;	O
that	O
is	O
,	O
the	O
regular	B-General_Concept
languages	I-General_Concept
.	O
</s>
<s>
The	O
converse	O
of	O
Glushkov	B-General_Concept
's	I-General_Concept
algorithm	I-General_Concept
is	O
Kleene	B-General_Concept
's	I-General_Concept
algorithm	I-General_Concept
,	O
which	O
transforms	O
a	O
finite	O
automaton	O
into	O
a	O
regular	B-Language
expression	I-Language
.	O
</s>
<s>
The	O
automaton	O
obtained	O
by	O
Glushkov	O
's	O
construction	O
is	O
the	O
same	O
as	O
the	O
one	O
obtained	O
by	O
Thompson	B-General_Concept
's	I-General_Concept
construction	I-General_Concept
algorithm	I-General_Concept
,	O
once	O
its	O
ε-transitions	O
are	O
removed	O
.	O
</s>
<s>
Given	O
a	O
regular	B-Language
expression	I-Language
,	O
the	O
Glushkov	O
Construction	O
Algorithm	O
creates	O
a	O
non-deterministic	O
automaton	O
that	O
accepts	O
the	O
language	O
accepted	O
by	O
.	O
</s>
<s>
The	O
computation	O
of	O
the	O
sets	O
,	O
,	O
,	O
and	O
is	O
done	O
inductively	O
over	O
the	O
regular	B-Language
expression	I-Language
.	O
</s>
<s>
The	O
obtained	O
automaton	O
is	O
non-deterministic	O
,	O
and	O
it	O
has	O
as	O
many	O
states	O
as	O
the	O
number	O
of	O
letters	O
of	O
the	O
regular	B-Language
expression	I-Language
,	O
plus	O
one	O
.	O
</s>
<s>
Furthermore	O
,	O
it	O
has	O
been	O
shown	O
that	O
Glushkov	O
's	O
automaton	O
is	O
the	O
same	O
as	O
Thompson	B-General_Concept
's	I-General_Concept
automaton	I-General_Concept
when	O
the	O
ε-transitions	O
are	O
removed	O
.	O
</s>
<s>
The	O
computation	O
of	O
the	O
automaton	O
by	O
the	O
expression	O
occurs	O
often	O
;	O
it	O
has	O
been	O
systematically	O
used	O
in	O
search	O
functions	O
,	O
in	O
particular	O
by	O
the	O
Unix	B-Application
grep	B-Application
command	O
.	O
</s>
<s>
Similarly	O
,	O
XML	B-Protocol
's	O
specification	O
also	O
uses	O
such	O
constructions	O
;	O
for	O
more	O
efficiency	O
,	O
regular	B-Language
expressions	I-Language
of	O
a	O
certain	O
kind	O
,	O
called	O
deterministic	O
expressions	O
,	O
have	O
been	O
studied	O
.	O
</s>
