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change of state of the algorithm
Al
g
1
, the state of the algorithm
Al
g
2
and the state
of the environment
X
0
.
Summing up, it can be informally said that a given algorithm (e.g.,
Al
g
1
)is
autonomous towards the other algorithm (e.g.,
Al
g
2
) when in order to appoint its
next state, apart from the information about its own state, the only thing it needs is
the information about the state of the environment, and the information about the
state of the other algorithm is not necessary.
However, the algorithm
Al
g
1
is not autonomous towards the algorithm
Al
g
2
if
there is an inter-information relationship, inter-action relationship or inter-operation
relationship.
We may say that the algorithms
Al
g
1
and
Al
g
2
, cooperating through the environ-
ment
X
0
, are mutually autonomous if the algorithm
Al
g
1
is autonomous towards the
algorithm
Al
g
2
and the algorithm
Al
g
2
is autonomous towards the algorithm
Al
g
1
.If
we deal with a large number of cooperating algorithms, then the property of auton-
omy may be extended to the whole group. A given algorithm is autonomous towards
the whole group of algorithms if it is autonomous towards each algorithm in the
group.
2.5.1.4 Summary of the Autonomy Problem
and Algorithm Decomposition
Agiven problemdenoted as the state of the environment
x
0
∈
X
, whose solution is the
state of the environment
x
k
∈
X
, may also be solved by two cooperating algorithms
Al
g
1
and
Al
g
2
(Fig.
2.10
).
We may consider the algorithm
Al
g
=
(
which is decomposed into two com-
ponent, autonomous, cooperating algorithms
Al
g
1
X
,
f
)
,
and the set of parameters
X
0
, representing the state of the environment, i.e., the
global data. The sets
X
1
and
X
2
correspond to the internal data of the appropriate
algorithms
Al
g
1
and
Al
g
2
which define their states and also
X
0
—the global data. The
partial functions
f
1
and
f
2
define the action of the algorithms, i.e., the evolution of
their states. We may consider the following cases of the autonomy influence on the
realization of decomposition:
=
(
X
1
,
f
1
)
and
Al
g
2
=
(
X
2
,
f
2
)
•
The algorithms
Al
g
1
and
Al
g
2
are mutually autonomous, which means that the
functions accept the following forms:
f
1
:
X
0
×
X
1
ₒ
X
0
×
X
1
and
f
2
:
X
0
×
X
2
. In this case component algorithms may be formed (designed,
realized) independently, separately and at the same time (Fig.
2.10
).
X
2
ₒ
X
0
×
•
The component algorithms are not mutually autonomous, whichmeans that there is
inter-information, inter-action or inter-operation relationship. The algorithm
Al
g
1
needs for the assignment of its next state not only knowledge about the state of an
environment but also information on the state of the other algorithm (in this case
Al
g
2
), and changing its state it modifies not only the state of the environment but
also the state of the algorithm
Al
g
2
. This case can be often found in practice, and
