Definition:
Let
L
be
a
language over
S
.
For i
³
0,
the
i
-th
power
of
L
,
L
i
,
is defined as:
1)
L
0
=
{
e
}
2)
if
i
³
1 then
L
i
=
LL
i
-1
L
2
=
LL
1
0
0
0
01
01
0
01
01
L
0
01
L
1
=
LL
0
0
01
e
e
0
01
L
0
e
Power of Language
Gist:
L
i
= LL…L
i
-times
19/20
Example:
Consider
L
=
{
0
,
01
}
Task:
L
2