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It is necessary to analyze again and define such a property as the autonomy
of one algorithm towards another it can cooperate with through the environment.
Therefore, such terms as the cooperation between algorithms, the equivalence of
algorithms, and the autonomy of algorithms should be considered, analyzed and
updated.
2.5.1.1 The Cooperation Between the Algorithms
To analyze more complex methods of decomposition of algorithms we have to define
precisely the term of autonomy which requires considering a cooperation process of
algorithms. Therefore, let us consider two cooperating algorithms
.
The set
X
0
represents global data describing the state of the environment available
to both cooperating algorithms. The algorithms have the following form:
(
X
0
,
Al
g
1
,
Al
g
2
)
Al
g
1
=
(
X
0
×
X
1
,
f
1
),
Al
g
2
=
(
X
0
×
X
2
,
f
2
),
f
1
:
X
0
×
X
1
ₒ
X
0
×
X
1
,
(2.33)
f
2
:
X
0
×
X
2
ₒ
X
0
×
X
2
The concept of the environment used for the realization of cooperation between
the algorithms may be presented with a scenario of cooperation of algorithms, which
is shown in Fig.
2.10
.
Let us accept that a problem is a pair
where
x
0
is the initial state,
being the task of the problem, and
x
0
is the final state, representing a solution to the
problem. It is necessary to emphasize that
x
0
and
x
0
are the states of the environment
and thus are not the states of either of algorithm.
x
0
,
and x
0
)
(
Alg
1
x
1
k1-1
x
1
0
x
1
1
x
1
2
x
1
k1
f
1
f
1
f
1
x
0
0
x
0
1
x
0
2
x
0
3
x
0
4
x
0
5
x
0
k-1
x
0
k
X
0
f
2
f
2
f
2
x
2
0
x
2
1
x
2
2
x
2
3
x
2
k2
Alg
2
Fig. 2.10
The concept of the
environment
and the model of cooperation between the algorithms
Al
g
1
and
Al
g
2
through the environment
X
0
