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In further considerations, we will try to answer these questions and solve the
problems, and particularly discuss the notion of autonomy, define it more precisely
and show that by using appropriate methods it is possible to realize decomposition
of a given algorithm into component algorithms that are considered as autonomous.
2.4.2 The Autonomy of an Algorithm
In our considerations as well as in the literature in the field, we may encounter a
statement that an algorithm is (or is not) autonomous. The notion has been introduced
intuitively (see [174, 185]).
Let us try to define more precisely what should be understood by the notion
autonomous and let us accept the following statement:
The notion of autonomy of a
certain algorithm may only be considered towards another algorithm, which means
that the autonomy of the algorithm Alg1 may be considered towards the algorithm
Al
g
2
. However, neither the autonomy of an algorithm can be defined without taking
into consideration other algorithms, nor can the autonomy be defined only towards
the environment (Fig.
2.5
).
In order to define the notion of autonomy, we consider two algorithms
Al
g
1
=
(
X
1
×
X
2
,
f
1
)
i
Al
g
2
=
(
X
1
×
X
2
,
f
2
)
. The transition function
f
1
is denoted by
f
1
:
X
1
×
X
2
ₒ
X
2
.
It should be emphasized that the function
f
1
as well as the function
f
2
are partial
functions. Let us denote the domain of the function
f
1
as
Df
1
and the domain of the
function
f
2
as
Df
2
.
The domain
Df
1
and
Df
2
are the subsets of the set
X
1
×
X
1
×
X
2
, similarly the function
f
2
is denoted by
f
2
:
X
1
×
X
2
ₒ
X
1
×
X
2
. Let us try to define
what it means that the algorithm
Al
g
1
is autonomous (or non-autonomous) towards
(a)
(b)
Fig. 2.5
Schema of the relationships between the algorithms; the case when the algorithm
Al
g
1
is not
autonomous
towards the algorithm
Al
g
2
(the interoperating relationship),
a
for calculating
the transition function
f
1
both states are indispensable; the state of the algorithm
Al
g
1
as well as
the state of the algorithm
Al
g
2
,
b
the calculation of the transition function
f
1
has an influence on the
change of states of the algorithms
Al
g
1
and
Al
g
2
