Information Technology Reference
In-Depth Information
the algorithm
Al
g
2
. The problem of autonomy should be considered, taking account
of the cooperation of algorithms, and the forms of the functions
f
1
and
f
2
are crucial.
The following cases of the autonomy of the algorithm
Al
g
1
towards the algorithm
Al
g
2
may be considered:
•
The algorithm
Al
g
1
is autonomous towards the algorithm
Al
g
2
if for the transition
function
f
1
of the algorithm
Al
g
1
the following relationships occur:
x
2
)
∀
(
x
1
,
x
2
)
∈
Df
1
,(
x
1
,
x
2
)
∈
Df
1
:
f
1
(
x
1
,
x
2
)
=
f
1
(
x
1
,
(2.13)
and
∀
(
x
1
,
x
2
)
∈
Df
1
:
(
Proj
2
ⓦ
f
1
)(
x
1
,
x
2
)
=
x
2
,
(2.14)
which can be briefly (informally) denoted by:
f
1
:
X
1
ₒ
X
1
.
(2.15)
It means that the state of the algorithm
Al
g
1
is only needed for the calculation
of the transition function
f
1
whereas the state of algorithm
Al
g
2
is not necessary.
However, the calculation of the transition function
f
1
influences only the change
of the state of the algorithm
Al
g
1
and does not have any influence on the state of
the algorithm
Al
g
2
. The schema of that relationship is shown in Fig.
2.6
.
•
The algorithm
Al
g
1
is not autonomous towards the algorithm
Al
g
2
with
inter-
information
relationship if for the transition function
f
1
of the algorithm
Al
g
1
the
following relationships occur:
x
2
x
2
))
∃
(
x
1
,
x
2
)
∈
Df
1
,(
x
1
,
x
2
)
∈
Df
1
,(
x
2
=
⇒
f
1
(
x
1
,
x
2
)
=
f
1
(
x
1
,
(2.16)
(a)
(b)
Fig. 2.6
Schema of the relationships between the algorithms; the case when the algorithm
Al
g
1
is
autonomous
towards the algorithm
Al
g
2
,
a
for calculating the transition function
f
1
only the state
of the algorithm
Al
g
1
is necessary,
b
the calculation of the transition function
f
1
influences only
the change of the state of the algorithm
Al
g
1
, and does not have any influence on the state of the
algorithm
Al
g
2
