Information Technology Reference
In-Depth Information
x
v
u'
u
u'
v
v'
u
v'
x
x
x
u'
v
v'
u
+
x
x
Figure 10.4
Circular/circular recombination.
DEFINITION 2 Let
J
⊆ Σ
+
be a set of plugs. We define the set of elementary
cables (respectively, left elementary cables and right elementary cables) with
plugs in
J
as
=
(J
Σ
+
∩ Σ
+
J)
\ Σ
+
J
Σ
+
,
E
J
= Σ
∗
J
\ Σ
∗
J
Σ
+
,
L
J
Σ
∗
\ Σ
+
J
Σ
∗
.
R
J
=
J
vz
2
, where
z
1
,z
2
∈
J
are plugs. In other words, an elementary cable starts with a plug, ends with
a plug, and contains no other plugs as subwords. The start and end plug can
overlap.
A left elementary cable is of the form
wz
, where
z
Note that an elementary cable in
E
J
is of the form
z
1
u
=
J
is a plug and
wz
does
not contain any other plug as a subword. In other words, if we scan
wz
from
left to right,
z
is the first plug we encounter. Analogously, a right elementary
cable is of the form
zw
, where
z
∈
J
is a plug and
wz
does not contain any
other plug as a subword.
∈
DEFINITION 3 For a set of plugs
J
⊆ Σ
+
and a linear word
w
∈ Σ
+
, the set
of elementary cables with plugs in
J
occurring in
w
is defined as
