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(a)
f
1
(…)
f
2
(…)
x
0
x
1
x
2
(b)
f
1
(…)
f
2
(…)
x
0
x
1
x
2
Fig. 2.11
Schema of decomposition of an algorithm based on the notion of autonomy,
a
for the
calculation of the transition function
f
1
the state of the algorithm
Al
g
1
, the state of the algorithm
Al
g
2
and the state of the environment
X
0
are all indispensable,
b
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
and the change of state of
the environment
X
0
then decomposition of a given algorithm into component algorithms does not give
possibilities to form component algorithms independently (and especially parallel
in time).
The above-presented definition of the autonomy of cooperating algorithms has
the principal meaning for further considerations.
In practice there are cases when the implementation of the concept of the
environment does not solve completely the problem of algorithm decomposition
into component algorithms. Although decomposition of a given algorithm
Al
g
into
component, mutually autonomous algorithms is not always possible (Fig.
2.11
),
decomposition into component algorithms, which not necessarily have to bemutually
autonomous, is easier and more often possible.
The question arises whether it is possible to use that kind of “non-autonomous”
decomposition as a starting point for finding a method of reducing (bringing) coop-
erating, non-autonomous, component algorithms to mutually autonomous (at least
in some scope) algorithms.
These methods will be presented as another step of decomposition of algorithms
and will be dealt with in later chapters.
2.5.2 Step Two-Modes of Access to Internal
Data of Another Algorithm
Let us accept that a given algorithm
Al
g
=
(
X
,
f
)
may be decomposed into two
component algorithms
Al
g
1
=
(
cooperating through the
external environment
X
0
. In effect, a given problem encoded as
x
0
X
1
,
f
1
)
and
Al
g
2
=
(
X
2
,
f
2
)
X
0
and solved
with the use of the algorithm
Al
g
may also be solved with two cooperating algorithms
Al
g
1
and
Al
g
2
(Sect. 2.5, Fig.
2.10
).
∈
