<s>
A	O
schema	B-Algorithm
(	O
)	O
is	O
a	O
template	O
in	O
computer	B-General_Concept
science	I-General_Concept
used	O
in	O
the	O
field	O
of	O
genetic	B-Algorithm
algorithms	I-Algorithm
that	O
identifies	O
a	O
subset	O
of	O
strings	O
with	O
similarities	O
at	O
certain	O
string	O
positions	O
.	O
</s>
<s>
The	O
schema	B-Algorithm
1**0*1	O
describes	O
the	O
set	O
of	O
all	O
words	O
of	O
length	O
6	O
with	O
1	O
's	O
at	O
the	O
first	O
and	O
sixth	O
positions	O
and	O
a	O
0	O
at	O
the	O
fourth	O
position	O
.	O
</s>
<s>
The	O
*	O
is	O
a	O
wildcard	B-Algorithm
symbol	O
,	O
which	O
means	O
that	O
positions	O
2	O
,	O
3	O
and	O
5	O
can	O
have	O
a	O
value	O
of	O
either	O
1	O
or	O
0	O
.	O
</s>
<s>
The	O
order	O
of	O
a	O
schema	B-Algorithm
is	O
defined	O
as	O
the	O
number	O
of	O
fixed	O
positions	O
in	O
the	O
template	O
,	O
while	O
the	O
defining	B-General_Concept
length	I-General_Concept
is	O
the	O
distance	O
between	O
the	O
first	O
and	O
last	O
specific	O
positions	O
.	O
</s>
<s>
The	O
order	O
of	O
1**0*1	O
is	O
3	O
and	O
its	O
defining	B-General_Concept
length	I-General_Concept
is	O
5	O
.	O
</s>
<s>
The	O
fitness	O
of	O
a	O
schema	B-Algorithm
is	O
the	O
average	O
fitness	O
of	O
all	O
strings	O
matching	O
the	O
schema	B-Algorithm
.	O
</s>
<s>
The	O
length	O
of	O
a	O
schema	B-Algorithm
,	O
called	O
,	O
is	O
defined	O
as	O
the	O
total	O
number	O
of	O
nodes	O
in	O
the	O
schema	B-Algorithm
.	O
</s>
<s>
If	O
the	O
child	O
of	O
an	O
individual	O
that	O
matches	O
schema	B-Algorithm
H	O
does	O
not	O
itself	O
match	O
H	O
,	O
the	O
schema	B-Algorithm
is	O
said	O
to	O
have	O
been	O
disrupted	O
.	O
</s>
<s>
In	O
evolutionary	O
computing	O
such	O
as	O
genetic	B-Algorithm
algorithms	I-Algorithm
and	O
genetic	B-Algorithm
programming	I-Algorithm
,	O
propagation	O
refers	O
to	O
the	O
inheritance	O
of	O
characteristics	O
of	O
one	O
generation	O
by	O
the	O
next	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
schema	B-Algorithm
is	O
propagated	O
if	O
individuals	O
in	O
the	O
current	O
generation	O
match	O
it	O
and	O
so	O
do	O
those	O
in	O
the	O
next	O
generation	O
.	O
</s>
<s>
Recently	O
schema	B-Algorithm
have	O
been	O
studied	O
using	O
order	O
theory	O
.	O
</s>
<s>
Two	O
basic	O
operators	O
are	O
defined	O
for	O
schema	B-Algorithm
:	O
expansion	O
and	O
compression	O
.	O
</s>
<s>
The	O
expansion	O
maps	O
a	O
schema	B-Algorithm
onto	O
a	O
set	O
of	O
words	O
which	O
it	O
represents	O
,	O
while	O
the	O
compression	O
maps	O
a	O
set	O
of	O
words	O
on	O
to	O
a	O
schema	B-Algorithm
.	O
</s>
<s>
denotes	O
all	O
schema	B-Algorithm
of	O
length	O
over	O
the	O
alphabet	O
as	O
well	O
as	O
the	O
empty	O
schema	B-Algorithm
.	O
</s>
<s>
For	O
any	O
schema	B-Algorithm
the	O
following	O
operator	O
,	O
called	O
the	O
of	O
,	O
which	O
maps	O
to	O
a	O
subset	O
of	O
words	O
in	O
:	O
</s>
<s>
Where	O
subscript	O
denotes	O
the	O
character	O
at	O
position	O
in	O
a	O
word	O
or	O
schema	B-Algorithm
.	O
</s>
<s>
Conversely	O
,	O
for	O
any	O
we	O
define	O
,	O
called	O
the	O
of	O
,	O
which	O
maps	O
on	O
to	O
a	O
schema	B-Algorithm
:	O
</s>
<s>
where	O
is	O
a	O
schema	B-Algorithm
of	O
length	O
such	O
that	O
the	O
symbol	O
at	O
position	O
in	O
is	O
determined	O
in	O
the	O
following	O
way	O
:	O
if	O
for	O
all	O
then	O
otherwise	O
.	O
</s>
<s>
The	O
schematic	O
lattice	O
is	O
similar	O
to	O
the	O
concept	B-Algorithm
lattice	I-Algorithm
found	O
in	O
Formal	B-Algorithm
concept	I-Algorithm
analysis	I-Algorithm
.	O
</s>
